| {"question": "This is the concept of Rational Numbers: All numbers that can be written in the form\n<<<Answer>>>, where a and b are integers and $b\\neq 0$", "options": ["$a\\cdot b$", "$a\\sqrt{b}$", "$\\frac{b}{a}$", "$\\frac{a}{b}$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "This is the concept of Irrational Numbers: Real numbers that cannot be written as\nthe quotient of 2 integers but can be represented on the <<<Answer>>>", "options": ["the set of rational numbers", "the set of real numbers", "number line", "the set of irrational numbers"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "This is the concept of Real Numbers: Include all numbers that can be represented on the number line, \nthat is, all <<<Answer1>>> and <<<Answer2>>>.", "options": ["rational, prime numbers", "rational, irrational numbers", "irrational, composite numbers", "irrationl, prime numbers"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A prime number is a number greater than 1 that has only <<<Answer1>>> and <<<Answer2>>>\nas factors.", "options": ["1, 0", "itself, 1", "itself, 0", "itself, 2"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "A composite number is a number that is not <<<Answer>>>. For example, 8 is a composite number since.", "options": ["rational", "irrational", "prime", "real"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "The absolute value of a number is always $\\geq 0$.\nIf a>0, |a|=<<<Answer1>>>\nIf a<0, |a| = <<<Answer2>>>", "options": ["-a, a", "a, -a", "a, a", "-a, -a"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the smallest number that is a multiple of all the given numbers?", "options": ["2", "All the other options are wrong", "The LCM", "The GCF"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the largest number that can be evenly divided into each of the given numbers?", "options": ["The GCF", "All the other options are wrong.", "The LCM", "2"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Fractions are anothor way to express", "options": ["multiplication", "subtraction", "addition", "division"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "The numerator of fractions is the () number.", "options": ["bottom", "top", "middle", "All the other options are wrong"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "The denominator of fractions is the () number.", "options": ["All the other options are wrong", "top", "bottom", "middle"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Fractions must have the same () before they can be added or subtracted.", "options": ["cut-off score", "All the other options are wrong", "denominator", "numerator"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "With d≠0，$\\frac{a}{d} +\\frac{b}{d} $=", "options": ["$\\frac{ad+bd}{d}$", "$\\frac{a+b}{d^{2}}$", "$\\frac{a-b}{d}$", "$\\frac{a+b}{d}$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "With d≠0，$\\frac{a}{d} -\\frac{b}{d} $=", "options": ["$\\frac{a+b}{d}$", "$\\frac{a-b}{d^{2}}$", "$\\frac{a-b}{d}$", "$\\frac{ad-bd}{d}$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "$\\frac{a}{b} \\cdot \\frac{c}{d} $=", "options": ["$\\frac{a+c}{bd} $", "$\\frac{ac}{bd} $", "$\\frac{ac}{b+d} $", "$\\frac{a+c}{b+d} $"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "$\\frac{a}{b} {\\div} \\frac{c}{d} $=", "options": ["$\\frac{ad}{bc}$", "$\\frac{ac}{bd}$", "$\\frac{a+d}{bc}$", "$\\frac{ad}{b+c}$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "What does a mixed number consist of?", "options": ["two whole number parts", "two fractional parts", "All the other options are wrong", "a whole number part and a fractional part"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Which of the following forms is a representation of scientific notation?", "options": ["$a\\times 2^{n}$,$1\\le \\left|a\\right |< 10 $,n is an integer", "$a\\times 10^{n}$,$0\\le \\left|a\\right |< 10 $,n is an integer", "$a\\times 10^{n}$,$1\\le \\left|a\\right |< 10 $,n is an integer", "$a\\times 10^{n^{2}}$,$1\\le \\left|a\\right |< 10 $,n is an integer"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "How to multiply and divide in scientific notation?", "options": ["Do nothing", "All the other options are wrong", "Just multiply and divide", "To multiply or divide numbers in scientific notation, we can change the order and grouping, so that we multiply or divide first the decimal parts and then the powers of 10."], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is pythagorean theorem in any right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse?", "options": ["$a^2+b^2=c^2$", "$a^2+b^2={(a+b)}^2$", "$a^2+b^2=c$", "$a+b=c$"], "answer": "A", "topic": "Middle--Basic Geometry--Basics of Triangles"} | |
| {"question": "What is pythagorean theorem in any right triangle, if a and b are the lengths of the legs and c is the length of the hypotenuse?", "options": ["$a^2+b^2=c$", "$a^2+b^2=c^2$", "$a^2+b^2={(a+b)}^3$", "$a+b=c$"], "answer": "B", "topic": "Middle--Basic Geometry--Basics of Triangles"} | |
| {"question": "What is the definition of a variable in mathematics?", "options": ["A set of numbers that follow a specific pattern.", "A constant value that does not change.", "A letter that represents an unknown or changing number.", "A mathematical function."], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the definition of a constant in mathematics?", "options": ["A term that changes with time.", "A term that does not change.", "A term that follows a specific pattern.", "A term that represents an unknown value."], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is an algebraic expression?", "options": ["A mathematical formula that represents a specific value.", "A mathematical statement that includes a variable and an equals sign.", "A set of numbers that follow a certain pattern.", "A combination of constants, variables, and at least one operation."], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is an equation in mathematics?", "options": ["A combination of constants, variables, and at least one operation.", "A mathematical statement that includes a variable and an equals sign.", "A set of numbers that follow a certain pattern.", "A mathematical sentence indicating that two expressions are equal."], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the term used for a number that makes an equation true?", "options": ["Coefficient", "Solution", "Variable", "Constant"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the definition of a linear equation with one variable?", "options": ["A polynomial equation that contains only one unknown, the degree of the unknown is 1, and the coefficient of the term containing the unknown is not zero", "A polynomial equation that contains only one unknown, the degree of the unknown is 2, and the coefficient of the term containing the unknown is not zero", "A polynomial equation that contains only one unknown, the degree of the unknown is 3, and the coefficient of the term containing the unknown is not zero", "A polynomial equation that contains only one unknown, the degree of the unknown is 4, and the coefficient of the term containing the unknown is not zero"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "What is the standard form of a linear equation in one variable?", "options": ["$a^2x+b=0$($x$ is the unknown, $a, b$ are known numbers, and $a\\ne 0$)", "$ax+b=0$($x$ is the unknown, $a, b$ are known numbers, and $a\\ne 0$)", "$a^4x+b=0$($x$ is the unknown, $a, b$ are known numbers, and $a\\ne 0$)", "$a^3x+b=0$($x$ is the unknown, $a, b$ are known numbers, and $a\\ne 0$)"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "Below are some general steps for solving linear equations with one variable, which sequence is correct?", "options": ["Organize the equation, eliminate the denominator, remove brackets, transpose, combine like terms, make the coefficient one, check the solution of the equation", "Organize the equation, make the coefficient one, remove brackets, transpose, combine like terms, eliminate the denominator, check the solution of the equation", "Organize the equation, check the solution of the equation, remove brackets, transpose, combine like terms, make the coefficient one, eliminate the denominator", "Organize the equation, combine like terms, remove brackets, transpose, eliminate the denominator, make the coefficient one, check the solution of the equation"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "What kinds of problems are commonly solved by applying the problem-solving method to linear equations in one variable?", "options": ["Rocket launch problems", "Chicken and rabbit in the same cage problems", "Satellite orbit calculation problems", "Sum, difference, multiple, fraction problems"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "When applying drawing analysis method to solve application problems of linear equations in one variable, what kind of problems is it mostly used for?", "options": ["Problems of sum, difference, multiple, and division", "Problems involving distances.", "Sudoku problems", "Chickens and rabbits in the same cage problems"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "When solving application problems of linear equations in one variable using the graph analysis method, what relationship is key to solving the problem?", "options": ["Finding equal relationships through the graph is key to solving the problem", "Finding equal relationships through the equation is key to solving the problem", "Finding equal relationships through textual information is key to solving the problem", "Finding equal relationships through voice information is key to solving the problem"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "In the process of setting up equations to solve application problems, what are the common formulas for trip problems?", "options": ["Downstream speed = Still water speed + Current speed, Upstream speed = Still water speed - Current speed", "$Distance = Speed \\cdot Time$, $Speed = \\frac{Distance}{Time}$, $Time = \\frac{Distance}{Speed}$", "$Workload = Efficiency \\cdot Work hours$, $Efficiency = \\frac{Workload}{Work hours}$, $Work hours = \\frac{Workload}{Efficiency}$", "$Part = Whole \\cdot Ratio$, $Ratio = \\frac{Part}{Whole}$, $Whole = \\frac{Part}{Ratio}$"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "What are the common formulas used in solving application problems involving equations in engineering problems?", "options": ["$Work = Efficiency \\cdot Time$、$Efficiency = \\frac{Work}{Time}$、$Time = \\frac{Work}{Efficiency}$", "$Part = Total \\cdot Rate$、$Rate = \\frac{Part}{Total}$、$Total = \\frac{Part}{Rate}$", "Downstream speed = Still water speed + Stream speed、Upstream speed = Still water speed - Stream speed", "$Distance = Speed \\cdot Time$、$Speed = \\frac{Distance}{Time}$ 、$Time = \\frac{Distance}{Speed} $"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "In the process of solving application problems by setting up equations, what are the common formulas for moving problems?", "options": ["$Distance = Speed \\cdot Time$, $Speed =\\frac{Distance}{Time}$, $Time =\\frac{Distance}{Speed}$", "$Work = Efficiency \\cdot Time$, $Efficiency =\\frac{Work}{Time}$, $Time =\\frac{Work}{Efficiency}$", "$Part = Whole \\cdot Ratio$, $Ratio =\\frac{Part}{Whole}$, $Whole =\\frac{Part}{Ratio}$", "Downstream speed = Still water speed + Flow speed, Upstream speed = Still water speed - Flow speed"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "In the process of solving application problems by setting up equations, what are the common formulas for fluid problems?", "options": ["$Distance = Speed \\cdot Time$, $Speed = \\frac{Distance}{Time}$, $Time = \\frac{Distance}{Speed} $", "$Part = Whole \\cdot Ratio$, $Ratio = \\frac{Part}{Whole}$, $Whole = \\frac{Part}{Ratio}$", "$Work = Efficiency \\cdot Time$, $Efficiency = \\frac{Work}{Time}$, $Time = \\frac{Work}{Efficiency}$", "Downstream Speed = Still Water Speed + Stream Speed, Upstream Speed = Still Water Speed - Stream Speed"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "In the process of solving applied problems using equations, what are some common formulas for problems involving product prices?", "options": ["$Workload = Efficiency \\cdot Working Hours$、$Efficiency = \\frac{Workload}{Working Hours}$、$Working Hours = \\frac{Workload}{Efficiency}$", "$Distance = Speed \\cdot Time$、$Speed = \\frac{Distance}{Time}$ 、$Time = \\frac{Distance}{Speed} $", "$Selling Price = Marked Price \\cdot Discount \\cdot \\frac{1}{10}$、Profit = Selling Price - Cost、$Profit Margin = \\frac{Selling Price - Cost}{Cost} \\cdot 100%$", "$Part = Whole \\cdot Ratio$、$Ratio = \\frac{Part}{Whole}$、$Whole = \\frac{Part}{Ratio}$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in One Variable"} | |
| {"question": "In the process of solving application problems by setting up equations, what are the common formulas for perimeter problems?", "options": ["$Part = Total \\cdot Ratio$, $Ratio = \\frac{Part}{Total}$, $Total = \\frac{Part}{Ratio}$", "$C_{circle} = 2\\pi R$, $C_{rectangle} = 2(a+b)$, $C_{square} = 4a$", "$V_{rectangular prism} = abc$, $V_{cube} = a^3$, $V_{cylinder} = \\pi R^2h$, $V_{cone} = \\frac{1}{3}\\pi R^2h$", "$S_{circle} = \\pi R^2$, $S_{rectangle} = ab$, $S_{square} = a^2$, $S_{annulus} = \\pi (R^2-r^2)$"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "In the process of solving application problems through equation, what are the common formulas for area problems?", "options": ["$Part = Whole \\cdot Ratio$, $Ratio = \\frac{Part}{Whole}$, $Whole = \\frac{Part}{Ratio}$", "$V_{rectangular prism} =abc$, $V_{cube} =a^3$, $V_{cylinder} =\\pi R^2h$, $V_{cone} =\\frac{1}{3}\\pi R^2h$", "$S_{circle} =\\pi R^2$, $S_{rectangle} =ab$, $S_{square} =a^2$, $S_{annulus} =\\pi (R^2-r^2)$", "$C_{circle} =2\\pi R$, $C_{rectangle} =2(a+b)$, $C_{square} =4a$"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "In the process of solving application problems by setting up equations, what are the common formulas for volume problems?", "options": ["$A_{circle} =\\pi R^2$, $A_{rectangle} =ab$, $A_{square} =a^2$, $A_{annulus} =\\pi (R^2-r^2)$", "$C_{circle} =2\\pi R$, $C_{rectangle} =2(a+b)$, $C_{square} =4a$", "$V_{cuboid} =abc$, $V_{cube} =a^3$, $V_{cylinder} =\\pi R^2h$, $V_{cone} =\\frac{1}{3}\\pi R^2h$", "$Part=Whole\\cdot Ratio$, $Ratio=\\frac{Part}{Whole}$, $Whole=\\frac{Part}{Ratio}$"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "A binomial equation with two unknowns, where the exponent of both unknowns is 1, is called what?", "options": ["Binomial First Degree Equation", "Uninomial First Degree Equation", "Uninomial Second Degree Equation", "Binomial Second Degree Equation"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "What is the general form of a linear equation in two variables?", "options": ["$ax+by=c(a\\neq 0,b\\neq 0)$", "$ax+by=0(a\\neq 0,b\\neq 0)$", "$ax+by=c(a\\neq 0)$", "$ax+by=c(b\\neq 0)$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "Putting two linear equations with two variables together forms what?", "options": ["System of linear equations in two variables", "System of quadratic equations in two variables", "System of quadratic equations in one variable", "System of linear equations in one variable"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "What is called the solution of a linear equation in two variables?", "options": ["In general, the value of x that makes both sides of the linear equation in two variables equal is called the solution of the system of linear equations in two variables.", "In general, the value of the exponent that makes both sides of the linear equation in two variables equal is called the solution of the system of linear equations in two variables.", "In general, the value of the coefficient that makes both sides of the linear equation in two variables equal is called the solution of the system of linear equations in two variables.", "In general, the value of the unknowns that makes both sides of the linear equation in two variables equal is called the solution of the system of linear equations in two variables."], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "What is called the solution of a system of linear equations in two variables?", "options": ["Generally, the two solutions of the two equations of a system of linear equations in two variables are called a system of linear equations in two variables.", "Generally, all the solutions of the two equations of a system of linear equations in two variables are called a system of linear equations in two variables.", "Generally, one of the solutions of the two equations of a system of linear equations in two variables is called a system of linear equations in two variables.", "Generally, the common solution of the two equations of a system of linear equations in two variables is called a system of linear equations in two variables."], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "What is the idea called that reduces the number of unknowns to fewer and solves them one by one?", "options": ["Increase element thought", "Simplification thought", "Elimination thought", "Solving element thought"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "Express one variable in terms of another and substitute it into another equation to eliminate variables and then solve the system of linear equations. This method is called <<<Answer>>>, commonly known as the substitution method.", "options": ["Addition and Subtraction Elimination Method", "Exhaustive Method", "Substitution Elimination Method", "Change of Variable Method"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "When the coefficients of the same variable are opposite or equal in two equations, adding or subtracting the two sides of the two equations respectively can eliminate this variable. This method is called <<<Answer>>>, known for short as the method of addition and subtraction.", "options": ["Substitution method", "Method of addition and subtraction elimination", "Exhaustive method", "Substitution elimination method"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "In general, what is an algebraic expression of the form $\\sqrt{a} (a \\ge 0)$ called?", "options": ["Cubic root", "Square root", "Quartic root", "Square boot"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What does $\\sqrt{a}$ represent when $a > 0$?", "options": ["The arithmetic square root of a", "The integral square root of a", "The differential square root of a", "The geometric square root of a"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is $\\sqrt{0}$?", "options": ["0", "3", "2", "1"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What type of number is the result of $\\sqrt{a} (a \\ge 0)$?", "options": ["Rational number", "Negative number", "Non-negative number", "Integer"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the result of $(\\sqrt{a}) ^{2} (a \\ge 0) $?", "options": ["a", "3", "1", "2"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What is the result of $\\sqrt{a^{2}}$ (given $a \\ge 0$)?", "options": ["a", "1", "2", "3"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "What are both sides of a quadratic equation called?", "options": ["Indeterminate", "Fraction", "Inequality", "Polynomial"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "How many unknowns are there in a quadratic equation?", "options": ["1", "0", "3", "2"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "What is the highest power of the unknown in a quadratic equation?", "options": ["1", "3", "0", "2"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "What is the general form of a quadratic equation in one variable?", "options": ["ax^2 + bx + c = 0, where a, b, c are constants, and a ≠ 0", "ax + b = 0, where a, b are constants, and a ≠ 0", "ax^2 + bx = 0, where a, b are constants, and a ≠ 0", "ax^2 = c, where a, c are constants, and a ≠ 0"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "After organizing a quadratic equation into the form $a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0$, what respectively are $a\\mathop{{x}}\\nolimits^{{2}}$, $bx$, $b$, $c$?", "options": ["Quadratic term, linear term, constant term, coefficient of the linear term", "Quadratic term, coefficient of the linear term, linear term, constant term", "Quadratic term, linear term, coefficient of the linear term, constant term", "Linear term, quadratic term, coefficient of the linear term, constant term"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "When solving the quadratic equation $a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0$ using the completing the square method, and transforming the left side into a perfect square trinomial in the form of $(x+p)^{2} = q$, what is the solution?", "options": ["If $q \\ge 0$, the roots of the equation are $\\frac{{-b \\pm \n \\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}}$, if $q< 0$, the equation has no real roots", "No real roots", "0", "$\\frac{{-b \\pm \n \\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}}$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "By applying the formula method to solve the quadratic equation $a\\mathop{{x}}\\nolimits^{{2}}+bx+c=0$ where $a\\neq0$, what are the roots of the equation when $\\mathop{{b}}\\nolimits^{{2}}-4ac> 0$?", "options": ["1", "0", "No real roots", "$\\frac{{-b \\pm \\sqrt{{\\mathop{{b}}\\nolimits^{{2}}-4ac}}}}{{2a}}$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "What symbols are used to represent the relationship of inequality in expressions called inequalities?", "options": ["$<,>$", "$<,>,\\leq,\\geq$", "$<,>,\\leq,\\geq,\\neq$", "$<,>,\\leq,\\geq,=$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} | |
| {"question": "What is called the solution of an inequality?", "options": ["The value of the coefficient that makes both sides of the inequality equal", "The value of the unknown that makes the inequality hold", "The value of the coefficient that makes the inequality hold", "The value of the unknown that makes both sides of the inequality equal"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} | |
| {"question": "All solutions of an inequality with an unknown form what of this inequality?", "options": ["Solution set", "Set", "Eigenvalue", "Solution"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} | |
| {"question": "The left and right sides of the inequality are both <<<Answer1>>> with only one unknown, and the highest degree of the unknown is <<<Answer2>>>. Such inequalities are called linear inequalities in one variable", "options": ["polynomial, 2", "polynomial, 1", "monomial, 2", "monomial, 1"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} | |
| {"question": "Generally, several single-variable linear inequalities about the same unknown combined together form what?", "options": ["Single-variable linear equation", "System of single-variable linear inequalities", "System of single-variable linear equations", "Single-variable linear inequality"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} | |
| {"question": "Examine the properties of inequalities. What happens to the direction of the inequality sign when both sides of the inequality are added to (or subtracted from) by the same number (or expression)?", "options": ["Unchanged", "Changes", "It depends", "None of the above"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Basic Concepts of Inequalities"} | |
| {"question": "If the relationship between two variables x, y can be expressed in the form of $y=kx+b(k\\ne 0)$, then y is called what of x?", "options": ["Exponential function", "Trigonometric function", "Linear function", "Quadratic function"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "If the relationship between two variables x and y can be expressed in the form $y=kx+b(k\\ne 0)$, then y is called a linear function of x. When is b such that y is a direct proportion function of x?", "options": ["$b\\ge 0$", "$b<0$", "$b=0$", "$b>0$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "The direct proportion function must pass through which coordinates?", "options": ["Origin", "None", "x-axis", "y-axis"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "For the direct proportion function $y=kx$, when $k>0$, through which quadrants does the line pass?", "options": ["II, IV", "Only III", "I, III", "Only I"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "For the direct proportion function $y=kx$, when $k<0$, through which quadrants does the line pass?", "options": ["II, IV", "Only II", "Only IV", "I, III"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "When the direct proportion function $y=kx(k>0)$ passes through the first and third quadrants, how does y change as x increases?", "options": ["Decrease", "Increase first then decrease", "Increase", "Remains unchanged"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "When the direct proportion function $y=kx(k<0)$ passes through the second and fourth quadrants, what happens to y as x increases?", "options": ["Decrease", "Unchanged", "Increase", "Decrease then increase"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Functions"} | |
| {"question": "What method can be used to find the equation of a function given the coordinates of two points?", "options": ["Point-Slope Method ", "Factorization method", "Completing the square", "Parametric equations method"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Linear Equations in Two Variables"} | |
| {"question": "What is the function in the form $y=\\frac{k}{x} $ (where k is a constant, $k \\ne 0$) called?", "options": ["Inverse proportion function", "Hyperbolic function", "Constant function", "Monotonic function"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "What type of graph does an inverse proportion function have?", "options": ["Arc", "Parabola", "Curve", "Hyperbola"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "To what kind of symmetrical figure does the graph of an inverse proportion function belong?", "options": ["Neither axial nor central symmetry", "Only axial symmetry", "Only central symmetry", "Both axial and central symmetry"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "What is the center of symmetry of the inverse proportion function?", "options": ["$(0,1)$", "$(1,0)$", "The origin", "$(1,1)$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "Regarding the graph of the hyperbolic function, when $k>0$, in which quadrants are the two branches of the hyperbola located?", "options": ["Second, Third", "Second, Fourth", "First, Third", "First, Fourth"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "Regarding the graph of the hyperbolic function, when $k<0$, in which quadrants are the two branches of the hyperbola located?", "options": ["First, Fourth", "Second, Fourth", "First, Third", "Second, Third"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "Regarding the graph of the hyperbolic function, when $k>0$, in each quadrant what happens to the values of y as the values of x increase?", "options": ["Remain unchanged", "Decrease", "Increase", "Uncertain"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "Regarding the graph of the hyperbolic function, when $k<0$, within each quadrant, how does the value of y change as the value of x increases?", "options": ["Decreases", "Increases", "Remains the same", "Uncertain"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "Regarding the inverse proportion function $y=\\frac{k}{x}$, what is the geometric meaning of $|k|$?", "options": ["The absolute value of the intercept", "Uncertain", "The area of the rectangle formed by the perpendicular segments drawn from the points on the graph of the inverse proportion function to the two axes", "The absolute value of the slope"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Inverse Proportion Functions"} | |
| {"question": "Generally, among the following relationships between the independent variable x and the dependent variable y, which one is called a quadratic function of x?", "options": ["$y=ax^{2}bx+c (a, b, c are constants)$", "None of the above", "$y=ax^{2}+bx+c$", "$y=ax^{2}+bx+c (a\\neq0, a, b, c are constants)$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "Generally, there exists the following relationship between the independent variable x and the dependent variable y: General form: $y=ax^{2}+bx+c (a\\neq0, a, b, c are constants)$, then y is called a", "options": ["Quadratic function", "Linear function", "Cubic function", "None of these"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "Which of the following expressions is the general form of a quadratic function?", "options": ["$y=ax^{2}+bx+c (a\\neq0)$", "$y=a(x-h)^{2}+k$", "$y=a(x-x_{1} )(x-x_{2})$", "$y=a(x-\\frac{b}{2a})^{2}+\\frac{4ac-b^{2}}{4a}$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "Which of the following expressions is the vertex form of a quadratic function?", "options": ["None", "$y=a(x-x_{1} )(x-x_{2})$", "$y=a(x-\\frac{b}{2a} )^{2}+\\frac{4ac-b^{2}}{4a} $", "$y=ax^{2}+bx+c （a≠0）$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "Which of the following expressions is the intersection form of a quadratic function?", "options": ["$y=a(x-\\frac{b}{2a} )^{2}+\\frac{4ac-b^{2}}{4a} $", "None of them", "$y=ax^{2}+bx+c (a\\neq0)$", "$y=a(x-x_{1} )(x-x_{2})$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "How is the axis of symmetry of a quadratic function represented?", "options": ["None of the above", "$x=-\\frac{b}{a} $", "$x=-\\frac{2b}{a} $", "$x=-\\frac{b}{2a} $"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "How is the vertex coordinate of a quadratic function represented?", "options": ["$(-\\frac{b}{2a} ,\\frac{4ac-b^{2}}{4a} )$", "$(-\\frac{b}{2a} ,\\frac{4ac-b^{2}}{2a} )$", "Neither", "$(-\\frac{b}{a} ,\\frac{4ac-b^{2}}{4a} )$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "How is the intersection point of a quadratic function with the y-axis represented?", "options": ["$(0,c)$", "$(0,b)$", "$(0,a)$", "None of the above"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "In the quadratic function $y=ax^{2}+bx+c (a≠0)$, when $a > 0$, how does y change with an increase in x to the left of the axis of symmetry? And how does it change to the right of the axis of symmetry?", "options": ["Decreases, Decreases", "Increases, Increases", "Decreases, Increases", "Increases, Decreases"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "In the quadratic function $y=ax^{2}+bx+c (a\\neq 0)$, when $a > 0$, how does y change as x increases to the left of the axis of symmetry? How does y change as x increases to the right of the axis of symmetry?", "options": ["Decreases, Decreases", "Increases, Decreases", "Decreases, Increases", "Increases, Increases"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "What are the key points in sketching the graph of a quadratic function?", "options": ["Direction of opening", "Vertex\nE: Intersection points with x-axis\nF: Intersection point with y-axis", "All of the above", "Axis of symmetry"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "What are the translation rules for the quadratic function $y=a(x-h)^{2}+k$?", "options": ["x-axis: left subtract right add, y-axis: up add down subtract", "x-axis: left add right subtract, y-axis: up add down subtract", "x-axis: left subtract right add, y-axis: up subtract down add", "x-axis: left add right subtract, y-axis: up subtract down add"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "For a quadratic function, when the x-coordinates are $x_{1}$ and $x_{2}$, and their corresponding y-coordinates are equal, then the axis of symmetry is", "options": ["$x=\\frac{x_{1}^{2}+x_{2}^{2}}{2}$", "$x=\\frac{x_{1}^{2}-x_{2}^{2}}{2}$", "$x=\\frac{x_{1}+x_{2}}{2} $", "$x=\\frac{x_{1}-x_{2}}{2} $"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "In the quadratic function $y=ax^{2}+bx+c (a≠0)$, a is used to determine", "options": ["Vertex position", "Direction of opening", "Neither", "Position of the function graph"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Functions"} | |
| {"question": "For the parabola $y=ax^{2}+bx+c (a≠0)$, when $b^{2}-4ac>0$, how many real roots does the quadratic equation have, and how many points of intersection does the graph of the quadratic function have with the x-axis?", "options": ["1,2", "2,1", "1,1", "2,2"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "For the parabola $y=ax^{2}+bx+c$ (where $a≠0$), when $b^{2}-4ac=0$, how many real roots does the quadratic equation have, and how many points of intersection does the graph of the quadratic function have with the x-axis?", "options": ["1,2", "1,1", "2,1", "2,2"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Quadratic Equations in One Variable"} | |
| {"question": "What is the survey method that examines all members of the population called?", "options": ["Comprehensive survey", "Partial survey", "Sample survey", "Member survey"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "What is the method of investigation called, where part of the data is surveyed to estimate the whole?", "options": ["Sampling survey", "Universal survey", "Comprehensive survey", "One-sided survey"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "What is the name of the entire set of objects to be examined?", "options": ["Universal Set", "Total Set", "Partial", "Population"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "What is each object under investigation that makes up the population called?", "options": ["Population", "Individual", "Partial", "Universal set"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "What do all the individuals drawn make up?", "options": ["Partial set", "Sample", "Population", "Individual"], "answer": "B", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "What is the number of individuals in a sample called?", "options": ["Sample volume", "Number of samples", "Sample total", "Sample size"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "Generally, we call the number of data points that fall into different groups as the group's <<<Answer>>>", "options": ["frequency", "probability", "capacity", "rate"], "answer": "A", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "The ratio of the frequency to the total number of data is <<<Answer>>>", "options": ["Frequency", "Frame rate", "Slope", "Probability"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Analysis"} | |
| {"question": "When collecting statistical data, dividing the data into several groups according to a certain range, the number of groups is called <<<Answer1>>>, and the difference between the two endpoints of each group is called <<<Answer2>>>", "options": ["Number of categories, Group difference", "Group, Distance", "Group interval, Number of groups", "Number of groups, Group interval"], "answer": "D", "topic": "Middle--Basic Probability and Statistics--Data Collection and Organization"} | |
| {"question": "What is a monomial?", "options": ["In algebra, if it involves only multiplication (including exponentiation) operations, or it involves division operations with the divisor containing letters, such an algebraic expression is called a monomial.", "In algebra, if it involves only addition operations, or it involves division operations but the divisor does not contain letters, such an algebraic expression is called a monomial.", "In algebra, if it involves only subtraction operations, or it involves division operations but the divisor does not contain letters, such an algebraic expression is called a monomial.", "In algebra, if it involves only multiplication (including exponentiation) operations, or it involves division operations but the divisor does not contain letters, such an algebraic expression is called a monomial."], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the coefficient of a monomial?", "options": ["The non-zero numeric factor in a monomial", "The zero numeric factor in a monomial", "The numeric factor that is 2 in a monomial", "The numeric factor that is 1 in a monomial"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the degree of a monomial?", "options": ["When the coefficient of the monomial is not zero, the difference of all the exponents of letters in the monomial.", "When the coefficient of the monomial is not zero, the product of all the exponents of letters in the monomial.", "When the coefficient of the monomial is zero, the sum of all the exponents of letters in the monomial.", "When the coefficient of the monomial is not zero, the sum of all the exponents of letters in the monomial."], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the definition of a polynomial?", "options": ["The product of several monomials is called a polynomial", "The exponentiation of several monomials is called a polynomial", "The difference of several monomials is called a polynomial", "The sum of several monomials is called a polynomial"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the number of terms in a polynomial?", "options": ["The fourth power of the number of monomials contained in the polynomial", "The number of monomials contained in the polynomial", "The square of the number of monomials contained in the polynomial", "The cube of the number of monomials contained in the polynomial"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the degree of a polynomial?", "options": ["In a polynomial, the degree of the third-highest term", "In a polynomial, the degree of the highest term", "In a polynomial, the degree of the lowest term", "In a polynomial, the degree of the second-highest term"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Which of the following is the multiplication rule for powers with the same base?", "options": ["$a^m \\times b^m = (a\\times b)^m$", "$(ab)^n = a^n \\times b^n$", "$a^m\\cdot a^n=a^{m+n}$", "$(a^m)^n = a^{mn}$"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is $(a^m)^n$ equal to?", "options": ["$a^{mn}$", "$a^{m-n}$", "$a^{m^n}$", "$a^{m+n}$"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Real Numbers"} | |
| {"question": "Regarding the multiplication rule for monomials, which of the following is correct?", "options": ["For letters present in only one monomial, along with its exponent, should be discarded", "Multiply coefficients, divide same letters", "Divide coefficients, same letters separately", "Multiply their coefficients, same letters separately"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Multiplying a monomial by a polynomial converts it into monomial-by-monomial multiplication through the application of which law of addition to multiplication?", "options": ["Inverse associative law", "Commutative law", "Distributive law", "Associative law"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "For the multiplication of polynomials, which of the following is correct?", "options": ["Each term in the two polynomials only needs to be multiplied and then added in sequence", "First multiply each term of one polynomial by every term of the other polynomial, then add up the products obtained", "Each term in the two polynomials only needs to be multiplied and then subtracted in sequence", "First multiply each term of one polynomial by every term of the other polynomial, then subtract the products obtained"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Which of the following is the formula for the difference of squares?", "options": ["$(a+b)^2 = a^2 + 2ab + b^2$", "$(a-b)^2 = a^2 - 2ab + b^2$", "$(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$", "$(a+b)(a-b)=a^2-b^2$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is the formula for $(a\\pm b)^2=a^2\\pm 2ab+b^2$?", "options": ["Difference of Squares Formula", "Sum and Difference of Squares Formula", "Sum of Squares Formula", "Perfect Square Trinomial"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What is $a^0 (a\\neq 0)$?", "options": ["0", "a", "-1", "1"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "The negative power of any number not equal to 0, equals the ? of the number's pth power.", "options": ["reciprocal", "square root", "logarithm", "cube root"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Under what condition is the value of $a^{-p}$ always positive?", "options": ["$a\\ge 0$", "$a\\le 0$", "$a<0$", "$a>0$"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Which of the following is correct regarding the division of one monomial by another?", "options": ["Divide coefficients and powers with the same base respectively", "Letters that only appear in the divisor must be discarded", "Multiply coefficients and powers with the same base respectively", "Multiply coefficients and divide powers with the same base"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Regarding the division of a polynomial by a monomial, which of the following is correct?", "options": ["First multiply each term of the polynomial by the monomial, then subtract the resulting quotients", "First divide each term of the polynomial by the monomial, then subtract the resulting quotients", "First multiply each term of the polynomial by the monomial, then add up the resulting products", "First divide each term of the polynomial by the monomial, then add up the resulting quotients"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Transforming a polynomial into the form of the product of several whole expressions is called what for this polynomial?", "options": ["Grouping decomposition", "Cross multiplication", "Factorization", "Extracting common factor"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Which of the following is not a general method for factoring?", "options": ["Cross multiplication", "Using formulas", "Factoring out the common factor", "Pivotal method"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "What must be the final result of factorization?", "options": ["The product of several fractions", "Several entire expressions subtracted", "Several entire expressions added", "The product of several entire expressions"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "Which of the following is incorrect regarding the steps of factorization?", "options": ["Check if formula method can be applied", "Check if there are common factors in all terms, if so, extract the common factor first", "The final result of factorization must be the sum of several integral expressions", "The result of factorization must be carried out until each factor cannot be further decomposed within the range of rational numbers"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Polynomials and Factorization"} | |
| {"question": "In the form of $A/B$, where A and B are polynomials, and B contains an unknown variable but is not equal to 0, this kind of expression is called a fractional expression, wherein A and B are called what of the fractional expression respectively?", "options": ["Denominator, Denominator", "Numerator, Numerator", "Denominator, Numerator", "Numerator, Denominator"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "What is the condition for a rational expression to be meaningful?", "options": ["The numerator and denominator are not equal", "The numerator is not equal to 1", "The denominator is not equal to 0", "Both numerator and denominator are not equal to 0"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "What is it called when the common factors (not 1) of the numerator and denominator of a fraction are canceled?", "options": ["Reduction", "Common denominator", "Product", "General term"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "The process of converting fractions with different denominators to fractions with the same denominator is called what?", "options": ["Finding a common denominator", "Finding a common term", "Simplification", "Reduction"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "How does the value of a fractional expression change if both its numerator and denominator are multiplied by the same nonzero polynomial?", "options": ["Decreases", "Increases", "Remains unchanged", "Uncertain"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "How does the value of a fraction change if both the numerator and the denominator are divided by the same non-zero polynomial?", "options": ["Uncertain", "Increases", "Decreases", "Remains unchanged"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "What is a fraction called when its numerator and denominator have no common factors?", "options": ["Simplest form", "Fraction without common factors", "Monotonic fraction", "Simple fraction"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "What is the rule for adding or subtracting fractions with the same denominator?", "options": ["Denominator remains the same, numerators are added or subtracted", "Denominator remains the same, denominators are added or subtracted", "Numerator remains the same, denominators are added or subtracted", "Numerator remains the same, numerators are added or subtracted"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "To add or subtract fractions with different denominators, what operation must be performed first to convert them into fractions with the same denominator and then calculate according to the rules of fractions with the same denominator?", "options": ["Simplify", "Reduce", "Find a common denominator", "Multiply by the least common multiple"], "answer": "C", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "When multiplying two fractions, what are the numerator and denominator of the product?", "options": ["Product of the numerators, Product of the denominators", "Product of the denominators, Product of the denominators", "Product of the numerators, Product of the numerators", "Product of the denominators, Product of the numerators"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "To divide two fractions, you need to invert the numerator and denominator of what and then multiply by what?", "options": ["Divisor, Dividend", "Larger fraction, Smaller fraction", "Dividend, Divisor", "Smaller fraction, Larger fraction"], "answer": "A", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Fractional equation refers to fractions containing the unknown number where?", "options": ["Numerator", "Uncertain", "Denominator", "Anywhere"], "answer": "D", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "What is the correct order for solving a fractional equation?", "options": ["Solve for the unknown, remove the denominator, check the root", "Remove the denominator, solve for the unknown, check the root", "Remove the denominator, solve for the unknown", "Solve for the unknown, check the root"], "answer": "B", "topic": "Middle--Basic Numbers and Algebra--Fractions"} | |
| {"question": "Among the four angles formed by the intersection of two straight lines, which are the two angles that have a common vertex and share one side?", "options": ["Complementary angles", "Parallel angles", "Adjacent supplementary angles", "Vertically opposite angles"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If the sides of one angle are the extensions in the opposite direction of the sides of another angle, what are these two angles to each other?", "options": ["Vertically opposite angles", "Complementary angles", "Adjacent angles", "Parallel angles"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "When two lines intersect at a right angle, they are called mutually perpendicular. One of them is called the other's?", "options": ["Parallel line", "Intersecting line", "Complementary line", "Perpendicular line"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "In the same plane, what are two non-intersecting lines called?", "options": ["Intersecting lines", "Perpendicular lines", "Parallel lines", "Supplementary lines"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "What is a statement that judges something called?", "options": ["Proposition", "Definition", "Description", "Portrayal"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "In a plane, moving a shape a certain distance in a certain direction is called what?", "options": ["Translation", "Move right", "Move left", "Move"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "In the new figure obtained after translation, each point is obtained by moving a certain point from the original figure. What are these two points called?", "options": ["Equivalent points", "Corresponding points", "Similar points", "Likewise points"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "What is the relationship between vertical angles?", "options": ["Equal", "Twice", "Unrelated", "Not equal"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "How many lines at most can pass through a point and be perpendicular to a given line?", "options": ["3", "1", "2", "4"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "Among all the line segments connecting a point outside a line to all points on the line, which line segment is the shortest?", "options": ["Parallel line segment", "Perpendicular line segment", "Intersecting but not perpendicular line segment", "There is no shortest line segment"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "How many lines, passing through a point outside a given line, are parallel to the given line?", "options": ["4", "2", "1", "3"], "answer": "C", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If two lines are both parallel to a third line, what is the positional relationship between the two lines?", "options": ["Unrelated", "Perpendicular to each other", "Intersect", "Parallel to each other"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If two lines are parallel, what is the relationship between the corresponding angles?", "options": ["Twice", "Equal", "Unrelated", "Three times"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If two lines are parallel, what is the relationship between their alternate interior angles?", "options": ["Unrelated", "Triple", "Double", "Equal"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If two lines are parallel, what is the relationship between the same-side interior angles?", "options": ["Equal", "Complementary", "Double", "Triple"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If corresponding angles are equal, what is the positional relationship between the two lines?", "options": ["Intersecting", "Parallel", "Unrelated", "Perpendicular"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If the interior alternate angles are equal, what is the positional relationship between the two lines?", "options": ["Perpendicular", "Parallel", "Irrelevant", "Intersecting"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If the corresponding angles are equal, what is the positional relationship between the two lines?", "options": ["Unrelated", "Parallel", "Intersecting", "Perpendicular"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "What is a pair of numbers a and b, arranged in order, called?", "options": ["Pair of numbers", "Ordered array", "Array", "Ordered pair"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "In a plane, what is formed by two mutually perpendicular number axes with a common origin?", "options": ["Set of number axes", "Number axis space", "Coordinate space", "Cartesian coordinate system"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "What is called the horizontal number axis? What is called the vertical number axis? What is the intersection point of the two coordinate axes in the Cartesian coordinate system called?", "options": ["x-axis; y-axis; origin", "y-axis; y-axis; origin", "y-axis; x-axis; origin", "x-axis; x-axis; origin"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "For any point in the plane, perpendicular lines are drawn from the point to the x-axis and y-axis, respectively, with the feet of the perpendiculars lying on the x-axis and y-axis. What are the corresponding numbers a, b called for that point?", "options": ["abscissa; ordinate", "ordinate; abscissa", "ordinate; ordinate", "abscissa; abscissa"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "Two coordinate axes divide the plane into four parts, what is the name of the upper right part? What are they called in counterclockwise order?", "options": ["First quadrant; Third quadrant; Second quadrant; Fourth quadrant", "First quadrant; Second quadrant; Third quadrant; Fourth quadrant", "First quadrant; Second quadrant; Fourth quadrant; Third quadrant", "Second quadrant; First quadrant; Third quadrant; Fourth quadrant"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "In a plane, what is the motion called when a figure is rotated around a fixed point in a certain direction by an angle?", "options": ["Symmetry", "Central Symmetry", "Translation", "Rotation"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "What do you call a shape that overlaps with the original shape after rotating it around a fixed point by an angle?", "options": ["Centrally symmetrical figure", "Rotational figure", "Symmetrical figure", "Rotationally symmetrical figure"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "What must the angle of rotational symmetry be less than and greater than?", "options": ["0;360", "360;720", "180;360", "0;180"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If a figure can coincide with itself after rotating 180 degrees around a certain point, what is this figure called?", "options": ["Rotational symmetry figure", "Centrosymmetric figure", "Translation symmetry figure", "Symmetric figure"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "If a figure rotates 180 degrees around a certain point and coincides with another figure, what relationship do these two figures have?", "options": ["Translation symmetry", "Rotational symmetry", "Symmetry", "Central symmetry"], "answer": "D", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "What is the relationship between two centrally symmetrical figures?", "options": ["Coincide", "Congruent", "No specific relationship", "Similar but not congruent"], "answer": "B", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "For two figures that are centrally symmetric, through which point do the lines connecting symmetric points pass?", "options": ["Center of symmetry", "Point outside the figure", "Point on the figure", "Does not pass through a fixed point"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |
| {"question": "For two centrally symmetric figures, what is the relationship between the corresponding segments?", "options": ["Parallel and equal", "Equal but not parallel", "Intersecting", "Parallel but not equal"], "answer": "A", "topic": "Middle--Basic Geometry--Basic Concepts of Geometry"} | |