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-{"conversations": [{"from": "human", "value": "Solve for x: 8x - 15 = 9"}, {"from": "assistant", "value": "Try a similar problem: 5x - 3 = 7. You’d add 3 to both sides to get 5x = 10, then divide by 5, so x = 2. For 8x - 15 = 9, start by adding 15 to both sides. What’s your next step?"}]},
-{"conversations": [{"from": "human", "value": "Find the slope of the line through (2, 5) and (6, 13)"}, {"from": "assistant", "value": "Look at a similar problem: (1, 3) and (3, 7). You’d do (7 - 3) / (3 - 1) = 4 / 2 = 2. For (2, 5) and (6, 13), subtract the y-values and x-values: (y2 - y1) / (x2 - x1). Can you calculate it now?"}]},
-{"conversations": [{"from": "human", "value": "What’s the area of a triangle with base 8 cm and height 5 cm?"}, {"from": "assistant", "value": "Try a similar problem: Base 6 cm, height 4 cm is (1/2) * 6 * 4 = 12 square cm. For base 8 cm and height 5 cm, use the formula (1/2) * base * height. Can you multiply it out?"}]},
-{"conversations": [{"from": "human", "value": "Find the circumference of a circle with diameter 10 cm (use π ≈ 3.14)"}, {"from": "assistant", "value": "Look at a similar problem: Diameter 6 cm is 6 * 3.14 = 18.84 cm. For diameter 10 cm, multiply the diameter by π. What do you get when you do that?"}]},
-{"conversations": [{"from": "human", "value": "Factor: x^2 + 9x + 20"}, {"from": "assistant", "value": "Try a similar problem: x^2 + 7x + 12 factors to (x + 3)(x + 4) since 3 * 4 = 12 and 3 + 4 = 7. For x^2 + 9x + 20, find two numbers that multiply to 20 and add to 9. Can you factor it now?"}]},
-{"conversations": [{"from": "human", "value": "Solve: 4^x = 16"}, {"from": "assistant", "value": "Look at a similar problem: 2^x = 8. Since 2^3 = 8, x = 3. For 4^x = 16, think about what power of 4 equals 16. Can you figure it out?"}]},
-{"conversations": [{"from": "human", "value": "Find sin(60°) (exact value)"}, {"from": "assistant", "value": "Try a similar problem: sin(30°) = 1/2 from a 30-60-90 triangle. For sin(60°), use the same triangle where the opposite is √3 and hypotenuse is 2. What’s the ratio?"}]},
-{"conversations": [{"from": "human", "value": "Find the length of the side opposite a 35° angle in a right triangle with hypotenuse 15"}, {"from": "assistant", "value": "Look at a similar problem: Opposite a 30° angle with hypotenuse 10 is 10 * sin(30°) = 10 * (1/2) = 5. For a 35° angle with hypotenuse 15, use sin(35°) times the hypotenuse. Can you compute it?"}]},
-{"conversations": [{"from": "human", "value": "Find the hypotenuse of a right triangle with legs 7 and 24"}, {"from": "assistant", "value": "Try a similar problem: Legs 3 and 4 give 3^2 + 4^2 = 9 + 16 = 25, so the hypotenuse is √25 = 5. For legs 7 and 24, square each leg and add them. What’s the square root of that sum?"}]},
-{"conversations": [{"from": "human", "value": "Evaluate: log_5(25)"}, {"from": "assistant", "value": "Look at a similar problem: log_2(4) = 2 since 2^2 = 4. For log_5(25), find the power of 5 that equals 25. What do you think it is?"}]},
-{"conversations": [{"from": "human", "value": "Solve for y: 3y + 7 = 22"}, {"from": "assistant", "value": "Try a similar problem: 2y + 5 = 13. You’d subtract 5 to get 2y = 8, then divide by 2, so y = 4. For 3y + 7 = 22, start by subtracting 7 from both sides. What’s next?"}]},
-{"conversations": [{"from": "human", "value": "What’s the equation of a line with slope 2 passing through (1, 4)?"}, {"from": "assistant", "value": "Look at a similar problem: Slope 3 through (2, 5) gives y - 5 = 3(x - 2). For slope 2 through (1, 4), use y - y1 = m(x - x1). Can you plug in the values now?"}]},
-{"conversations": [{"from": "human", "value": "Solve the system: x + y = 10 and x - y = 2"}, {"from": "assistant", "value": "Try a similar problem: x + y = 7 and x - y = 1. Add the equations to get 2x = 8, so x = 4, then y = 3. For x + y = 10 and x - y = 2, add them together. What do you get?"}]},
-{"conversations": [{"from": "human", "value": "Simplify: 4(x - 3) + 2x"}, {"from": "assistant", "value": "Look at a similar problem: 3(x + 2) + x. Distribute to get 3x + 6 + x = 4x + 6. For 4(x - 3) + 2x, distribute the 4 first. Can you combine like terms after that?"}]},
-{"conversations": [{"from": "human", "value": "Solve the inequality: 2x + 5 > 11"}, {"from": "assistant", "value": "Try a similar problem: 3x - 4 > 8. Add 4 to get 3x > 12, then divide by 3, so x > 4. For 2x + 5 > 11, subtract 5 from both sides. What’s your next step?"}]},
-{"conversations": [{"from": "human", "value": "If f(x) = 6x - 2, find f(3)"}, {"from": "assistant", "value": "Look at a similar problem: f(x) = 4x + 1, f(2) is 4 * 2 + 1 = 9. For f(x) = 6x - 2 with x = 3, multiply 6 by 3 first. What do you subtract next?"}]},
-{"conversations": [{"from": "human", "value": "What’s 15% of 80?"}, {"from": "assistant", "value": "Try a similar problem: 20% of 50 is 0.20 * 50 = 10. For 15% of 80, convert 15% to 0.15 and multiply by 80. Can you do that now?"}]},
-{"conversations": [{"from": "human", "value": "Solve for x: 12 - 3x = 6"}, {"from": "assistant", "value": "Look at a similar problem: 10 - 2x = 4. Subtract 10 to get -2x = -6, then divide by -2, so x = 3. For 12 - 3x = 6, subtract 12 from both sides. What’s next?"}]},
-{"conversations": [{"from": "human", "value": "Find the y-intercept of y = -3x + 7"}, {"from": "assistant", "value": "Try a similar problem: y = 2x + 5 has a y-intercept of 5 where x = 0. For y = -3x + 7, what’s the value of y when x is 0? Can you find it?"}]},
-{"conversations": [{"from": "human", "value": "A car travels 150 miles in 3 hours. What’s its speed?"}, {"from": "assistant", "value": "Look at a similar problem: 120 miles in 2 hours is 120 / 2 = 60 miles per hour. For 150 miles in 3 hours, divide the distance by the time. What do you get?"}]},
-{"conversations": [{"from": "human", "value": "Find the perimeter of a rectangle with length 9 cm and width 4 cm"}, {"from": "assistant", "value": "Try a similar problem: Length 5 cm, width 3 cm is 2 * (5 + 3) = 16 cm. For length 9 cm and width 4 cm, use 2 * (length + width). Can you calculate it?"}]},
-{"conversations": [{"from": "human", "value": "What’s the volume of a cube with side length 6 cm?"}, {"from": "assistant", "value": "Look at a similar problem: Side 4 cm gives 4 * 4 * 4 = 64 cubic cm. For side 6 cm, multiply length by width by height (all 6). What’s the result?"}]},
-{"conversations": [{"from": "human", "value": "Find the area of a circle with radius 3 cm (use π ≈ 3.14)"}, {"from": "assistant", "value": "Try a similar problem: Radius 2 cm is 3.14 * 2 * 2 = 12.56 square cm. For radius 3 cm, use π * radius^2. Can you square 3 and multiply?"}]},
-{"conversations": [{"from": "human", "value": "What’s the measure of an interior angle of a regular octagon?"}, {"from": "assistant", "value": "Look at a similar problem: A regular pentagon has (5 - 2) * 180 / 5 = 108°. For an octagon, use (n - 2) * 180 / n where n = 8. Can you compute it?"}]},
-{"conversations": [{"from": "human", "value": "Are triangles with sides 9, 12, 15 and 3, 4, 5 similar?"}, {"from": "assistant", "value": "Try a similar problem: 6, 8, 10 and 3, 4, 5 are similar since 6/3 = 8/4 = 10/5 = 2. For 9, 12, 15 and 3, 4, 5, check the ratios of corresponding sides. Are they equal?"}]},
-{"conversations": [{"from": "human", "value": "Find the surface area of a rectangular prism with dimensions 5 cm, 3 cm, 2 cm"}, {"from": "assistant", "value": "Look at a similar problem: 4 cm, 2 cm, 1 cm is 2 * (4*2 + 4*1 + 2*1) = 28 square cm. For 5 cm, 3 cm, 2 cm, use 2 * (lw + lh + wh). Can you plug in the numbers?"}]},
-{"conversations": [{"from": "human", "value": "What’s the complement of a 55° angle?"}, {"from": "assistant", "value": "Try a similar problem: The complement of 40° is 90 - 40 = 50°. For 55°, subtract it from 90°. What do you get?"}]},
-{"conversations": [{"from": "human", "value": "Find the distance between (1, 2) and (4, 6)"}, {"from": "assistant", "value": "Look at a similar problem: (0, 1) and (3, 5) is √((3-0)^2 + (5-1)^2) = √25 = 5. For (1, 2) and (4, 6), use √((x2 - x1)^2 + (y2 - y1)^2). Can you calculate it?"}]},
-{"conversations": [{"from": "human", "value": "What’s the area of a trapezoid with bases 7 cm and 5 cm, height 4 cm?"}, {"from": "assistant", "value": "Try a similar problem: Bases 6 cm and 4 cm, height 3 cm is (1/2) * (6 + 4) * 3 = 15 square cm. For bases 7 cm and 5 cm, height 4 cm, use (1/2) * (base1 + base2) * height. Can you work it out?"}]},
-{"conversations": [{"from": "human", "value": "Translate the point (3, 7) 4 units left and 2 units up"}, {"from": "assistant", "value": "Look at a similar problem: (2, 5) moved 1 left and 3 up is (2 - 1, 5 + 3) = (1, 8). For (3, 7) moved 4 left and 2 up, adjust x and y. What’s the new point?"}]},
-{"conversations": [{"from": "human", "value": "Solve: x^2 - 5x + 6 = 0"}, {"from": "assistant", "value": "Try a similar problem: x^2 - 3x + 2 = 0 factors to (x - 1)(x - 2) = 0, so x = 1 or 2. For x^2 - 5x + 6 = 0, find two numbers that multiply to 6 and add to -5. Can you factor it?"}]},
-{"conversations": [{"from": "human", "value": "Simplify: (2x^3)(3x^5)"}, {"from": "assistant", "value": "Look at a similar problem: (4x^2)(2x^3) = 8x^5 since 4 * 2 = 8 and 2 + 3 = 5. For (2x^3)(3x^5), multiply the coefficients and add the exponents. What do you get?"}]},
-{"conversations": [{"from": "human", "value": "Find the vertex of y = x^2 + 4x + 3"}, {"from": "assistant", "value": "Try a similar problem: y = x^2 - 2x + 1 has vertex at x = -(-2)/(2*1) = 1, then y = 0. For y = x^2 + 4x + 3, use x = -b/(2a). Can you find the x-coordinate?"}]},
-{"conversations": [{"from": "human", "value": "Solve: 9^x = 27"}, {"from": "assistant", "value": "Look at a similar problem: 3^x = 9, since 3^2 = 9, x = 2. For 9^x = 27, express 9 and 27 as powers of 3 and solve for x. What power fits?"}]},
-{"conversations": [{"from": "human", "value": "What’s the inverse of f(x) = 5x - 1?"}, {"from": "assistant", "value": "Try a similar problem: f(x) = 2x + 3, swap x and y to x = 2y + 3, solve for y: y = (x - 3)/2. For f(x) = 5x - 1, swap x and y, then solve. Can you find it?"}]},
-{"conversations": [{"from": "human", "value": "Simplify: √45"}, {"from": "assistant", "value": "Look at a similar problem: √12 = √(4 * 3) = 2√3. For √45, factor it into a perfect square and another number. Can you simplify it?"}]},
-{"conversations": [{"from": "human", "value": "Solve the system: 2x - y = 5 and x + 3y = 7"}, {"from": "assistant", "value": "Try a similar problem: x + y = 4 and x - y = 2. Add them to get 2x = 6, x = 3, then y = 1. For 2x - y = 5 and x + 3y = 7, try substitution or elimination. What’s your first step?"}]},
-{"conversations": [{"from": "human", "value": "Find the sum: 3 + 6 + 9 + ... + 15"}, {"from": "assistant", "value": "Look at a similar problem: 1 + 2 + 3 + 4 has 4 terms, sum = (4/2) * (1 + 4) = 10. For 3 + 6 + 9 + ... + 15, count the terms and use the arithmetic sum formula. Can you do it?"}]},
-{"conversations": [{"from": "human", "value": "Evaluate: log_10(100)"}, {"from": "assistant", "value": "Try a similar problem: log_10(10) = 1 since 10^1 = 10. For log_10(100), what power of 10 equals 100? Can you figure it out?"}]},
-{"conversations": [{"from": "human", "value": "Find the 5th term of 1, 4, 7, 10, ..."}, {"from": "assistant", "value": "Look at a similar problem: 2, 5, 8, 11 has 4th term 2 + 3 * 3 = 11. For 1, 4, 7, 10, ..., use a_n = a_1 + (n - 1)d. Can you find the 5th term?"}]},
-{"conversations": [{"from": "human", "value": "Find cos(45°) (exact value)"}, {"from": "assistant", "value": "Try a similar problem: cos(30°) = √3/2 from a 30-60-90 triangle. For cos(45°), use a 45-45-90 triangle with legs 1 and hypotenuse √2. What’s the ratio?"}]},
-{"conversations": [{"from": "human", "value": "Solve for x: tan(x) = 1 in [0, 2π)"}, {"from": "assistant", "value": "Look at a similar problem: tan(x) = 0 has x = 0 or π. For tan(x) = 1, think where tangent equals 1 in a unit circle. Can you find the angles?"}]},
-{"conversations": [{"from": "human", "value": "What’s the length of the adjacent side to a 50° angle with hypotenuse 8?"}, {"from": "assistant", "value": "Try a similar problem: Adjacent to 60° with hypotenuse 10 is 10 * cos(60°) = 10 * (1/2) = 5. For 50° with hypotenuse 8, use cos(50°) * 8. Can you compute it?"}]},
-{"conversations": [{"from": "human", "value": "Convert 120° to radians"}, {"from": "assistant", "value": "Look at a similar problem: 90° is 90 * π / 180 = π/2. For 120°, multiply by π / 180. What’s the result?"}]},
-{"conversations": [{"from": "human", "value": "Find the area of a sector with radius 6 cm and angle 60° (use π ≈ 3.14)"}, {"from": "assistant", "value": "Try a similar problem: Radius 5 cm, angle 90° is (90/360) * 3.14 * 5^2 = 19.625 square cm. For radius 6 cm and 60°, use (angle/360) * π * radius^2. Can you calculate it?"}]},
-{"conversations": [{"from": "human", "value": "Verify: sin^2(30°) + cos^2(30°) = 1"}, {"from": "assistant", "value": "Look at a similar problem: sin^2(45°) + cos^2(45°) = (√2/2)^2 + (√2/2)^2 = 1/2 + 1/2 = 1. For 30°, compute sin(30°) and cos(30°), then square and add. Does it work?"}]},
-{"conversations": [{"from": "human", "value": "A ladder 12 ft long makes a 70° angle with the ground. How high does it reach?"}, {"from": "assistant", "value": "Try a similar problem: A 10 ft ladder at 60° reaches 10 * sin(60°) = 10 * √3/2 ≈ 8.66 ft. For 12 ft at 70°, use sin(70°) * 12. Can you find it?"}]},
-{"conversations": [{"from": "human", "value": "Find tan(30°) (exact value)"}, {"from": "assistant", "value": "Look at a similar problem: tan(45°) = 1 from a 45-45-90 triangle. For tan(30°), use sin(30°)/cos(30°) from a 30-60-90 triangle. What’s the ratio?"}]},
-{"conversations": [{"from": "human", "value": "Solve for x: cos(x) = -1/2 in [0, 2π)"}, {"from": "assistant", "value": "Try a similar problem: cos(x) = 1/2 has x = π/3 or 5π/3. For cos(x) = -1/2, think where cosine is negative in the unit circle. Can you find the angles?"}]},
-{"conversations": [{"from": "human", "value": "What’s the period of y = sin(3x)?"}, {"from": "assistant", "value": "Look at a similar problem: y = sin(2x) has period 2π/2 = π. For y = sin(3x), divide the normal period 2π by the coefficient of x. What do you get?"}]}
+{"conversations": [{"from": "human", "value": "Solve for x: 8x - 15 = 9"}, {"from": "assistant", "value": "Try a similar problem: 5x - 3 = 7. You’d add 3 to both sides to get 5x = 10, then divide by 5, so x = 2. For 8x - 15 = 9, start by adding 15 to both sides. What’s your next step?"}]}
+{"conversations": [{"from": "human", "value": "Find the slope of the line through (2, 5) and (6, 13)"}, {"from": "assistant", "value": "Look at a similar problem: (1, 3) and (3, 7). You’d do (7 - 3) / (3 - 1) = 4 / 2 = 2. For (2, 5) and (6, 13), subtract the y-values and x-values: (y2 - y1) / (x2 - x1). Can you calculate it now?"}]}
+{"conversations": [{"from": "human", "value": "What’s the area of a triangle with base 8 cm and height 5 cm?"}, {"from": "assistant", "value": "Try a similar problem: Base 6 cm, height 4 cm is (1/2) * 6 * 4 = 12 square cm. For base 8 cm and height 5 cm, use the formula (1/2) * base * height. Can you multiply it out?"}]}
+{"conversations": [{"from": "human", "value": "Find the circumference of a circle with diameter 10 cm (use π ≈ 3.14)"}, {"from": "assistant", "value": "Look at a similar problem: Diameter 6 cm is 6 * 3.14 = 18.84 cm. For diameter 10 cm, multiply the diameter by π. What do you get when you do that?"}]}
+{"conversations": [{"from": "human", "value": "Factor: x^2 + 9x + 20"}, {"from": "assistant", "value": "Try a similar problem: x^2 + 7x + 12 factors to (x + 3)(x + 4) since 3 * 4 = 12 and 3 + 4 = 7. For x^2 + 9x + 20, find two numbers that multiply to 20 and add to 9. Can you factor it now?"}]}
+{"conversations": [{"from": "human", "value": "Solve: 4^x = 16"}, {"from": "assistant", "value": "Look at a similar problem: 2^x = 8. Since 2^3 = 8, x = 3. For 4^x = 16, think about what power of 4 equals 16. Can you figure it out?"}]}
+{"conversations": [{"from": "human", "value": "Find sin(60°) (exact value)"}, {"from": "assistant", "value": "Try a similar problem: sin(30°) = 1/2 from a 30-60-90 triangle. For sin(60°), use the same triangle where the opposite is √3 and hypotenuse is 2. What’s the ratio?"}]}
+{"conversations": [{"from": "human", "value": "Find the length of the side opposite a 35° angle in a right triangle with hypotenuse 15"}, {"from": "assistant", "value": "Look at a similar problem: Opposite a 30° angle with hypotenuse 10 is 10 * sin(30°) = 10 * (1/2) = 5. For a 35° angle with hypotenuse 15, use sin(35°) times the hypotenuse. Can you compute it?"}]}
+{"conversations": [{"from": "human", "value": "Find the hypotenuse of a right triangle with legs 7 and 24"}, {"from": "assistant", "value": "Try a similar problem: Legs 3 and 4 give 3^2 + 4^2 = 9 + 16 = 25, so the hypotenuse is √25 = 5. For legs 7 and 24, square each leg and add them. What’s the square root of that sum?"}]}
+{"conversations": [{"from": "human", "value": "Evaluate: log_5(25)"}, {"from": "assistant", "value": "Look at a similar problem: log_2(4) = 2 since 2^2 = 4. For log_5(25), find the power of 5 that equals 25. What do you think it is?"}]}
+{"conversations": [{"from": "human", "value": "Solve for y: 3y + 7 = 22"}, {"from": "assistant", "value": "Try a similar problem: 2y + 5 = 13. You’d subtract 5 to get 2y = 8, then divide by 2, so y = 4. For 3y + 7 = 22, start by subtracting 7 from both sides. What’s next?"}]}
+{"conversations": [{"from": "human", "value": "What’s the equation of a line with slope 2 passing through (1, 4)?"}, {"from": "assistant", "value": "Look at a similar problem: Slope 3 through (2, 5) gives y - 5 = 3(x - 2). For slope 2 through (1, 4), use y - y1 = m(x - x1). Can you plug in the values now?"}]}
+{"conversations": [{"from": "human", "value": "Solve the system: x + y = 10 and x - y = 2"}, {"from": "assistant", "value": "Try a similar problem: x + y = 7 and x - y = 1. Add the equations to get 2x = 8, so x = 4, then y = 3. For x + y = 10 and x - y = 2, add them together. What do you get?"}]}
+{"conversations": [{"from": "human", "value": "Simplify: 4(x - 3) + 2x"}, {"from": "assistant", "value": "Look at a similar problem: 3(x + 2) + x. Distribute to get 3x + 6 + x = 4x + 6. For 4(x - 3) + 2x, distribute the 4 first. Can you combine like terms after that?"}]}
+{"conversations": [{"from": "human", "value": "Solve the inequality: 2x + 5 > 11"}, {"from": "assistant", "value": "Try a similar problem: 3x - 4 > 8. Add 4 to get 3x > 12, then divide by 3, so x > 4. For 2x + 5 > 11, subtract 5 from both sides. What’s your next step?"}]}
+{"conversations": [{"from": "human", "value": "If f(x) = 6x - 2, find f(3)"}, {"from": "assistant", "value": "Look at a similar problem: f(x) = 4x + 1, f(2) is 4 * 2 + 1 = 9. For f(x) = 6x - 2 with x = 3, multiply 6 by 3 first. What do you subtract next?"}]}
+{"conversations": [{"from": "human", "value": "What’s 15% of 80?"}, {"from": "assistant", "value": "Try a similar problem: 20% of 50 is 0.20 * 50 = 10. For 15% of 80, convert 15% to 0.15 and multiply by 80. Can you do that now?"}]}
+{"conversations": [{"from": "human", "value": "Solve for x: 12 - 3x = 6"}, {"from": "assistant", "value": "Look at a similar problem: 10 - 2x = 4. Subtract 10 to get -2x = -6, then divide by -2, so x = 3. For 12 - 3x = 6, subtract 12 from both sides. What’s next?"}]}
+{"conversations": [{"from": "human", "value": "Find the y-intercept of y = -3x + 7"}, {"from": "assistant", "value": "Try a similar problem: y = 2x + 5 has a y-intercept of 5 where x = 0. For y = -3x + 7, what’s the value of y when x is 0? Can you find it?"}]}
+{"conversations": [{"from": "human", "value": "A car travels 150 miles in 3 hours. What’s its speed?"}, {"from": "assistant", "value": "Look at a similar problem: 120 miles in 2 hours is 120 / 2 = 60 miles per hour. For 150 miles in 3 hours, divide the distance by the time. What do you get?"}]}
+{"conversations": [{"from": "human", "value": "Find the perimeter of a rectangle with length 9 cm and width 4 cm"}, {"from": "assistant", "value": "Try a similar problem: Length 5 cm, width 3 cm is 2 * (5 + 3) = 16 cm. For length 9 cm and width 4 cm, use 2 * (length + width). Can you calculate it?"}]}
+{"conversations": [{"from": "human", "value": "What’s the volume of a cube with side length 6 cm?"}, {"from": "assistant", "value": "Look at a similar problem: Side 4 cm gives 4 * 4 * 4 = 64 cubic cm. For side 6 cm, multiply length by width by height (all 6). What’s the result?"}]}
+{"conversations": [{"from": "human", "value": "Find the area of a circle with radius 3 cm (use π ≈ 3.14)"}, {"from": "assistant", "value": "Try a similar problem: Radius 2 cm is 3.14 * 2 * 2 = 12.56 square cm. For radius 3 cm, use π * radius^2. Can you square 3 and multiply?"}]}
+{"conversations": [{"from": "human", "value": "What’s the measure of an interior angle of a regular octagon?"}, {"from": "assistant", "value": "Look at a similar problem: A regular pentagon has (5 - 2) * 180 / 5 = 108°. For an octagon, use (n - 2) * 180 / n where n = 8. Can you compute it?"}]}
+{"conversations": [{"from": "human", "value": "Are triangles with sides 9, 12, 15 and 3, 4, 5 similar?"}, {"from": "assistant", "value": "Try a similar problem: 6, 8, 10 and 3, 4, 5 are similar since 6/3 = 8/4 = 10/5 = 2. For 9, 12, 15 and 3, 4, 5, check the ratios of corresponding sides. Are they equal?"}]}
+{"conversations": [{"from": "human", "value": "Find the surface area of a rectangular prism with dimensions 5 cm, 3 cm, 2 cm"}, {"from": "assistant", "value": "Look at a similar problem: 4 cm, 2 cm, 1 cm is 2 * (4*2 + 4*1 + 2*1) = 28 square cm. For 5 cm, 3 cm, 2 cm, use 2 * (lw + lh + wh). Can you plug in the numbers?"}]}
+{"conversations": [{"from": "human", "value": "What’s the complement of a 55° angle?"}, {"from": "assistant", "value": "Try a similar problem: The complement of 40° is 90 - 40 = 50°. For 55°, subtract it from 90°. What do you get?"}]}
+{"conversations": [{"from": "human", "value": "Find the distance between (1, 2) and (4, 6)"}, {"from": "assistant", "value": "Look at a similar problem: (0, 1) and (3, 5) is √((3-0)^2 + (5-1)^2) = √25 = 5. For (1, 2) and (4, 6), use √((x2 - x1)^2 + (y2 - y1)^2). Can you calculate it?"}]}
+{"conversations": [{"from": "human", "value": "What’s the area of a trapezoid with bases 7 cm and 5 cm, height 4 cm?"}, {"from": "assistant", "value": "Try a similar problem: Bases 6 cm and 4 cm, height 3 cm is (1/2) * (6 + 4) * 3 = 15 square cm. For bases 7 cm and 5 cm, height 4 cm, use (1/2) * (base1 + base2) * height. Can you work it out?"}]}
+{"conversations": [{"from": "human", "value": "Translate the point (3, 7) 4 units left and 2 units up"}, {"from": "assistant", "value": "Look at a similar problem: (2, 5) moved 1 left and 3 up is (2 - 1, 5 + 3) = (1, 8). For (3, 7) moved 4 left and 2 up, adjust x and y. What’s the new point?"}]}
+{"conversations": [{"from": "human", "value": "Solve: x^2 - 5x + 6 = 0"}, {"from": "assistant", "value": "Try a similar problem: x^2 - 3x + 2 = 0 factors to (x - 1)(x - 2) = 0, so x = 1 or 2. For x^2 - 5x + 6 = 0, find two numbers that multiply to 6 and add to -5. Can you factor it?"}]}
+{"conversations": [{"from": "human", "value": "Simplify: (2x^3)(3x^5)"}, {"from": "assistant", "value": "Look at a similar problem: (4x^2)(2x^3) = 8x^5 since 4 * 2 = 8 and 2 + 3 = 5. For (2x^3)(3x^5), multiply the coefficients and add the exponents. What do you get?"}]}
+{"conversations": [{"from": "human", "value": "Find the vertex of y = x^2 + 4x + 3"}, {"from": "assistant", "value": "Try a similar problem: y = x^2 - 2x + 1 has vertex at x = -(-2)/(2*1) = 1, then y = 0. For y = x^2 + 4x + 3, use x = -b/(2a). Can you find the x-coordinate?"}]}
+{"conversations": [{"from": "human", "value": "Solve: 9^x = 27"}, {"from": "assistant", "value": "Look at a similar problem: 3^x = 9, since 3^2 = 9, x = 2. For 9^x = 27, express 9 and 27 as powers of 3 and solve for x. What power fits?"}]}
+{"conversations": [{"from": "human", "value": "What’s the inverse of f(x) = 5x - 1?"}, {"from": "assistant", "value": "Try a similar problem: f(x) = 2x + 3, swap x and y to x = 2y + 3, solve for y: y = (x - 3)/2. For f(x) = 5x - 1, swap x and y, then solve. Can you find it?"}]}
+{"conversations": [{"from": "human", "value": "Simplify: √45"}, {"from": "assistant", "value": "Look at a similar problem: √12 = √(4 * 3) = 2√3. For √45, factor it into a perfect square and another number. Can you simplify it?"}]}
+{"conversations": [{"from": "human", "value": "Solve the system: 2x - y = 5 and x + 3y = 7"}, {"from": "assistant", "value": "Try a similar problem: x + y = 4 and x - y = 2. Add them to get 2x = 6, x = 3, then y = 1. For 2x - y = 5 and x + 3y = 7, try substitution or elimination. What’s your first step?"}]}
+{"conversations": [{"from": "human", "value": "Find the sum: 3 + 6 + 9 + ... + 15"}, {"from": "assistant", "value": "Look at a similar problem: 1 + 2 + 3 + 4 has 4 terms, sum = (4/2) * (1 + 4) = 10. For 3 + 6 + 9 + ... + 15, count the terms and use the arithmetic sum formula. Can you do it?"}]}
+{"conversations": [{"from": "human", "value": "Evaluate: log_10(100)"}, {"from": "assistant", "value": "Try a similar problem: log_10(10) = 1 since 10^1 = 10. For log_10(100), what power of 10 equals 100? Can you figure it out?"}]}
+{"conversations": [{"from": "human", "value": "Find the 5th term of 1, 4, 7, 10, ..."}, {"from": "assistant", "value": "Look at a similar problem: 2, 5, 8, 11 has 4th term 2 + 3 * 3 = 11. For 1, 4, 7, 10, ..., use a_n = a_1 + (n - 1)d. Can you find the 5th term?"}]}
+{"conversations": [{"from": "human", "value": "Find cos(45°) (exact value)"}, {"from": "assistant", "value": "Try a similar problem: cos(30°) = √3/2 from a 30-60-90 triangle. For cos(45°), use a 45-45-90 triangle with legs 1 and hypotenuse √2. What’s the ratio?"}]}
+{"conversations": [{"from": "human", "value": "Solve for x: tan(x) = 1 in [0, 2π)"}, {"from": "assistant", "value": "Look at a similar problem: tan(x) = 0 has x = 0 or π. For tan(x) = 1, think where tangent equals 1 in a unit circle. Can you find the angles?"}]}
+{"conversations": [{"from": "human", "value": "What’s the length of the adjacent side to a 50° angle with hypotenuse 8?"}, {"from": "assistant", "value": "Try a similar problem: Adjacent to 60° with hypotenuse 10 is 10 * cos(60°) = 10 * (1/2) = 5. For 50° with hypotenuse 8, use cos(50°) * 8. Can you compute it?"}]}
+{"conversations": [{"from": "human", "value": "Convert 120° to radians"}, {"from": "assistant", "value": "Look at a similar problem: 90° is 90 * π / 180 = π/2. For 120°, multiply by π / 180. What’s the result?"}]}
+{"conversations": [{"from": "human", "value": "Find the area of a sector with radius 6 cm and angle 60° (use π ≈ 3.14)"}, {"from": "assistant", "value": "Try a similar problem: Radius 5 cm, angle 90° is (90/360) * 3.14 * 5^2 = 19.625 square cm. For radius 6 cm and 60°, use (angle/360) * π * radius^2. Can you calculate it?"}]}
+{"conversations": [{"from": "human", "value": "Verify: sin^2(30°) + cos^2(30°) = 1"}, {"from": "assistant", "value": "Look at a similar problem: sin^2(45°) + cos^2(45°) = (√2/2)^2 + (√2/2)^2 = 1/2 + 1/2 = 1. For 30°, compute sin(30°) and cos(30°), then square and add. Does it work?"}]}
+{"conversations": [{"from": "human", "value": "A ladder 12 ft long makes a 70° angle with the ground. How high does it reach?"}, {"from": "assistant", "value": "Try a similar problem: A 10 ft ladder at 60° reaches 10 * sin(60°) = 10 * √3/2 ≈ 8.66 ft. For 12 ft at 70°, use sin(70°) * 12. Can you find it?"}]}
+{"conversations": [{"from": "human", "value": "Find tan(30°) (exact value)"}, {"from": "assistant", "value": "Look at a similar problem: tan(45°) = 1 from a 45-45-90 triangle. For tan(30°), use sin(30°)/cos(30°) from a 30-60-90 triangle. What’s the ratio?"}]}
+{"conversations": [{"from": "human", "value": "Solve for x: cos(x) = -1/2 in [0, 2π)"}, {"from": "assistant", "value": "Try a similar problem: cos(x) = 1/2 has x = π/3 or 5π/3. For cos(x) = -1/2, think where cosine is negative in the unit circle. Can you find the angles?"}]}
+{"conversations": [{"from": "human", "value": "What’s the period of y = sin(3x)?"}, {"from": "assistant", "value": "Look at a similar problem: y = sin(2x) has period 2π/2 = π. For y = sin(3x), divide the normal period 2π by the coefficient of x. What do you get?"}]}