qid int64 9 9.87k | dataset stringclasses 4
values | image imagewidth (px) 56 1.27k | question stringlengths 52 645 | answer stringclasses 6
values |
|---|---|---|---|---|
8,158 | geometry3k | Find $x$. $A=357$ in$^2$.
Choices:
A: 21
B: 22
C: 23
D: 24 | A | |
8,173 | geometry3k | Circle $A$ has diameters $\overline{D F}$ and $\overline{P G}$
If $D F=10$, find $D A$
Choices:
A: 5
B: 10
C: 20
D: 25 | A | |
8,198 | geometry3k | If $PR \parallel KL$, KN = 9, LN = 16, PM = 2 KP, find PR
Choices:
A: 15
B: 32 / 2
C: \frac { 50 } { 3 }
D: 17 | C | |
8,203 | geometry3k | Polygon ABCD ~ polygon AEFG, $m\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.
Find $m\angle ADC$
Choices:
A: 14
B: 72
C: 108
D: 120 | C | |
8,204 | geometry3k | Chords $\overline{A C}$ and $\overline{D F}$ are equidistant from the center. If the radius of $\odot G$ is 26 find $A C$
Choices:
A: 5
B: 10
C: 13
D: 48 | D | |
8,211 | geometry3k | If PR || KL, KN = 9, LN = 16, PM = 2 KP, find MN
Choices:
A: 7
B: 12
C: 15
D: 16 | B | |
8,239 | geometry3k | Find the perimeter of $\triangle W Z X$, if $\triangle W Z X \sim \triangle S R T, S T=6$, $W X=5,$ and the perimeter of $\triangle S R T=15$.
Choices:
A: 12.5
B: 13
C: 15
D: 18 | A | |
8,277 | geometry3k | Circle $O$ has a radius of 13 inches. Radius $\overline{O B}$ is perpendicular to chord $\overline{C D}$ which is 24 inches long.
If $m \widehat{C D}=134,$ find $m \widehat{C B}$
Choices:
A: 24
B: 33
C: 67
D: 134 | C | |
8,324 | geometry3k | Use the Pythagorean Theorem to find the length of the hypotenuse of each right triangle.
Choices:
A: 5
B: \sqrt { 119 }
C: 12
D: 13 | D | |
8,328 | geometry3k | $Q$ is the centroid and $BE=9$. Find $BQ$.
Choices:
A: 3
B: 6
C: 9
D: 12 | B | |
8,344 | geometry3k | $m$ is the perpendicular bisector of $XZ$, $WZ=14.9$. Find $WX$.
Choices:
A: 7.45
B: 14.9
C: 22.4
D: 25.3 | B | |
8,345 | geometry3k | In rhombus $A B C D, A B=2 x+3$ and $B C=5 x$. Find $m \angle AEB$.
Choices:
A: 45
B: 60
C: 90
D: 180 | C | |
8,357 | geometry3k | A square is inscribed in a circle having a radius of $6$ inches. Find the length of each side of the square.
Choices:
A: \frac { 3 } { \sqrt 2 }
B: 3 \sqrt 2
C: 6 \sqrt 2
D: 12 \sqrt 2 | C | |
8,368 | geometry3k | Find the perimeter of $\triangle D E F,$ if $\triangle D E F \sim \triangle C B F,$ perimeter of $\triangle C B F=27, D F=6,$ and $F C=8$
Choices:
A: 20.25
B: 21
C: 27
D: 36 | A | |
8,394 | geometry3k | In $\odot M$, $FL=24,HJ=48$, and $m \widehat {HP}=65$. Find $m \widehat {HJ}$.
Choices:
A: 65
B: 120
C: 130
D: 155 | C | |
8,409 | geometry3k | Find x. Round the side measure to the nearest tenth.
Choices:
A: 69.0
B: 69.8
C: 76.4
D: 77.2 | B | |
8,418 | geometry3k | In the figure, $m∠3 = 43$. Find the measure of $\angle 11$.
Choices:
A: 43
B: 53
C: 63
D: 137 | A | |
8,420 | geometry3k | Find the value of $x$ in each diagram
Choices:
A: 68
B: 78
C: 79
D: 136 | A | |
8,421 | geometry3k | If $m \widehat{F E}=118, m \widehat{A B}=108$, $m \angle E G B=52,$ and $m \angle E F B=30$, find $m \widehat{C F}$
Choices:
A: 30
B: 44
C: 108
D: 118 | B | |
8,432 | geometry3k | Quadrilateral EFGH is a rectangle. If FK = 32 feet, find EG.
Choices:
A: 13
B: 30
C: 57
D: 64 | D | |
8,438 | geometry3k | $\overline{A C}$ is a diagonal of rhombus $A B C D$ If $m \angle C D E$ is $116,$ what is $m \angle A C D ?$
Choices:
A: 58
B: 90
C: 116
D: 180 | A | |
8,439 | geometry3k | Find the perimeter of $\triangle R U W$ if $\triangle R U W \sim \triangle S T V$, $S T=24, V S=12, V T=18$ and $U W=21$
Choices:
A: 63
B: 68
C: 70
D: 75 | A | |
8,453 | mathvision | Eve has taken 2 bananas to school. At first she changed each of them into 4 apples, later on she exchanged each apple into 3 mandarins. How many mandarins has Eve got?
Choices:
A: $2+4+3$
B: $2 \cdot 4+3$
C: $2+4 \cdot 3$
D: $2 \cdot 4 \cdot 3$
E: $2+4-3$ | D | |
8,555 | mathvision | In the diagram, $A B$ has length $1 ; \angle A B C=\angle A C D=90^{\circ}$; $\angle C A B=\angle D A C=\theta$. What is the length of $A D$?
Choices:
A: $\cos \beta+\tg \beta$
B: $\frac{1}{\cos (2 \beta)}$
C: $\cos ^{2} \beta$
D: $\cos (2 \beta)$
E: $\frac{1}{\cos ^{2} \beta}$ | E | |
8,583 | mathvision | The picture on the right shows a tile pattern. The side length of the bigger tiles is a and of the smaller ones b. The dotted lines (horizontal and tilted) include an angle of $30^{\circ}$. How big is the ratio a:b?
Choices:
A: $(2 \cdot \sqrt{3}): 1$
B: $(2+\sqrt{3}): 1$
C: $(3+\sqrt{2}): 1$
D: $(3 \cdot \sqrt{2}): 1... | B | |
8,621 | mathvision | Bettina chooses five points $A, B, C, D$ and $E$ on a circle and draws the tangent to the circle at point $A$. She realizes that the five angles marked $x$ are all equally big. (Note that the diagram is not drawn to scale!) How big is the angle $\angle A B D$?
Choices:
A: $66^{\circ}$
B: $70.5^{\circ}$
C: $72^{\circ}$... | C | |
8,627 | mathvision | Which quadrant contains no points of the graph of the linear function $f(x)=-3.5 x+7$?
Choices:
A: I
B: II
C: III
D: IV
E: Every quadrant contains at least one point of the graph. | C | |
8,672 | mathvision | Four circles with radius 1 intersect each other as seen in the diagram. What is the perimeter of the grey area?
Choices:
A: $\pi$
B: $\frac{3 \pi}{2}$
C: a number between $\frac{3 \pi}{2}$ and $2 \pi$
D: $2 \pi$
E: $\pi^{2}$ | D | |
8,865 | mathvision | The side of the square $A B C D$ is $10 \mathrm{~cm}$. The inner point $E$ of the square is such that $\angle E A B=75^{\circ}, \angle A B E=30^{\circ}$. The length of the segment $E C$ is:
Choices:
A: $8 \mathrm{~cm}$
B: $9 \mathrm{~cm}$
C: $9.5 \mathrm{~cm}$
D: $10 \mathrm{~cm}$
E: $11 \mathrm{~cm}$ | D | |
8,932 | mathvision | Raphael has three squares. The first one has side length $2 \mathrm{~cm}$, the second one has side length $4 \mathrm{~cm}$ and one corner is the centre of the first square. The third square has side length $6 \mathrm{~cm}$ and one corner is the centre of the second square. What is the total area of the figure shown?
C... | A | |
8,990 | mathvision | The sides of the square $A B C D$ are $10 \mathrm{~cm}$ long. What is the total area of the shaded part?
Choices:
A: $40 \mathrm{~cm}^{2}$
B: $45 \mathrm{~cm}^{2}$
C: $50 \mathrm{~cm}^{2}$
D: $55 \mathrm{~cm}^{2}$
E: $60 \mathrm{~cm}^{2}$ | C | |
9,012 | mathvision | Two quadrates with the same size cover a circle, the radius of which is $3 \mathrm{~cm}$. Find the total area (in $\mathrm{cm}^{2}$ ) of the shaded figure.
Choices:
A: $8(\pi-1)$
B: $6(2 \pi-1)$
C: $9 \pi-25$
D: $9(\pi-2)$
E: $\frac{6 \pi}{5}$ | D | |
9,021 | mathvision | Let $a$ and $b$ be two shorter sides of the right-angled triangle. Then the sum of the diameter of the incircle and that of the circumcircle of this triangle is equal to:
Choices:
A: $\sqrt{a^{2}+b^{2}}$
B: $\sqrt{a b}$
C: $0.5(a+b)$
D: $2(a+b)$
E: $a+b$ | E | |
9,101 | mathvision | If the letters of the Word MAMA are written underneath each other then the word has a vertical axis of symmetry. For which of these words does that also hold true?
Choices:
A: ADAM
B: BAUM
C: BOOT
D: LOGO
E: TOTO | E | |
9,159 | mathvision | In the picture, three strips of the same horizontal width $a$ are marked 1,2,3. These strips connect the two parallel lines. Which strip has the biggest area?
Choices:
A: All three strips have the same area
B: Strip 1
C: Strip 2
D: Strip 3
E: Impossible to answer without knowing $a$ | A | |
9,207 | mathvision | The area of the grey rectangle shown on the right is $13 \mathrm{~cm}^{2}. X$ and $Y$ are the midpoints of the sides of the trapezium. How big is the area of the trapezium?
Choices:
A: $24 \mathrm{~cm}^{2}$
B: $25 \mathrm{~cm}^{2}$
C: $26 \mathrm{~cm}^{2}$
D: $27 \mathrm{~cm}^{2}$
E: $28 \mathrm{~cm}^{2}$ | C | |
9,226 | mathvision | The side lengths of the large regular hexagon are twice the length of those of the small regular hexagon. What is the area of the large hexagon if the small hexagon has an area of $4 \mathrm{~cm}^{2}$?
Choices:
A: $16 \mathrm{~cm}^{2}$
B: $14 \mathrm{~cm}^{2}$
C: $12 \mathrm{~cm}^{2}$
D: $10 \mathrm{~cm}^{2}$
E: $8 \m... | A | |
9,251 | mathvision | In the three regular hexagons shown, $X, Y$ and $Z$ describe in this order the areas of the grey shaded parts. Which of the following statements is true?
Choices:
A: $X=Y=Z$
B: $Y=Z \neq X$
C: $Z=X \neq Y$
D: $X=Y \neq Z$
E: Each of the areas has a different value. | A | |
9,260 | mathvision | The diagram consists of three circles of equal radius $R$. The centre of those circles lie on a common straight line where the middle circle goes through the centres of the other two circles (see diagram). How big is the perimeter of the figure?
Choices:
A: $\frac{10 \pi R}{3}$
B: $\frac{5 \pi R}{3}$
C: $\frac{2 \pi R... | A | |
9,300 | mathvision | There used to be 5 parrots in my cage. Their average value was $€ 6000$. One day while I was cleaning out the cage the most beautiful parrot flew away. The average value of the remaining four parrots was $€ 5000$. What was the value of the parrot that escaped?
Choices:
A: $€ 1000$
B: $€ 2000$
C: $€ 5500$
D: $€ 6000$
E... | E | |
9,303 | mathvision | Two squares of the same size, and with their edges parallel, cover a circle with a radius of $3 \mathrm{~cm}$, as shown. In square centimetres, what is the total shaded area?
Choices:
A: $8(\pi-1)$
B: $6(2 \pi-1)$
C: $(9 \pi-25)$
D: $9(\pi-2)$
E: $\frac{6\pi}{5}$ | D | |
9,320 | mathvision | Let $a$ and $b$ be the lengths of the two shorter sides of the right-angled triangle shown in the diagram. The longest side, $D$, is the diameter of the large circle and $d$ is the diameter of the small circle, which touches all three sides of the triangle.
Which one of the following expressions is equal to $D+d$ ?
Ch... | A | |
9,388 | mathvision | In the isosceles triangle $A B C$, points $K$ and $L$ are marked on the equal sides $A B$ and $B C$ respectively so that $A K=K L=L B$ and $K B=A C$.
What is the size of angle $A B C$ ?
Choices:
A: $36^{\circ}$
B: $38^{\circ}$
C: $40^{\circ}$
D: $42^{\circ}$
E: $44^{\circ}$ | A | |
9,423 | mathvision | The square $A B C D$ consists of four congruent rectangles arranged around a central square. The perimeter of each of the rectangles is $40 \mathrm{~cm}$. What is the area of the square $A B C D$ ?
Choices:
A: $400 \mathrm{~cm}^{2}$
B: $200 \mathrm{~cm}^{2}$
C: $160 \mathrm{~cm}^{2}$
D: $120 \mathrm{~cm}^{2}$
E: $80 \... | A | |
9,426 | mathvision | Maddie has a paper ribbon of length $36 \mathrm{~cm}$. She divides it into four rectangles of different lengths. She draws two lines joining the centres of two adjacent rectangles as shown.
What is the sum of the lengths of the lines that she draws?
Choices:
A: $18 \mathrm{~cm}$
B: $17 \mathrm{~cm}$
C: $20 \mathrm{~c... | A | |
9,456 | mathvision | In the picture, the three strips labelled 1,2,3 have the same horizontal width $a$. These three strips connect two parallel lines. Which of these statements is true?
Choices:
A: All three strips have the same area.
B: Strip 1 has the largest area.
C: Strip 2 has the largest area.
D: Strip 3 has the largest area.
E: It... | A | |
9,525 | mathvision | The diagram shows three congruent regular hexagons. Some diagonals have been drawn, and some regions then shaded. The total shaded areas of the hexagons are $X, Y, Z$ as shown. Which of the following statements is true?
Choices:
A: $X, Y$ and $Z$ are all the same
B: $\quad Y$ and $Z$ are equal, but $X$ is different
C:... | A | |
9,575 | mathvision | A regular octagon $ ABCDEFGH$ has an area of one square unit. What is the area of the rectangle $ ABEF$?
Choices:
A: $1-\frac{\sqrt{2}}{2}$
B: $\frac{\sqrt{2}}{4}$
C: $\sqrt{2}-1$
D: $\frac{1}{2}$
E: $\frac{1+\sqrt{2}}{4}$ | D | |
9,581 | mathvision | An annulus is the region between two concentric circles. The concentric circles in the figure have radii $ b$ and $ c$, with $ b > c$. Let $ \overline{OX}$ be a radius of the larger circle, let $ \overline{XZ}$ be tangent to the smaller circle at $ Z$, and let $ \overline{OY}$ be the radius of the larger circle that co... | A | |
9,639 | mathvision | A closed box with a square base is to be wrapped with a square sheet of wrapping paper. The box is centered on the wrapping paper with the vertices of the base lying on the midlines of the square sheet of paper, as shown in the figure on the left. The four corners of the wrapping paper are to be folded up over the side... | A | |
9,681 | mathvision | In this figure the radius of the circle is equal to the altitude of the equilateral triangle $ABC$. The circle is made to roll along the side $AB$, remaining tangent to it at a variable point $T$ and intersecting lines $AC$ and $BC$ in variable points $M$ and $N$, respectively. Let $n$ be the number of degrees in arc $... | E | |
9,723 | mathvision | Circles with centers $A ,~ B,$ and $C$ each have radius $r$, where $1 < r < 2$. The distance between each pair of centers is $2$.
If $B'$ is the point of intersection of circle $A$ and circle $C$ which is outside circle $B$, and if $C'$ is the point of intersection of circle $A$ and circle $B$ which is outside circle ... | D | |
9,737 | mathvision | In the adjoining plane figure, sides $AF$ and $CD$ are parallel, as are sides $AB$ and $EF$, and sides $BC$ and $ED$. Each side has length of 1. Also, $\measuredangle FAB = \measuredangle BCD = 60^\circ$. The area of the figure is
Choices:
A: $\frac{\sqrt{3}}{2}$
B: $1$
C: $\frac{3}{2}$
D: $\sqrt{3}$
E: $2$ | D | |
9,746 | mathvision | In a circle with center $ O$, $ AD$ is a diameter, $ ABC$ is a chord, $ BO = 5$, and $ \angle ABO = \stackrel{\frown}{CD} = 60^{\circ}$. Then the length of $ BC$ is:
Choices:
A: $3$
B: $3 + \sqrt{3}$
C: $5 - \frac{\sqrt{3}}{2}$
D: $5$
E: $\text{none of the above}$ | D | |
9,859 | mathvision | An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractional part of the original area of the black triangle remains black?
Choices:
A: $\frac{1}{1024}$
B: $\frac{15}{64}$
C: $\frac{243}{1024}$
D: $\f... | C | |
9,870 | mathvision | Each of the three large squares shown below is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?
Choices:
A: $\text{The shaded areas in all three are equal.}$
B: $\text{Only the shaded areas of }I\text{ and }II\t... | A |
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