images
images listlengths 1
1
| problem
stringlengths 14
1.13k
| answer
stringlengths 1
102
| problem_id
stringlengths 14
17
|
|---|---|---|---|
<image>Calculate the area of the following figure.
Give your answer as an exact value.
|
Area $=\frac{147 \pi}{4} \mathrm{~cm}^{2}$
|
mathverse_vi_2003
|
|
<image>Find the exact area of the shape shown.
|
Area $=347.4248 \pi \mathrm{cm}^{2}$
|
mathverse_vi_2008
|
|
<image>Find the exact area of the shape shown, which is two thirds of a circle.
|
Area $=\frac{338 \pi}{3} \mathrm{~mm}^{2}$
|
mathverse_vi_2013
|
|
<image>Consider the sector below.
Calculate the area. Give your answer correct to four decimal places.
|
7298.6737 \mathrm{~mm}^{2}
|
mathverse_vi_2018
|
|
<image>Consider the sector below.
Calculate the area. Give your answer correct to two decimal places.
|
Area $=1115.94 \mathrm{~cm}^{2}$
|
mathverse_vi_2023
|
|
<image>Consider the sector below.
Calculate the area. Give your answer correct to two decimal places.
|
Area $=3426.49 \mathrm{~m}^{2}$
|
mathverse_vi_2028
|
|
<image>Calculate the total perimeter of the sector shown, correct to one decimal place.
|
Perimeter $=18.8 \mathrm{~cm}$
|
mathverse_vi_2033
|
|
<image>Find the perimeter of the sector shown, correct to two decimal places.
|
Perimeter $=18.89 \mathrm{~cm}$
|
mathverse_vi_2038
|
|
<image>Find the perimeter of the figure shown, correct to two decimal places.
|
Perimeter $=60.68 \mathrm{~cm}$
|
mathverse_vi_2043
|
|
<image>Consider the sector below.
Calculate the perimeter. Round your answer to two decimal places.
|
Perimeter $=492.14 \mathrm{~mm}$
|
mathverse_vi_2048
|
|
<image>Consider the sector below.
Calculate the perimeter of the sector. Round your answer to two decimal places.
|
Perimeter $=257.73 \mathrm{~m}$
|
mathverse_vi_2053
|
|
<image>This is part of a piece of jewellery. It is made out of a metal plate base, and gold plated wire (of negligible thickness) runs around the outside.
What is the area covered by the metal plate base?
Give your answer correct to two decimal places.
|
Area $=70.69 \mathrm{~mm}^{2}$
|
mathverse_vi_2058
|
|
<image>The area of the sector below is 140.28 (cm)^2.
Find the length of the radius, $r$. Give your answer correct to one decimal place.
|
$r=24.4$
|
mathverse_vi_2063
|
|
<image>Find the area of the sector shown.
Round your answer to two decimal places.
|
Area $=73.52\mathrm{~cm}^{2}$
|
mathverse_vi_2068
|
|
<image>Calculate the area of the following sector.
Round your answer to one decimal place.
|
Area $=315.4 \mathrm{~m}^{2}$
|
mathverse_vi_2073
|
|
<image>Arc $JK$ has a length measuring 2\pi cm. Determine the exact area of sector $OJK$.
|
Area of sector $=6 \pi \mathrm{cm}^{2}$
|
mathverse_vi_2078
|
|
<image>Find the perimeter of the figure shown.
|
Perimeter $=94 \mathrm{~cm}$
|
mathverse_vi_2083
|
|
<image>Find the perimeter of the figure shown.
|
Perimeter $=74 \mathrm{~mm}$
|
mathverse_vi_2088
|
|
<image>Find the perimeter of the figure shown.
|
Perimeter $=28 \mathrm{~mm}$
|
mathverse_vi_2093
|
|
<image>Find the length of the missing side of the figure shown.
|
$5=s$
|
mathverse_vi_2098
|
|
<image>How much area is remaining?
|
96
|
mathverse_vi_2103
|
|
<image>How much area is remaining?
|
36
|
mathverse_vi_2108
|
|
<image>The meteoroid projected in the direction of B is moving at a speed of 7860 km/h.
What distance will the meteoroid travelling towards point B have covered after 29 minutes?
|
3799 km
|
mathverse_vi_2113
|
|
<image>Calculate the area of the following triangle.
Round your answer to two decimal places.
|
60.21 \mathrm{m}^2
|
mathverse_vi_2118
|
|
<image>An industrial site in the shape of a triangle is to take up the space between where three roads intersect.
Calculate the area of the site.
Round your answer to two decimal places.
|
1389.32 \mathrm{m}^2
|
mathverse_vi_2123
|
|
<image>Find d to the nearest metre.
|
729
|
mathverse_vi_2128
|
|
<image>A boat is at the current point. Write down the bearing that the boat should travel on to return to the starting point.
|
N 34° W
|
mathverse_vi_2133
|
|
<image>The perimeter of the whole shape is 14\pi units. The entire shape is to be enlarged by a factor of 5 to form a logo sticker on the window of a shop front. What area of the shop front window will the sticker take up?
|
\frac{1225\pi }{2} \text { units }^2
|
mathverse_vi_2138
|
|
<image>True or false: According to the angle A, the distance from the driver to the building would be the opposite side.
Choice:
A. True
B. False
|
False
|
mathverse_vi_2143
|
|
<image>True or False : The quickest way to get there will be through the playground.
Choice:
A. False
B. True
|
False
|
mathverse_vi_2148
|
|
<image>Iain first walks west and then south looking for a petrol station.
If he is now $h$ km directly from his starting point, find the value of $h$.
|
$h=15$
|
mathverse_vi_2153
|
|
<image>Find the distance between the two endpoints. Round to three decimal places.
|
8.246
|
mathverse_vi_2158
|
|
<image>Find the coordinates of the midpoint for each diagonal.
|
(2,-2)
|
mathverse_vi_2163
|
|
<image>Determine the equation of the graph.
|
\frac{x^2}{81}+\frac{y^2}{9}=1
|
mathverse_vi_2168
|
|
<image>Determine the equation of the graph.
|
\frac{(x+2)^2}{4}+\frac{(y-2)^2}{9}=1
|
mathverse_vi_2173
|
|
<image>Find the equation of the graph.
|
\frac{y^2}{16}-\frac{x^2}{25}=1
|
mathverse_vi_2178
|
|
<image>Find the equation of the graph.
|
\frac{y^2}{9}-\frac{(x+1)^2}{9}=1
|
mathverse_vi_2183
|
|
<image>Find the equation of the graph.
|
\frac{(x+3)^2}{25}-\frac{(y+3)^2}{25}=1
|
mathverse_vi_2188
|
|
<image>What are the coordinates of point $A$ ?
Enter an exact value or round to the nearest hundredth.
|
$\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$
|
mathverse_vi_2193
|
|
<image>Which two of the following expressions are OPPOSITE of $\tan (\theta)$ ?
Choose 2 answers:
Choices:
A:$\tan (\pi+\theta)$
B:$\tan \left(\frac{\pi}{2}-\theta\right)$
C:$\tan (2 \pi-\theta)$
D:$\tan (\pi-\theta)$
|
C
D
|
mathverse_vi_2198
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(\frac{3}{5}, \frac{4}{5}\right)$.
Find the value of $\sin a$.
|
$\frac{4}{5}$
|
mathverse_vi_2203
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(\frac{3}{5}, \frac{4}{5}\right)$.
Find the value of $\tan a$.
|
$\frac{4}{3}$
|
mathverse_vi_2208
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$.
Find the value of $\cos a$.
|
$-\frac{21}{29}$
|
mathverse_vi_2213
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$.
Find the value of $\tan a$.
|
$-\frac{20}{21}$
|
mathverse_vi_2218
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$.
Find the value of $\sin a$.
|
$\frac{20}{29}$
|
mathverse_vi_2223
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$.
Find the value of $\cos a$.
|
$-\frac{21}{29}$
|
mathverse_vi_2228
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(\frac{20}{29},-\frac{21}{29}\right)$.
Find the value of $\cos a$.
|
$\frac{20}{29}$
|
mathverse_vi_2233
|
|
<image>The graph shows an angle $a$ in standard position with its terminal side intersecting the figure at $P\left(\frac{20}{29},-\frac{21}{29}\right)$.
Find the value of $\tan a$.
|
$-\frac{21}{20}$
|
mathverse_vi_2238
|
|
<image>What is the value of $\sec \theta$ ?
Choices:
A:$\frac{1}{x}$
B:$x$
C:$y$
D:$\frac{1}{y}$
|
A
|
mathverse_vi_2243
|
|
<image>Find the equation of the figure.
Use exact numbers.
y = _ x + _
|
y=-2 x+5
|
mathverse_vi_2248
|
|
<image>Write an equation that represents the figure.
Use exact numbers.
|
$y+3=\frac{3}{4}(x-2)$
|
mathverse_vi_2253
|
|
<image>Find the equation of the figure in point-slope form .
|
$y-3=\frac{2}{3}(x-8)$
|
mathverse_vi_2258
|
|
<image>State the coordinates of the centre of the figure in the form $(a, b)$.
|
(0,0)
|
mathverse_vi_2263
|
|
<image>State the radius.
|
2
|
mathverse_vi_2268
|
|
<image>State the diameter.
|
8
|
mathverse_vi_2273
|
|
<image>State the equation of the circle.
|
$x^{2}+y^{2}=49$
|
mathverse_vi_2278
|
|
<image>Consider the circle on the graph.
Find the equation of the circle in standard form.
|
$(x-1)^{2}+(y-3)^{2}=36$
|
mathverse_vi_2283
|
|
<image>Find the value of $\cos \theta$. Rationalise the denominator if necessary.
|
$\frac{-2 \sqrt{13}}{13}$
|
mathverse_vi_2288
|
|
<image>Complete the statement.
Every point on the circle is exactly _ units away from the point
( _ , _ ).
|
Complete the statement.Every point on the circle is exactly 5 units away from the point (0,0).
|
mathverse_vi_2293
|
|
<image>Find the centre of the figure. Write your answer in the form ( _ , _ )
|
(-3,-3)
|
mathverse_vi_2298
|
|
<image>Find the radius of the figure.
|
3
|
mathverse_vi_2303
|
|
<image>Find the radius of the figure.
|
6
|
mathverse_vi_2308
|
|
<image>Find the centre of the figure. Write your answer in the form ( _ , _ ).
|
(-3,-3)
|
mathverse_vi_2313
|
|
<image>Find the radius of the figure.
|
3
|
mathverse_vi_2318
|
|
<image>Write the equation of the figure.
|
(x+3)^2+(y+3)^2=9
|
mathverse_vi_2323
|
|
<image>Describe the translation to get from x^2+y^2=4^2 to the graph shown.
Choices:
A:The graph has been translated 4 units downwards.
B:The graph has been translated 4 units right.
C:The graph has been translated 4 units left.
D:The graph has been translated 4 units upwards.
|
A
|
mathverse_vi_2328
|
|
<image>State the equation of the figure shown in the graph.
|
x^2+(y+4)^2=4^2
|
mathverse_vi_2333
|
|
<image>Find the centre of the figure.
|
(1,3)
|
mathverse_vi_2338
|
|
<image>State the centre of the figure.
|
(0,0)
|
mathverse_vi_2343
|
|
<image>State the radius of the figure.
Radius = _ units
|
7
|
mathverse_vi_2348
|
|
<image>Find the equation of this figure.
|
y=\sqrt{49-x^2}
|
mathverse_vi_2353
|
|
<image>State the centre of the figure.
|
(0,0)
|
mathverse_vi_2358
|
|
<image>A cake maker has rectangular boxes. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.
State the coordinates of the center of the cake in the form $(a, b)$.
|
Center $=(20,10)$
|
mathverse_vi_2363
|
|
<image>Write the set of numbers represented on the number line in interval notation.
|
(-2,1]
|
mathverse_vi_2368
|
|
<image>Write the set of numbers represented on the number line in interval notation.
|
(-\infty, 4]
|
mathverse_vi_2373
|
|
<image>Determine if this relation is a function.
Choices:
A:This is a function
B:This is not a function
|
B
|
mathverse_vi_2378
|
|
<image>Determine if this relation is a function.
Choices:
A:This is a function
B:This is not a function
|
A
|
mathverse_vi_2383
|
|
<image>Determine if this relation is a one-to-one function.
Choices:
A:This is a one-to-one function
B:This is not a one-to-one function
|
B
|
mathverse_vi_2388
|
|
<image>Determine if this relation is a one-to-one function.
Choices:
A:This is a one-to-one function
B:This is not a one-to-one function
|
A
|
mathverse_vi_2393
|
|
<image>Determine if this relation is a one-to-one function.
Choices:
A:This is a one-to-one function
B:This is not a one-to-one function
|
B
|
mathverse_vi_2398
|
|
<image>Find the domain and range of the function f using interval notation.
|
domain: [-4, 0) and range: (-3, 1]
|
mathverse_vi_2403
|
|
<image>Write the domain and range of the function using interval notation.
|
domain: (2,8] and range: [6,8)
|
mathverse_vi_2408
|
|
<image>Write the domain and range of the function using interval notation.
|
domain: [-4,4] and range: [0,2]
|
mathverse_vi_2413
|
|
<image>Write the domain and range of the function using interval notation.
|
domain: [-5,3) and range: [0,2]
|
mathverse_vi_2418
|
|
<image>Write the domain and range of the function using interval notation.
|
domain: (-\infty, 1] and range: [0, \infty)
|
mathverse_vi_2423
|
|
<image>Write the domain and range of the function using interval notation.
|
domain: [-6,-\frac{1}{6}] \cup[\frac{1}{6}, 6] and range: [-6,-\frac{1}{6}\right] \cup[\frac{1}{6}, 6]
|
mathverse_vi_2428
|
|
<image>Write the domain and range of the function using interval notation.
|
domain: [-3, \infty) and range: [0, \infty)
|
mathverse_vi_2433
|
|
<image>Estimate the intervals on which the function is increasing or decreasing.
|
The function is increasing on (-\infty,-2.5) \cup(1, \infty), and decreasing on (-2.5,1)
|
mathverse_vi_2438
|
|
<image>Estimate the intervals on which the function is increasing or decreasing.
|
\text { increasing on }(-\infty, 1) \cup(3,4) \text {, decreasing on }(1,3) \cup(4, \infty)
|
mathverse_vi_2443
|
|
<image>Estimate the point(s) at which the graph of f has a local maximum or a local minimum.
|
\text { local maximum: }(-3,60) \text {, local minimum: }(3, -60)
|
mathverse_vi_2448
|
|
<image>Estimate the point(s) at which the graph of f has a local maximum or a local minimum.
|
\text { Local minimum at }(-2,-2) \text {, decreasing on }(-3,-2) \text {, increasing on }(-2, \infty)
|
mathverse_vi_2453
|
|
<image>The point (1.333,5.185) is which of the following for function f?
Choices:
A.a relative (local) maximum of the function
B.the vertex of the function
C.the absolute maximum of the function
D.a zero of the function
|
A
|
mathverse_vi_2458
|
|
<image>Write an equation for the graphed function f.
|
When x<=3 $f(x)=-x+1$, when x>3, $f(x)=x-5$
|
mathverse_vi_2463
|
|
<image>Write an equation for the graphed function f.
|
When x<=-3 $f(x) = -x-5$, when x>3, $f(x)=x+1$
|
mathverse_vi_2468
|
|
<image>Write an equation for the graphed function f.
|
f(x)=-(x+1)^2+2
|
mathverse_vi_2473
|
|
<image>Determine whether the graph represents a one-to-one function.
Choices:
A.This is a one-to-one function
B.This is not a one-to-one function
|
B
|
mathverse_vi_2478
|
|
<image>Determine the function expression of f shown in the figure.
|
$-\frac{3}{2}x+3$
|
mathverse_vi_2483
|
|
<image>Determine if this relation is a function.
Choices:
A.This is a function
B.This is not a function
|
A
|
mathverse_vi_2488
|
|
<image>Determine if this relation is a function.
Choices:
A.This is a function
B.This is not a function
|
A
|
mathverse_vi_2493
|
|
<image>Determine the intervals on which the functions are increasing, decreasing, or constant.
|
Increasing at (2, \infty) and decreasing at (-\infty, 2)
|
mathverse_vi_2498
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.