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Area of the figure is a $=\frac{3}{4}$ of area of the circle. Calculate the area of the following figure.
Give your answer as an exact value. | Area $=\frac{147 \pi}{4} \mathrm{~cm}^{2}$ | |
The diameter of the figure is $ 52.72 \mathrm{~cm}$. The figure follows that half of a circle has area $\frac{1}{2} \pi r^{2}$. Find the exact area of the shape shown. | Area $=347.4248 \pi \mathrm{cm}^{2}$ | |
The radius of the figure is $ 13 \mathrm{~mm}$. It follows that a two thirds of a circle has area $\frac{2}{3} \pi r^{2}$. Find the exact area of the shape shown, which is two thirds of a circle. | Area $=\frac{338 \pi}{3} \mathrm{~mm}^{2}$ | |
The radius of the figure is $ 96.4 \mathrm{~mm}$. Consider the sector below.
Calculate the area. Give your answer correct to four decimal places. | 7298.6737 \mathrm{~mm}^{2} | |
The radius of the figure is $ 59.6 \mathrm{~cm}$. Consider the sector below.
Calculate the area. Give your answer correct to two decimal places. | Area $=1115.94 \mathrm{~cm}^{2}$ | |
The radius of the figure is $ 56.5 \mathrm{~m}$. Consider the sector below.
Calculate the area. Give your answer correct to two decimal places. | Area $=3426.49 \mathrm{~m}^{2}$ | |
The radius of the figure is $ 8 \mathrm{~cm}$. Perimeter=lengths of the two equal segments + the length of the arc.Calculate the total perimeter of the sector shown, correct to one decimal place. | Perimeter $=18.8 \mathrm{~cm}$ | |
The radius of the figure is $ 7 \mathrm{~cm}$. Find the perimeter of the sector shown, correct to two decimal places. | Perimeter $=18.89 \mathrm{~cm}$ | |
The radius of the figure is $ 8 \mathrm{~cm}$. Find the perimeter of the figure shown, correct to two decimal places. | Perimeter $=60.68 \mathrm{~cm}$ | |
The radius of the figure is $ 80.2 \mathrm{~mm}$. Consider the sector below.
Calculate the perimeter. Round your answer to two decimal places. | Perimeter $=492.14 \mathrm{~mm}$ | |
The radius of the figure is $ 32.2 \mathrm{~m}$. The marked angle measures 344°. Consider the sector below. The marked angle measures 344°.
Calculate the perimeter of the sector. Round your answer to two decimal places. | Perimeter $=257.73 \mathrm{~m}$ | |
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 $=70.69 \mathrm{~mm}^{2}$ | |
The area $A$ of the sector below is 140.28 (cm)^2. We wish to find the length of the radius, then the perimeter.
Find the length of the radius, $r$. (You may let \theta represent the angle of the sector). Give your answer correct to one decimal place. | $r=24.4$ | |
The radius of the figure is $5\mathrm{~cm}$. Find the area of the sector shown.
Round your answer to two decimal places. | Area $=73.52\mathrm{~cm}^{2}$ | |
The radius of the figure is $22.1\mathrm{~m}$. Calculate the area of the following sector.
Round your answer to one decimal place. | Area $=315.4 \mathrm{~m}^{2}$ | |
In the diagram, $O$ is the center of a circle with radius 6 cm. Arc $JK$ has a length measuring 2\pi cm. Determine the exact area of sector $OJK$. | Area of sector $=6 \pi \mathrm{cm}^{2}$ | |
The perimeter is the total length of all sides of a figure.Find the perimeter of the parallelogram shown. | Perimeter $=94 \mathrm{~cm}$ | |
The perimeter is the total length of all sides of a figure.Find the perimeter of the kite shown. | Perimeter $=74 \mathrm{~mm}$ | |
The perimeter is the total length of all sides of a figure.Find the perimeter of the rhombus shown. | Perimeter $=28 \mathrm{~mm}$ | |
The perimeter is equal to the sum of the four side lengths of the trapezium. Find the length of the missing side of the trapezium shown. | $5=s$ | |
The total area is 6096. How much area is remaining? | 96 | |
The total area is 6096. How much area is remaining? | 36 | |
After two meteoroids collide at point A, one starts travelling in the direction of point B, while the other starts travelling in the direction of point C, with an angle of 53^\circ between the two directions. The meteoroid projected in the direction of B is moving at a speed of 7860 km/h, while the other is moving at ... | 3799 km | |
As shown in the figure above, a triangle has an angle of 50° and two sides of 12m and 13.1m. Calculate the area of the following triangle.
Round your answer to two decimal places. | 60.21 \mathrm{m}^2 | |
An industrial site in the shape of a triangle is to take up the space between where three roads intersect. The triangle has an angle of 44° and two sides of 50m and 80m.
Calculate the area of the site.
Round your answer to two decimal places. | 1389.32 \mathrm{m}^2 | |
On an orienteering course, Valentina runs 550 metres north from point A to point B, then turns east and runs to point C. If the true bearing of C from A is 041 ^\circ T and the direct distance Valentina must run to get back to point A is d metres, find d to the nearest metre. | 729 | |
A boat travels S 14^\circ E for 12 km and then changes direction to S 49^\circ E for another 16 km.
Hence write down the bearing that the boat should travel on to return to the starting point. | N 34° W | |
The logo of a shop consists of five semicircles; four small semicircles each with the same radius, and one large semicircle. 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... | \frac{1225\pi }{2} \text { units }^2 | |
A driver glances up at the top of a building.
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 | |
Sally needs to walk from the school to the bus stop.
True or False : The quickest way to get there will be through the playground.
Choice:
A. False
B. True | False | |
Iain’s car has run out of petrol. He walks 12 km west and then 9 km south looking for a petrol station.
If he is now $h$ km directly from his starting point, find the value of $h$. | $h=15$ | |
Find the distance between the two endpoints using the distance formula. The two end points of the line are (-3, 4) and (5, 2), respectively. Round to three decimal places.
| 8.246 | |
There is a blue rectangular with four vertexes (-6,5), (-6,-1), (10,5), (10,-1). The two diagonals are red and intersect with each other at (2,2). Find the coordinates of the midpoint for each diagonal.
| (2,-2) | |
Given the graph of the ellipse that intersects with x-axis at 9 and -9 and with y-axis at 3 and -3, determine its equation.
| \frac{x^2}{81}+\frac{y^2}{9}=1 | |
Given the graph of the ellipse that intersects with x-axis at -0.5 and -3.5 and with y-axis at 2, determine its equation.
| \frac{(x+2)^2}{4}+\frac{(y-2)^2}{9}=1 | |
There is a hyperbola in blue with double arrows intersects with y-axis at -4 and 4. Its asymptote in dashed orange is $y=(4/5)x$ and $y=-(4/5)x$. There is also a green rectangular tangent to the hyperbola. Find the equation of the hyperbola.
| \frac{y^2}{16}-\frac{x^2}{25}=1 | |
There is a hyperbola in blue with two vertices highlighted at (-1,3) and (-1,-3). It's center is at (-1,0) highlighted by orange and its Foci is also hightlighted in lightgreen at (-1,$3\sqrt{2}$) and (-1, -$3\sqrt{2}$). Find the equation of the hyperbola.
| \frac{y^2}{9}-\frac{(x+1)^2}{9}=1 | |
There is a hyperbola in blue with two vertices highlighted at (2,-3) and (-8,-3). It's center is at (-3,-3) highlighted by orange and its Foci is also hightlighted in lightgreen at ($-3-5\sqrt{2}$,-3) and ($-3+5\sqrt{2}$,-3). Find the equation of the hyperbola.
| \frac{(x+3)^2}{25}-\frac{(y+3)^2}{25}=1 | |
Point $A$ is on the following unit circle with radius 1, and forms a red right triangle with an angle of $\frac{\pi}{4}$. What are the coordinates of point $A$ ?
Enter an exact value or round to the nearest hundredth.
| $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$ | |
On the following unit circle, an angle $\theta$ is formed by a radius and x-axis. 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 | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(\frac{3}{5}, \frac{4}{5}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\sin a$.
| $\frac{4}{5}$ | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(\frac{3}{5}, \frac{4}{5}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\tan a$.
| $\frac{4}{3}$ | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\cos a$.
| $-\frac{21}{29}$ | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\tan a$.
| $-\frac{20}{21}$ | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\sin a$.
| $\frac{20}{29}$ | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(-\frac{21}{29}, \frac{20}{29}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\cos a$.
| $-\frac{21}{29}$ | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(\frac{20}{29},-\frac{21}{29}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\cos a$.
| $\frac{20}{29}$ | |
The graph shows an angle $a$ in standard position with its terminal side intersecting the circle at $P\left(\frac{20}{29},-\frac{21}{29}\right)$. The center of the circle is the origin and the radius of the circle is 1.
Find the value of $\tan a$.
| $-\frac{21}{20}$ | |
A circle the center of the circle is the origin and the radius of the circle is 1. The point $P$ on the unit circle has the coordinates $(x, y)$. What is the value of $\sec \theta$ ?
Choices:
A:$\frac{1}{x}$
B:$x$
C:$y$
D:$\frac{1}{y}$ | A | |
The line passes (0,5) and (2.5,0). Find the equation of the line.
Use exact numbers.
y = _ x + _
| y=-2 x+5 | |
The line passes (-2,-6) and (2,-3). Write an equation that represents the line.
Use exact numbers.
| $y+3=\frac{3}{4}(x-2)$ | |
The line passes (2,-1), (5,1), (8,3), (11,5). Find the equation of the line in point-slope form .
| $y-3=\frac{2}{3}(x-8)$ | |
Consider the circle, which has 4 intersection points with axes, in the graph.
State the coordinates of the centre in the form $(a, b)$.
| (0,0) | |
Consider the circle, which has 4 intersection points with axes, in the graph.
State the radius.
| 2 | |
Consider the circle, which has 4 intersection points with axes, in the graph.
State the diameter.
| 8 | |
Consider the circle on the graph. Its center at the origin and its radius is 7. State the equation of the circle.
| $x^{2}+y^{2}=49$ | |
Consider the circle on the graph. Its center is at (1,3) and its radius is 6.
Find the equation of the circle in standard form.
| $(x-1)^{2}+(y-3)^{2}=36$ | |
The terminal side of an angle, $\theta$ passes through the point $(-4,-6)$. Use the diagram to answer the following question.
Find the value of $\cos \theta$. Rationalise the denominator if necessary.
| $\frac{-2 \sqrt{13}}{13}$ | |
Consider the graph of the circle, which has 4 intersection points with axes, shown below.
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). | |
Consider the circle, which has 2 intersection points with axes, on the graph.
Find the centre of the circle. Write your answer in the form ( _ , _ )
| (-3,-3) | |
Consider the circle, which has 2 intersection points with axes, on the graph.
Find the radius of the circle.
| 3 | |
Consider the circle, which has 4 intersection points with axes, on the graph.
Find the radius of the circle.
| 6 | |
Consider the circle, which has 2 intersection points with axes, on the graph.
Find the centre of the circle. Write your answer in the form ( _ , _ ).
| (-3,-3) | |
Consider the circle, which has 4 intersection points with axes, on the graph.
Find the radius of the circle.
| 3 | |
Consider the circle, which has 4 intersection points with axes, on the graph.
Write the equation of the circle in the form \left(x-h\right)^2+\left(y-k\right)^2=r^2.
| (x+3)^2+(y+3)^2=9 | |
Consider the graph of the circle, which has 2 intersection points with axes, below.
Describe the translation to get from x^2+y^2=4^2 to the circle 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... | A | |
Consider the graph of the circle, which has 2 intersection points with axes, below.
State the equation of the circle shown in the graph.
| x^2+(y+4)^2=4^2 | |
Consider the circle, which has 4 intersection points with axes, on the graph.
Find the centre of the circle.
| (1,3) | |
The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).
State the centre of the semicircle.
| (0,0) | |
The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).
State the radius of the semicircle.
Radius = _ units
| 7 | |
The following graph shows a semicircle which passes (-7,0), (-5,5), (0,7), (5,5), (7,0).
Find the equation of this semicircle.
| y=\sqrt{49-x^2} | |
The following graph shows a semicircle which passes (-7,0), (-5,-5), (0,7), (5,-5), (7,0).
State the centre of the semicircle.
| (0,0) | |
A rectangle contains an ellipse. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). The center of the ellipse is (20,10), and its four vertices are (0,10), (20,10), (20,20), (40,10). A cake maker has rectangular boxes measuring $40 \mathrm{~cm}$ in length and 20 $\mathrm{cm}$ in width. She often rec... | Center $=(20,10)$ | |
There are two points at -2 and 1 on the number line. Write the set of numbers represented on the number line in interval notation.
| (-2,1] | |
There is a point at 4 and a blue arrow goes to left from that point. Write the set of numbers represented on the number line in interval notation.
| (-\infty, 4] | |
Two curves are symmetrical about the x-axis. Use the vertical line test to determine if this relation is a function.
Choices:
A:This is a function
B:This is not a function | B | |
There is a curve goes through the origin. Use the vertical line test to determine if this relation is a function.
Choices:
A:This is a function
B:This is not a function | A | |
There is an ellipse, for which the domain is from -3 to -1 and the range is from -1 to 3. 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 | |
There is a curve that goes through (-3,0), (-2,1), and (-1,2). 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 | |
There are 4 labels on the x-axis $-\pi$, $-\frac{2}{\pi}$, $\frac{2}{\pi}$, $\pi$ and a curve that goes through ($\frac{2}{\pi}$,0). 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 | |
Find the domain and range of the function f using interval notation, which goes through (-2,-4), (-1,-2), (0,0), (1,-4), with a hollow point (-3,0).
| domain: [-4, 0) and range: (-3, 1] | |
There is a line goes through a hollow point (2,8) and a solid point (8,6). Write the domain and range of each function using interval notation.
| domain: (2,8] and range: [6,8) | |
There is a curve goes through (-4,0), (0,2), and (4,0). The points at (-4,0) and (4,0) are both solid points. Write the domain and range of the function using interval notation.
| domain: [-4,4] and range: [0,2] | |
There is a curve goes through (-5,2), (-1,0), and (3,2). The point at (-5,2) and (3,2) are respectively solid and hollow. Write the domain and range of the function using interval notation.
| domain: [-5,3) and range: [0,2] | |
There is a curve start from a solid point (1,0) with an end arrow going through (-4,4). Write the domain and range of the function using interval notation.
| domain: (-\infty, 1] and range: [0, \infty) | |
There is a hyperbolic function with its center at the origin. The graph approaches zero as $∣x∣$ increases, and the function is undefined at x=0. There are four points labeled at (1/6,6), (6,1/6), (-1/6,-6), (-6,-1/6). 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] | |
There is a piecewise function going through points (-3, 0), (0, 5), and (3, 5). Write the domain and range of the function using interval notation.
| domain: [-3, \infty) and range: [0, \infty) | |
There is a curve goes through (-4,1), (-1,3), and (0,0). 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) | |
There are two curves with a vertical asymptote x=3. One curve passes (1,0), and another curve passes (4,0). 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) | |
There is an odd function f going through (0,0). 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) | |
There is an odd function f going through (0,0). 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) | |
The graph of a cubic function f is shown in Figure 18 with a labeled point (1.333, 5.185) at its right part. Based on the calculator screen shot, the point (1.333,5.185) is which of the following?
Choices:
A.a relative (local) maximum of the function
B.the vertex of the function
C.the absolute maximum of the functi... | A | |
There is a piecewise function combind by straight lines going through (3, -2), (1, 0), and (0,1). Write an equation for the graphed function f.
| When x<=3 $f(x)=-x+1$, when x>3, $f(x)=x-5$ | |
There is a piecewise function combind by straight lines, which goes through (-3, -2), (0, 1), and (-1, 0). Write an equation for the graphed function f.
| When x<=-3 $f(x) = -x-5$, when x>3, $f(x)=x+1$ | |
There is a quadratic function going through (-2,1), (-1,2), (0,1). Write an equation for the graphed function f.
| f(x)=-(x+1)^2+2 | |
There is a quadratic function, which goes through (0,0), (20,0) and opens upward. 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 | |
There is a linear function with a y-intercept of 3 and a x-intercept of 2. Determine the function expression of f shown in the figure.
| $-\frac{3}{2}x+3$ | |
There is a curve goes through (-2,0), (0,0), (2,0). Use the vertical line test to determine if this relation is a function.
Choices:
A.This is a function
B.This is not a function | A | |
There are two curves symmetric to the orign and lie in the second and fourth quadrant. Use the vertical line test to determine if this relation is a function.
Choices:
A.This is a function
B.This is not a function | A | |
There is a quadratic function that opens upwards symmetric with respect to x=2. The vertex of the parabola is at the point (2,-2). Determine the intervals on which the functions are increasing, decreasing, or constant.
| Increasing at (2, \infty) and decreasing at (-\infty, 2) |
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