Question 1

Jeremiah is training as an architect and has drawn his house's floor plan to scale. The width of his living room is 5 metres in real life, and Jeremiah drew the floor plan to a 1 m = 3 cm scale. What is the width of the living room on the floor plan?

Accepted Answer

15 cm

Answer

5 cm

Answer

45 cm

Answer

$\frac{5}{3}$ m

Question 2

In Mary's map, the river next to his house is 25mm wide. In real life it is 300 metres wide. Which scale is the map using?

Accepted Answer

1 mm = 12 m

Answer

1 mm = 25 m

Answer

12 mm = 1m

Answer

25 mm = 1 m

Question 3

A shape $A$ is enlarged to a shape $B$. $A$ and $B$ are...

Accepted Answer

Similar

Answer

Congruent

Question 4

Triangle A is reflected to triangle B. About which line is it reflected?

Accepted Answer

y=0

Answer

x=0

Answer

x=3

Answer

y=x

Question 5

What's the name of a line that intersects a circle at only one point?

Accepted Answer

Tangent

Answer

Secant

Answer

Radius

Answer

Diameter

Question 6

What is highlighted in red in the figure below?

Accepted Answer

Diameter

Answer

Tangent

Answer

Radius

Answer

Arc

Question 7

Which of the following is true?

Accepted Answer

Tangents to a circle from the same point are equal

Answer

The angle between the tangent and radius is 180°

Answer

Tangents are always the same length

Answer

A tangent is a line which intersects a circle twice

Question 8

A cyclic quadrilateral is a figure in which all four vertices lie on the circumference of a circle. What is the sum of opposite angles of all cyclic quadrilaterals?

Accepted Answer

180°

Answer

90°

Answer

360°

Answer

120°

Question 9

Which solid would you generate if you were to revolve a right-angled triangle about one of its perpendicular sides?

Accepted Answer

Cone

Answer

Cylinder

Answer

Cube

Answer

Triangular Pyramid

Question 10

You have to construct a 3D figure made with a round base. Which of these could you make?

Accepted Answer

Cylinder

Answer

Triangular Pyramid

Answer

Cube

Answer

Triangular Prism

Question 11

A circle has a radius of $\frac{4}{\sqrt{\pi}}$. What is the area of a sector bounded by a 45 degree arc?

Accepted Answer

2

Answer

$\pi$

Answer

8

Answer

4

Question 12

A circle has a radius of length $\frac{3}{\pi}$. What is the length of on arc which spans 120°?

Accepted Answer

2

Answer

$\pi$

Answer

1

Answer

6

Question 13

What is the surface area of a cube of height 2?

Accepted Answer

24

Answer

8

Answer

4

Answer

128

Question 14

Which of the following formulas would you use to calculate the volume of a cone? (h= height, r= radius, l= length)

Accepted Answer

$\frac{1}{3}\pi r^2 h$

Answer

$\frac{4}{3}\pi r^3$

Answer

$l\pi r^2$

Answer

$h^3$

Question 15

There are two similar cylinders. Cylinder $A$ has a radius of $\frac{2}{\sqrt{\pi}}$ and a height of 4. Cylinder $B$ has a height of 2. What's the volume of cylinder $B$?

Accepted Answer

2

Answer

4

Answer

16

Answer

8

Question 16

Two triangular pyramids have the same area, but different height. Are the two pyramids congruent?

Accepted Answer

No

Answer

Yes

Question 17

A triangle has 3 sides with lengths 4, 5 and 6. Is it a right angle triangle?

Accepted Answer

No

Answer

Yes

Question 18

A right angle triangle has a base of length 4, a height of length 3 and a hypotenuse of length 5. What is the $sin$ of the angle opposite the base?

Accepted Answer

$sin(\frac{4}{5})$

Answer

$sin(\frac{5}{4})$

Answer

$sin(\frac{3}{4})$

Answer

$sin(\frac{5}{3})$

Question 19

Without using a calculator, select the value of the sine of an angle of 30°.

Accepted Answer

$\frac{1}{2}$

Answer

$\frac{\sqrt{2}}{2}$

Answer

0

Answer

1

Question 20

Without using a calculator, select the value of the tangent of an angle of 45°.

Accepted Answer

1

Answer

0

Answer

$\sqrt{3}$

Answer

not defined

Question 21

A triangle has a side $a$ and a side $b$ . The angle $A$, opposite of $a$, is 30°. Find the angle $B$, which is opposite of $b$.

Accepted Answer

$B=sin^{-1}(\frac{b}{2a})$

Answer

$B=sin(\frac{a}{2b})$

Answer

$B=sin^{-1}(\frac{a}{2b})$

Answer

$B=sin(\frac{b}{a})$

Question 22

A triangle has three vertices, $A$,$B$ and $C$. The angle at vertex $A$ is 60°. The lengths of $\overline{AB}$ and $\overline{AC}$ are known. What is the length of $\overline{BC}$.

Accepted Answer

$\overline{BC}=\sqrt{\overline{AB}^2 +\overline{AC}^2 - \overline{AB}\overline{AC}}$

Answer

$\overline{BC}=\sqrt{\overline{AB}^2 +\overline{AC}^2 + \overline{AB}\overline{AC}}$

Answer

Impossible, need more information

Answer

$\overlin{BC}=sin^{-1}(\frac{b}{2a})$

Question 23

What is the area of a triangle which has a side $a$ of length 4, a side $b$ of length 7 and the angle $C$ adjacent to $a$ and $b$ is 45°.

Accepted Answer

$area=\frac{1}{2}	imes 4 	imes 7 	imes sin(45°)$

Answer

$area=sin^{-1}(\frac{7}{4})$

Answer

Impossible, need more information

Answer

$area=\sqrt{4^2 +7^2 -2	imes cos(45°) 4	imes 7}$

Question 24

A triangle has an area of 15, a side $a$ of length 7 and the angle $C$ adjacent to sides $a$ and $b$ is 30°. What is the length of $b$.

Accepted Answer

$b=\frac{30}{7	imes sin(30°)}$

Answer

$b=sin^-1(\frac{15}{7})$

Answer

$b=\frac{7	imes sin(30°)}{30}$

Answer

Impossible, need more information

Question 25

A point $X(2,3)$ is translated to point $X'(3,-6)$. Select the correct displacement vector.

Accepted Answer

$\binom{1}{-9}$

Answer

$\binom{1}{9}$

Answer

$\binom{5}{3}$

Answer

$\binom{5}{-3}$

Question 26

A shape is translated by 4 units to the right and 3 units downwards. What's the displacement vector of this translation?

Accepted Answer

$\binom{4}{-3}$

Answer

$\binom{4}{3}$

Answer

$\binom{-4}{3}$

Answer

$\binom{-4}{-3}$

Question 27

Calculate the following vector sum. $$\binom{1}{5}+\binom{-3}{1}$$

Accepted Answer

$\binom{-2}{6}$

Answer

$\binom{4}{4}$

Answer

$\binom{2}{-6}$

Answer

$\binom{-4}{-4}$

Question 28

Carry out the following vector multiplication. $$6\binom{-2}{3}$$

Accepted Answer

$\binom{-12}{18}$

Answer

$\binom{12}{18}$

Answer

$\binom{4}{9}$

Answer

$\binom{-4}{9}$

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