Question 1

Only one of these triangles is right-angled. Which one?

Accepted Answer

#12ef649b-2873-4cf4-b055-f6da27921501/26_01_D.png

Answer

#12ef649b-2873-4cf4-b055-f6da27921501/26_01_B.png

Answer

#12ef649b-2873-4cf4-b055-f6da27921501/26_01_A.png

Answer

#12ef649b-2873-4cf4-b055-f6da27921501/26_01_C.png

Question 2

Point $A$ has coordinates $	ext{(–1, 3). }$ Point $B$ has coordinates $	ext{(2, 8). }$
Work out the length of the line segment $AB$ to $3$ significant figures.

Accepted Answer

$5.83$

Answer

$7.36$

Answer

$10.4$

Answer

$4.01$

Question 3

The diagram shows the dimensions of a prize-winning biscuit in a baking competition.
The biscuit is in the shape of an isosceles triangle.
Work out the height of the biscuit to $1$ decimal place.

Accepted Answer

$h	ext{=19.4 cm }$

Answer

$h	ext{=11.5 cm }$

Answer

$h	ext{=25.7 cm }$

Answer

$h	ext{=15.9 cm }$

Question 4

The diagram shows three identical steps.
Work out the height $h$ of each step to $1$ decimal place.

Accepted Answer

$	ext {h = 22.4 cm}$

Answer

$	ext {h = 9.3 cm}$

Answer

$	ext {h = 15.9 cm}$

Answer

$	ext {h = 27.3 cm}$

Question 5

Work out the length of the side labelled $x$ in this triangle, to $1$ decimal place.

Accepted Answer

$13.1 	ext { cm}$

Answer

$9.2 	ext { cm}$

Answer

$19.5 	ext { cm}$

Answer

$11.2 	ext { cm}$

Question 6

Work out the height of this trapezium to $3$ significant figures.

Accepted Answer

$	ext {19.1 cm}$

Answer

$	ext {15.2 cm}$

Answer

$	ext {10.9 cm}$

Answer

$	ext {24.5 cm}$

Question 7

From where Taylor is lying on the ground, the angle of elevation of a helicopter is $26 \degree$.
The helicopter is flying at a vertical height of $	ext {1000 m}$ above the ground.
How far is the helicopter from Taylor? Give your answer to $2$ significant figures.

Accepted Answer

$	ext {2300 m}$

Answer

$	ext {1850 m}$

Answer

$	ext {3210  m}$

Answer

$	ext {2825 m}$

Question 8

Work out the length of side $b$ in the diagram below. Give your answer to 1 decimal place.

Accepted Answer

$	ext {8.3 cm}$

Answer

$	ext {19.8 cm}$

Answer

$	ext {14.9 cm}$

Answer

$	ext {25.1 cm}$

Question 9

Work out the size of the angle $x$ in the triangle, to 1 decimal place.

Accepted Answer

$34.8 \degree$

Answer

$42.3 \degree$

Answer

$59.6 \degree$

Answer

$54.0 \degree$

Question 10

Work out the size of the angle $x$ in the triangle, to 1 decimal place.

Accepted Answer

$42.3 \degree$

Answer

$59.6 \degree$

Answer

$105.3 \degree$

Answer

$73.9 \degree$

Question 11

Work out the size of the angle $x$ in the triangle, to 1 decimal place.

Accepted Answer

$49.5 \degree$

Answer

$54.0 \degree$

Answer

$52.4 \degree$

Answer

$42.3 \degree$

Question 12

Triangle $PQR$ is an isosceles triangle. Work out angle $PQR$ to 1 decimal place.

Accepted Answer

$41.4 \degree$

Answer

$95.4 \degree$

Answer

$26.1 \degree$

Answer

$69.9 \degree$

Question 13

$ABC$ is a triangle. $AC = 7$ cm, $BC = 16$ cm and angle $BAC = 90 \degree$. Work out angle $BCA$.

Accepted Answer

$64.1 \degree$

Answer

$21.2 \degree$

Answer

$47.1 \degree$

Answer

$87.5 \degree$

Question 14

A hang glider is flying at an altitude of $1.2	ext{ km}$ when it starts its descent towards the ground.
Work out the angle of depression if the hang glider is $3	ext{ km}$ from its landing zone, to 3 significant figures.

Accepted Answer

$23.6 \degree$

Answer

$79.2 \degree$

Answer

$49.9 \degree$

Answer

$105.3 \degree$

Question 15

Point $B$ is $8	ext{ km}$ due north of point $A$. Point $C$ is $	ext {11 km}$ due east of point $A$. Work out the bearing of $B$ from $C$ to the nearest degree.

Accepted Answer

$306 \degree$

Answer

$390 \degree$

Answer

$240 \degree$

Answer

$365 \degree$

Question 16

A buoy is $ 30 	ext{ metres}$ away from a look-out post on a bearing of $045 \degree$.
A swimmer is $	ext {40 metres}$ from the same look-out post on a bearing of $315 \degree$.
Work out the distance of the swimmer from the buoy.

Accepted Answer

$	ext {50 m}$

Answer

$	ext {28 m}$

Answer

$	ext {80 m}$

Answer

$	ext {73 m}$

Question 17

Work out the length of the side labelled $x$ in this triangle.

Accepted Answer

$	ext {2 cm}$

Answer

$	ext {4 cm}$

Answer

$	ext {1 cm}$

Answer

$	ext {3 cm}$

Question 18

Work out the length of the side labelled $x$ in this triangle.

Accepted Answer

1cm

Answer

4cm

Answer

3cm

Answer

2cm

Question 19

Work out the length of the side labelled $x$ in this triangle.

Accepted Answer

12 cm

Answer

9 cm

Answer

6 cm

Answer

15 cm

Question 20

Work out the exact value of $x$ in the triangle shown. Rationalise the denominator if applicable.

Accepted Answer

$45 \degree$

Answer

$60 \degree$

Answer

$75 \degree$

Answer

$25 \degree$

Question 21

Work out the exact value of $x$ in the triangle shown. Rationalise the denominator if applicable.

Accepted Answer

$\frac{ 2  \sqrt{2} - \sqrt{6} }{ 2 }	ext{ cm}$

Answer

$\frac{ 5  \sqrt{7} }{ 3 }	ext{ cm}$

Answer

$\frac{3+ 2  \sqrt{5} }{ 6 }	ext{ cm}$

Answer

$3- 6  \sqrt{5}	ext{ cm}$

Question 22

The longest diagonal of the cuboid shown is $	ext{13 cm}.$
The length of the cuboid is $	ext{12 cm}$ and its width is $	ext{3 cm}.$
Work out the height, $h$, of the cuboid.

Accepted Answer

$	ext{4 cm}$

Answer

$	ext{12 cm}$

Answer

$	ext{7 cm}$

Answer

$	ext{19 cm}$

Question 23

The 3D shape below is made using $	ext{1 cm}$ cubes.
Vertices $P$ and $Q$ are labelled.
Work out the length of the line $PQ$.

Accepted Answer

$	ext{3 cm}$

Answer

$\sqrt{2}	ext{ cm}$

Answer

$\sqrt{5}	ext{ cm}$

Answer

$2\sqrt{2}	ext{ cm}$

Question 24

$ABCDE$ is a square-based pyramid with vertex $E$ directly above the centre of the base of the pyramid.
The square base has side length $\sqrt{2}	ext{ cm}$ and $AE$ is $\sqrt{3}	ext{ cm}.$
Work out the height of the pyramid.

Accepted Answer

$\sqrt{2}	ext{ cm}$

Answer

$5\sqrt{3}	ext{ cm}$

Answer

$\frac{ 3+  \sqrt{2} }{ 4 }$

Answer

$	ext{5 cm}$

Question 25

A cylindrical container is three-quarters full of water. The diameter of the container is $	ext{11 cm}.$
A solid triangular prism is added to the container and is completely submerged, with the water level rising to the very top of the container without overflowing.
The cross-section of the prism is an equilateral triangle of side length $	ext{4 cm}.$ The diagonal of each rectangular side of the prism is $	ext{14 cm}.$
Work out the height of the container to $3$ significant figures.

Accepted Answer

$	ext{3.91 cm}$

Answer

$	ext{7.08 cm}$

Answer

$	ext{9.27 cm}$

Answer

$	ext{4.83 cm}$

Question 26

$VWXY$ is a tetrahedron with faces that are all identical equilateral triangles of side length $	ext{3 m}$.
The vertex $Y$ is directly above the centre of the base of the tetrahedron.
Work out the angle between the side $XY$  and the base of the tetrahedron to the nearest degree.

Accepted Answer

$55 \degree$

Answer

$81 \degree$

Answer

$68 \degree$

Answer

$31 \degree$

Question 27

Graham is standing near his office block and measures the angle of elevation to the top of the building to be $72 \degree$.
He moves $45	ext{ m}$ further away from the block and measures the angle of elevation to be $36 \degree$.
How tall is his office block, to 3 significant figures?

Accepted Answer

$	ext {42.8 m}$

Answer

$	ext {71.9 m}$

Answer

$	ext {98.7 m}$

Answer

$	ext {56.3 m}$

Question 28

The hypotenuse of a right-angled triangle is $\frac{2 \sqrt 5}{3} 	ext{ cm}$ and its height is $\frac{ \sqrt 15}{3} 	ext{ cm}$.
Work out the angle of elevation.

Accepted Answer

$60 \degree$

Answer

$36 \degree$

Answer

$49 \degree$

Answer

$100 \degree$

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