1.
A triangle has sides 5 cm, 12 cm and 13 cm. Show that it is right-angled.
[3 marks]
- Pythagoras converse
- Final answer: 5²+12²=13² = 169
JD SCIENCE
Geometry and measures
Indicative marking points. Award marks for equivalent scientific or mathematical wording. Do not issue this sheet with the student worksheet.
2.
Find the length of the hypotenuse of a right-angled triangle with legs 12 cm and 8 cm.
[3 marks]
- √(l² + w²)
- Final answer: 14.42 cm
3.
A circle has radius 9 cm. Find the circumference. Use π = 3.14.
[2 marks]
- C = 2πr
- Final answer: 56.52 cm
4.
The same circle has radius 9 cm. Find the area. Use π = 3.14.
[2 marks]
- A = πr²
- Final answer: 254.34 cm²
5.
A rectangle is 12 cm by 8 cm. Find the area and the perimeter.
[2 marks]
- Final answer: Area 96 cm², perimeter 40 cm
6.
Find the volume of a cuboid 12 cm × 8 cm × 4 cm.
[2 marks]
- lwh
- Final answer: 384 cm³
7.
A cylinder has radius 3 cm and height 12 cm. Find the volume. Leave π in your answer.
[3 marks]
- πr²h
- Final answer: 108π cm³
8.
The area of a trapezium is ½(a + b)h. a = 10, b = 14, h = 5. Find the area.
[2 marks]
- Final answer: 60 cm²
9.
Describe the transformation that maps triangle A onto triangle B if B is a reflection of A in the line x = 2.
[2 marks]
- Reflection in the line x = 2
10.
A shape is enlarged by scale factor 3 from the origin. What happens to lengths and to area?
[3 marks]
- Lengths × 3
- Area × 9
11.
A map scale is 1 : 200. A path is 8 cm on the map. Find the real length in metres.
[2 marks]
- 8 × 200 = 1600 cm = 16 m
- Final answer: 16 m
12.
Find the interior angle of a regular hexagon.
[2 marks]
- (6−2)×180 / 6
- Final answer: 120°
13.
The exterior angle of a regular polygon is 30°. How many sides does it have?
[2 marks]
- 360 ÷ 30
- Final answer: 12
14.
Work out the missing angle in a triangle with angles 47° and 66°.
[1 mark]
- Angles in a triangle sum to 180°
- Final answer: 67°
15.
Corresponding angles on parallel lines: one is 76°. Write the corresponding angle and an allied/co-interior angle.
[2 marks]
- Final answer: Corresponding 76°,Co-interior 104°
16.
A sector has radius 9 cm and angle 90°. Find the arc length. Leave π in your answer.
[3 marks]
- Fraction of the circumference
- Final answer: 0.5πr = 4.5π cm
17.
Find the area of the same 90° sector. Leave π in your answer.
[2 marks]
- Quarter of πr²
- Final answer: 20.25π cm²
18.
SOHCAHTOA: in a right triangle, opposite = 5, hypotenuse = 13. Find sin θ.
[2 marks]
- Final answer: 5/13
19.
A right-angled triangle has an angle of 30° and the opposite side is 8 cm. Find the hypotenuse.
[2 marks]
- sin 30° = 1/2 = opposite/hypotenuse
- Final answer: 16 cm
20.
A ladder of length 5 m leans against a wall. The foot is 1.4 m from the wall. How high up the wall does it reach?
[3 marks]
- Pythagoras
- Final answer: 4.80 m
21.
Write the circle theorems: angle in a semicircle, and angle at the centre.
[3 marks]
- Angle in a semicircle is 90°
- Angle at the centre is twice the angle at the circumference
22.
Find the surface area of a cube of side 7 cm.
[2 marks]
- 6a²
- Final answer: 294 cm²
23.
A triangular prism has triangle 3-4-5 and length 12 cm. Find the volume.
[3 marks]
- Area of triangle × length
- Final answer: 72 cm³
24.
Describe a rotation of 90° clockwise about (0, 0) applied to the point (2, 1).
[2 marks]
- Image (−1, 2)
25.
The bearing of B from A is 060°. Work out the bearing of A from B.
[2 marks]
- Add 180°
- Final answer: 240°
26.
Find the midpoint of (2, 5) and (8, 13).
[2 marks]
- Average the coordinates
- Final answer: (5, 9)
27.
Find the distance between (0, 0) and (6, 8).
[2 marks]
- 3-4-5 scaled by 2
- Final answer: 10
28.
Explain why SSA is not a congruence condition for triangles.
[2 marks]
- Two triangles can have two sides and a non-included angle equal and not be congruent / ambiguous case
29.
A cone has radius 3 cm and slant height 5 cm. Find the curved surface area. Leave π in your answer.
[2 marks]
- πrl
- Final answer: 15π cm²
30.
Triangle ABC is similar to triangle DEF. AB = 6 cm, DE = 9 cm, BC = 10 cm.
(a) [1 mark]
- 1.5
(b) [2 marks]
- 15 cm
31.
Write the exact values of sin 30°, cos 60° and tan 45°.
[3 marks]
- 1/2
- 1/2
- 1
32.
A OCR geometry 4-mark question often needs a reason at each step. Give two acceptable circle-theorem reasons you should write.
[2 marks]
- Angle in a semicircle is 90°
- Opposite angles in a cyclic quadrilateral sum to 180°