1.
A triangle has sides 5 cm, 12 cm and 13 cm. Show that it is right-angled. [3]
JD SCIENCE
Geometry and measures
Answer all questions. Show working. Answers are in a separate file on the Worksheets page — do not look at them until you have finished.
2.
Find the length of the hypotenuse of a right-angled triangle with legs 10 cm and 6 cm. [3]
3.
A circle has radius 7 cm. Find the circumference. Use π = 3.14. [2]
4.
The same circle has radius 7 cm. Find the area. Use π = 3.14. [2]
5.
A rectangle is 10 cm by 6 cm. Find the area and the perimeter. [2]
6.
Find the volume of a cuboid 10 cm × 6 cm × 4 cm. [2]
7.
A cylinder has radius 3 cm and height 10 cm. Find the volume. Leave π in your answer. [3]
8.
The area of a trapezium is ½(a + b)h. a = 8, b = 12, h = 5. Find the area. [2]
9.
Describe the transformation that maps triangle A onto triangle B if B is a reflection of A in the line x = 2. [2]
10.
A shape is enlarged by scale factor 3 from the origin. What happens to lengths and to area? [3]
11.
A map scale is 1 : 200. A path is 8 cm on the map. Find the real length in metres. [2]
12.
Find the interior angle of a regular hexagon. [2]
13.
The exterior angle of a regular polygon is 30°. How many sides does it have? [2]
14.
Work out the missing angle in a triangle with angles 47° and 62°. [1]
15.
Corresponding angles on parallel lines: one is 70°. Write the corresponding angle and an allied/co-interior angle. [2]
16.
A sector has radius 7 cm and angle 90°. Find the arc length. Leave π in your answer. [3]
17.
Find the area of the same 90° sector. Leave π in your answer. [2]
18.
SOHCAHTOA: in a right triangle, opposite = 5, hypotenuse = 13. Find sin θ. [2]
19.
A right-angled triangle has an angle of 30° and the opposite side is 8 cm. Find the hypotenuse. [2]
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]
21.
Write the circle theorems: angle in a semicircle, and angle at the centre. [3]
22.
Find the surface area of a cube of side 5 cm. [2]
23.
A triangular prism has triangle 3-4-5 and length 10 cm. Find the volume. [3]
24.
Describe a rotation of 90° clockwise about (0, 0) applied to the point (2, 1). [2]
25.
The bearing of B from A is 060°. Work out the bearing of A from B. [2]
26.
Find the midpoint of (2, 3) and (8, 11). [2]
27.
Find the distance between (0, 0) and (6, 8). [2]
28.
Explain why SSA is not a congruence condition for triangles. [2]
29.
A cone has radius 3 cm and slant height 5 cm. Find the curved surface area. Leave π in your answer. [2]
30.
Triangle ABC is similar to triangle DEF. AB = 6 cm, DE = 9 cm, BC = 10 cm.
(a) Write the scale factor from ABC to DEF. [1]
(b) Find EF. [2]
31.
Write the exact values of sin 30°, cos 60° and tan 45°. [3]
32.
A AQA geometry 4-mark question often needs a reason at each step. Give two acceptable circle-theorem reasons you should write. [2]