Maths: Geometry & Measures

Two angles of a triangle are 65° and 48°. What is the third angle?

• A67°✓
• B77°
• C57°
• D113°

Answer: Angles in a triangle add up to 180°, so the third angle is 180 − 65 − 48 = 67°. 113° is 180 − 67, the exterior angle.

A circle has a radius of 4 cm. What is its area, to one decimal place?

• A100.5 cm²
• B12.6 cm²
• C50.3 cm²✓
• D25.1 cm²

Answer: Area = πr² = π × 4² = 16π = 50.3 cm² (1 d.p.). 25.1 cm is the circumference (2πr), 12.6 cm² uses the radius without squaring, and 100.5 cm² uses the diameter in place of the radius.

A triangle has a base of 6 cm and a perpendicular height of 4 cm. What is its area?

• A24 cm²
• B10 cm²
• C20 cm²
• D12 cm²✓

Answer: Area of a triangle is half of base × height: ½ × 6 × 4 = 12 cm². 24 cm² forgets to halve, and 10 cm is the sum of the two lengths.

A right-angled triangle has shorter sides of 8 cm and 15 cm. What is the length of the hypotenuse?

• A17 cm✓
• B19 cm
• C13 cm
• D23 cm

Answer: By Pythagoras, hypotenuse² = 8² + 15² = 64 + 225 = 289, and √289 = 17 cm. 23 cm simply adds the two sides.

How many millilitres are there in 2.5 litres?

• A2,500 ml✓
• B25,000 ml
• C250 ml
• D1,250 ml

Answer: There are 1,000 ml in a litre, so 2.5 litres is 2.5 × 1,000 = 2,500 ml.

A cuboid measures 4 m by 3 m by 2.5 m. What is its volume?

• A9.5 m³
• B35 m³
• C24 m³
• D30 m³✓

Answer: Volume of a cuboid is length × width × height: 4 × 3 × 2.5 = 30 m³. 9.5 m is the sum of the three lengths, 24 m³ leaves out the half metre, and 35 m³ is not a product of the three.

What is the size of each interior angle of a regular octagon?

• A144°
• B45°
• C120°
• D135°✓

Answer: The exterior angles of any polygon sum to 360°, so each exterior angle of a regular octagon is 360 ÷ 8 = 45°, and the interior angle is 180 − 45 = 135°. 120° is a hexagon's interior angle and 144° a decagon's.

A circle has a diameter of 14 cm. What is its circumference, to one decimal place?

• A153.9 cm
• B44.0 cm✓
• C22.0 cm
• D88.0 cm

Answer: Circumference = π × diameter = π × 14 = 44.0 cm. 22.0 cm uses the radius by mistake, 153.9 cm² is the area, and 88.0 cm doubles the correct answer.

Convert 5 metres into centimetres.

• A500 cm✓
• B50 cm
• C5,000 cm
• D0.05 cm

Answer: There are 100 centimetres in a metre, so 5 m = 5 × 100 = 500 cm.

A shape is translated by the vector (3, −2). What happens to every point of the shape?

• AIt moves 3 units to the right and 2 units down✓
• BIt is enlarged by a factor of 3 and rotated by 2 turns
• CIt is reflected in the line y = 3x − 2
• DIt moves 3 units up and 2 units to the left

Answer: A column vector (a, b) moves every point a units horizontally (positive is right) and b units vertically (positive is up). So (3, −2) is 3 right and 2 down; the shape's size and orientation are unchanged.

A ladder 10 m long leans against a wall with its foot 6 m from the base of the wall. How far up the wall does it reach?

• A4 m
• B8 m✓
• C11.7 m
• D16 m

Answer: By Pythagoras the height² = 10² − 6² = 100 − 36 = 64, so the height is √64 = 8 m. Adding the squares (√136 = 11.7 m) treats the ladder as a shorter side, and 4 m simply subtracts.

A trapezium has parallel sides of 6 cm and 10 cm and a perpendicular height of 4 cm. What is its area?

• A64 cm²
• B32 cm²✓
• C24 cm²
• D40 cm²

Answer: Area of a trapezium = ½ × (sum of the parallel sides) × height = ½ × (6 + 10) × 4 = 8 × 4 = 32 cm². Forgetting to halve gives 64 cm².