Geometry & Measures

A right-angled triangle has legs 3 cm and 4 cm. What is the hypotenuse?

• A5 cm✓
• B7 cm
• C25 cm
• D12 cm

Answer: By Pythagoras, h² = 3² + 4² = 9 + 16 = 25, so h = √25 = 5 cm.

In a right-angled triangle, which ratio is sin θ?

• Aadjacent/hypotenuse
• Bopposite/hypotenuse✓
• Copposite/adjacent
• Dhypotenuse/opposite

Answer: SOH: sin θ = opposite ÷ hypotenuse.

What is the area of a circle with radius 6 cm? (Use π ≈ 3.14)

• A18.8 cm²
• B37.7 cm²
• C113.0 cm²✓
• D36 cm²

Answer: Area = πr² = 3.14 × 6² = 3.14 × 36 ≈ 113.0 cm².

The angle in a semicircle (from the diameter to a point on the circle) is:

• A45°
• B60°
• C90°✓
• D180°

Answer: A circle theorem: the angle in a semicircle is always a right angle, 90°.

What is the sum of the interior angles of a hexagon?

• A360°
• B540°
• C720°✓
• D900°

Answer: Interior angle sum = (n − 2) × 180° = (6 − 2) × 180° = 720°.

Two shapes are similar with a length scale factor of 3. What is the area scale factor?

• A3
• B6
• C9✓
• D27

Answer: Area scale factor = (length scale factor)² = 3² = 9.

What is the volume of a cylinder with radius 2 cm and height 5 cm? (Use π ≈ 3.14)

• A31.4 cm³
• B62.8 cm³✓
• C20 cm³
• D125.6 cm³

Answer: Volume = πr²h = 3.14 × 2² × 5 = 3.14 × 20 = 62.8 cm³.

What is the value of cos 60°?

• A1
• B0.5✓
• C√3/2
• D0

Answer: cos 60° = 0.5 (a standard exact trig value).

A bearing is always measured:

• AAnticlockwise from south
• BClockwise from north, as 3 figures✓
• CFrom the nearest object
• DIn radians

Answer: Bearings are measured clockwise from north and written with three figures (e.g. 075°).