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Year 8 Maths · KS3 notes

Percentage change, angles and circles

Clear notes with worked examples, then 4 practice questions with answers. Written by Beyond Tutors tutors for the KS3 National Curriculum.

Percentage change

Percentage change = change ÷ original × 100

£40 → £46: change 6, $6 \div 40 \times 100 = 15\%$ increase

Multipliers

Increase by 12%: × 1.12. Decrease by 20%: × 0.8

£250 increased by 12% = $250 \times 1.12 = $ £280

Angles in parallel lines

Alternate angles (Z shape) are equal
Corresponding angles (F shape) are equal
Co-interior angles (C shape) add up to 180°

Polygons

Exterior angles always add up to 360°.

Regular octagon: each exterior angle = $360 \div 8 = 45$ °, so each interior angle = 135°.

Circles

Circumference $= \pi d$ (or $2\pi r$ )

Area $= \pi r^2$

Radius 5 cm: area $= 3.14 \times 25 = 78.5$ cm²

Volume of a cuboid

length × width × height, in cm³

Practice questions

Try each one, then tap to see the answer and why.

Question 1 · Percentage change
A price rises from £40 to £46. What is the percentage increase?
- A6%
- B15%
- C13%
- D46%
Show the answer
B: 15%
Increase £6. $\dfrac{6}{40} = 0.15 = 15\%$ .
Question 2 · Polygons
What is each exterior angle of a regular octagon?
- A30°
- B135°
- C60°
- D45°
Show the answer
D: 45°
Exterior angles add to 360°: $360 \div 8 = 45$ °.
Question 3 · Angles
Two parallel lines are crossed by a straight line. One alternate angle is 65°. What is the other?
- A25°
- B295°
- C115°
- D65°
Show the answer
D: 65°
Alternate angles (Z-angles) are equal.
Question 4 · Angles
Co-interior angles between parallel lines are $x$ and 110°. Find $x$ .
- A250°
- B110°
- C70°
- D20°
Show the answer
C: 70°
Co-interior angles add to 180°: $180 - 110 = 70$ °.

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