Year 9 Maths · KS3 notes

Graphs, Pythagoras and percentages

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

STRAIGHT-LINE GRAPHS: $y = mx + c$

$m$ = gradient (steepness), $c$ = where it crosses the $y$ -axis.

Gradient from two points = change in $y$ ÷ change in $x$

(1, 3) to (4, 12): $9 \div 3 = 3$

PYTHAGORAS (right-angled triangles only)

$a^2 + b^2 = c^2$ , where $c$ is the hypotenuse (longest side, opposite the right angle)

Finding $c$ : square, ADD, square root. 6 and 8 → $\sqrt{100} = 10$

Finding a shorter side: square, SUBTRACT, square root. 13 and 12 → $\sqrt{25} = 5$

Volume of a prism / cylinder

Volume = area of cross-section × length. Cylinder: $\pi r^2 h$

After a 20% increase the price is £60. £60 = 120%, so 100% = $60 \div 1.2 = $ £50

original × (multiplier) $^{\text{years}}$ : $1000 \times 1.1^2 = 1210$

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