RATIO, PROPORTION & GRAPHS

How to simplify a ratio (divide both sides by GCD)

Simplify 24

How to share an amount in a ratio (divide into total parts)

Share £90 in ratio 2

How to solve direct proportion (y = kx)

y ∝ x, y=10 when x=2. Find y when x=5

How to solve inverse proportion (y = k/x)

y ∝ 1/x, y=8 when x=2. Find y when x=4

How to solve more complex ratio problems (three quantities)

Divide £120 in ratio 2

How to convert units using ratio (scaling)

Recipe uses 300g flour for 4 people. Find amount for 10 people

How to use scale factor (length)

Model is 1

How to use scale factor (area)

Scale factor 1

How to use scale factor (volume)

Scale factor 1

How to find speed (distance ÷ time)

Car travels 150 km in 3 hours. Find speed

How to find time (distance ÷ speed)

Distance 200 km, speed 50 km/h. Find time

How to find distance (speed × time)

Speed 60 km/h, time 2.5 h. Find distance

How to calculate density (mass ÷ volume)

Mass 20 kg, volume 5 m³. Find density

How to calculate pressure (force ÷ area)

Force 200 N, area 10 m². Find pressure

How to draw and interpret distance-time graphs

A car travels at 60 km/h for 2 h. Draw graph.

How to read speed from gradient of distance-time graph

Find speed from line gradient

How to calculate area under velocity-time graph (distance)

Velocity-time graph shows 5 m/s for 6 s. Find distance

How to interpret acceleration from velocity-time graph (gradient)

Velocity changes from 0 to 20 m/s in 4 s. Find acceleration

How to calculate gradient of a line (change in y ÷ change in x)

Line passes through (2,3) and (5,9). Find gradient

How to find equation of a line (y=mx+c)

Line through (1,2) gradient 3. Find equation

How to interpret parallel lines (same gradient)

Line y=2x+3. Find equation of parallel line through (0,5)

How to interpret perpendicular lines (negative reciprocal)

Line y=2x+3. Find perpendicular through (1,4)

How to draw and interpret linear graphs (y = mx + c)

Draw graph y=2x+1 for x=0→5

How to draw and interpret quadratic graphs (y = ax² + bx + c)

Sketch graph of y=x²−2x+1

How to find intersection points from graphs (solve equations)

Solve y=x² and y=2x+3 graphically

How to interpret cubic and reciprocal graphs

Sketch y=x³ and y=1/x

How to estimate gradient from curve (tangent method)

Estimate gradient of y=x² at x=2

How to calculate area under a curve (count squares or trapezium rule)

Estimate area under y=x² from x=0→3

How to solve simultaneous equations graphically

Graph y=x² and y=2x+1. Find intersection

How to use real-life graphs (distance, speed, volume, population)

Graph shows population growth. Estimate population after 5 years

How to solve ratio problems in real context (mixing, recipes, speeds)

A mix is in ratio 3