Problem solving with direct and inverse proportion | Maths

Starter quiz

Two variables are in ______ proportion if they have a constant multiplicative relationship.

direct ✓

inverse

opposite

exact

proper
Which graph shows no proportional relationship?

'F' ✓
$y \propto x^2$ , when $y=192$ , $x=4$ . Work out the value of $y$ when $x=10$ .

'1200' ✓
$Which of these graphs show <Math>y \propto \frac{1}{x^n}</Math>?$

Which of these graphs show $y \propto \frac{1}{x^n}$ ?

A and B ✓

B and C

C and D

D and E

E and F
$y \propto \sqrt{x}$ , when $y=40$ , $x=4$ . Work out the value of $y$ when $x=100$ .

'200' ✓
$y \propto \frac{1}{x^2}$ , when $y=9.6$ , $x=5$ . Work out the value of $y$ when $x=10$ . Give your answer as a decimal.

'2.4' ✓

Exit quiz

Two variables are inversely proportional if there is a constant ______ relationship between one variable and the reciprocal of the other.

'multiplicative' ✓
When $y\propto \sqrt{x}$ , when $x$ , increases by 96%, what proportion does $y$ increase by?

96%

40% ✓

80%

12%
Given the following proportions, select which are the correct proportional relationships when : $a \propto c$ , $c \propto b$ , $b \propto \frac{1}{e}$ and $a \propto \frac{1}{f}$ .

$a \propto b$ ✓

$a \propto \frac{1}{e}$ ✓

$b \propto f$

$c \propto f$
When $y \propto x$ and $x \propto z^2$ , when $y=75$ , $x=3$ and when $x=128$ , $z=4$ . Write $y$ in terms of $z$ .

$y=200z^2$ ✓

$y=8z^2$

$y=25z^2$

$y=2z^2$
When $y\propto x^2$ , when $x$ increases by 20%, what proportion does $y$ increase by?

20%

40%

44% ✓

12%
Match the graph with the equations.

A

⇔

$y=x(x-5)(x+5)$ ✓

B

⇔

$y=4x^3$ ✓

C

⇔

$y=x^2-10x$ ✓

D

⇔

$y=9x^2$ ✓

E

⇔

$y=4^x$ ✓

F

⇔

$y=\frac{2}{x}$ ✓

Worksheet

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Lesson Details

Key learning points

Algebraic manipulation is needed to solve proportion problems.
Proportional relationships can be modelled graphically and algebraically.

Common misconception

Directly proportional graphs all start from (0,0) and are above the y axis.

Directly proportional means there is a multiplier between y and x. This graph is always y=kx and is linear passing through (0,0). A proportionality graphs show the multiplicative relationship between y and x^n and can be linear and non linear.

Keywords

Inversely proportional - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.
Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship.