Edexcel IGCSE Math A Higher 2.5 Proportion Questions

Practise forming direct and inverse proportion formulae, finding constants, and using powers or roots to calculate missing values.

Exam points

set up y=kx^n or y=k/x^n from wording, then find k from a given pair of values
calculate a missing variable by substituting into a proportion formula with squares, cubes or roots

Covered syllabus points

2.5.HA Direct and inverse proportion

[Maximum number: 4]

y is inversely proportional to $x^{3}$

y=4 \text { when } x=3

Work out the value of x when y=864

Since y is inversely proportional to $x^3$ ,

y=\frac{k}{x^3}

4=\frac{k}{3^3} \quad\Rightarrow\quad k=4\times3^3=108

864=\frac{108}{x^3} \quad\Rightarrow\quad x^3=\frac{108}{864}=\frac18

Final answer:

x=0.5

M1 for a correct inverse-proportion formula with a constant k.
M1 for substituting x=3 and y=4.
M1 for a method to find $x^3$ .
A1 for 0.5 oe.

[Maximum number: 5]

18 F is inversely proportional to the cube of r

F=6 \text { when } r=2

(a)

Find a formula for F in terms of r

[ 3 ]

Since F is inversely proportional to $r^{3}$ ,
$F=\frac{k}{r^{3}}$

Using F=6 when r=2:
$6=\frac{k}{2^{3}}$ k=48

Final answer:
$F=\frac{48}{r^{3}}=48r^{-3}$

Award full marks if $F=kr^{-3}$ and k=48 are clearly given.

(b)

Find the value of r when F=3072

[ 2 ]

From part (a):
$F=\frac{48}{r^3}$

When F=3072:
$r^3=\frac{48}{3072}=\frac{1}{64}$ $r=\sqrt[3]{\frac{1}{64}}=\frac14$

Final answer:
$r=\frac14$

[Maximum number: 6]

16 A is inversely proportional to the square of r A=5 when r=0.3

(a)

Find a formula for A in terms of r

[ 3 ]

Since A is inversely proportional to $r^{2}$ ,
$A=\frac{k}{r^{2}}$
Using A=5 when r=0.3:
$5=\frac{k}{0.3^{2}}$ k=0.45
Final answer:
$A=\frac{0.45}{r^{2}}$
Equivalent answer $A=\frac{9}{20r^{2}}$ accepted.

(b)

Find the value of A when r=7.5 A

[ 3 ]

Using the formula from part (a):
$A=\frac{0.45}{(7.5A)^2}$ $A^3=\frac{0.45}{56.25}=0.008=\frac1{125}$
Final answer:
A=0.2

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Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question 3

Question (a)

Question (b)