CAIE IGCSE Mathematics Proportion Questions

Practise forming and using direct or inverse proportion models involving linear, squared, rooted and bracketed quantities.

Exam points

translate proportional wording into y = kf(x) or y = k/f(x) with the correct power or root
substitute one known pair to determine k before calculating an unknown value
compare scale changes or combine proportional relationships to express one variable in terms of another

[Maximum number: 5]

(a)

y is directly proportional to $(x+3)^3$ .
When x=2, y=13.5.
Find x when y=108.
x=

[ 3 ]

7
M1 for $y=k(x+3)^3$ or better
M1 for $108=\text{their }k(x+3)^3$

(b)

g is inversely proportional to the square of d.
When d is halved, the value of g is multiplied by a factor n.
Find n.

[ 2 ]

4
M1 for $\left(\frac12\right)^2$ oe or equivalent inverse-square working

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