CAIE IGCSE Mathematics Extended Algebraic Direct and Inverse Proportion

Practise converting proportional notation into an equation with k, finding that constant and applying the model to new values.

Exam points

replace ∝ with an equals sign and k, placing inverse quantities in the denominator
use the given variable pair to solve for k without dropping brackets, powers or roots
substitute the new input into the completed formula and evaluate the requested output

[Maximum number: 3]

(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.

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

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