📚 Back
📚 MATHSKILLER TEXTBOOK SERIES
08

Variations

© 2025 MathsKiller
CHAPTER 8

Variations

8.1 Four Types of Variation
TypeRelationEquation
Direct$y \propto x$$y = kx$
Inverse$y \propto \dfrac{1}{x}$$y = \dfrac{k}{x}$
Joint$y \propto xz$$y = kxz$
Partial$y =$ const $+$ var$y = a + bx$
Example 1

If $y$ varies directly as $x$, and $y = 12$ when $x = 3$, find $y$ when $x = 5$.

📝 Solution

$y = kx$, $12 = 3k$ → $k = 4$

When $x = 5$: $y = 4(5) = 20$

📋 DSE Past Paper Questions

DSE 2022 Q13

$y$ is partly constant and partly varies as $x^2$. When $x = 2$, $y = 14$. When $x = 3$, $y = 27$. Find $y$ when $x = 4$.

📝 Solution

$y = a + bx^2$

$14 = a + 4b$, $27 = a + 9b$ → $b = 2.6$, $a = 3.6$

When $x = 4$: $y = 3.6 + 2.6(16) = 45.2$

📘 MathsKiller Textbook Series | Chapter 8: Variations

© 2025 MathsKiller