Direct & Inverse Proportion (OCR GCSE Maths)

Exam Questions

3 hours51 questions

Medium

Hard

Very Hard

3 marks

Yesterday it took $5$ cleaners $4 \frac{1}{2}$ hours to clean all the rooms in a hotel.

There are only $3$ cleaners to clean all the rooms in the hotel today.

Each cleaner is paid £ $8.20$ for each hour or part of an hour they work.

How much will each cleaner be paid today?

How did you do?

Did this page help you?

Type of proportionality	Graph letter
$y \propto x$
$y \propto x^{2}$
$y \propto \sqrt{x}$
$y \propto \frac{1}{x}$

	day 1	day 2	day 3	all other days
Number of machines working	3	4	5	6

$x$	1.5	2	3	4
$y$	16	9	4	2.25

$□$	$V$ is directly proportional to $H$
$□$	$V$ is inversely proportional to $H$
$□$	$V$ is directly proportional to $\frac{1}{H}$
$□$	$V$ is inversely proportional to $\frac{1}{H}$

$y$ is directly proportional to $x$	$y$ is directly proportional to $\frac{1}{x}$
$y$ is inversely proportional to $\frac{1}{x}$	$x$ is directly proportional to $y$

Proportionality relationship	Graph letter
$y$ is directly proportional to $x$
$y$ is inversely proportional to $x$
$y$ is proportional to the square of $x$
$y$ is inversely proportional to the square of $x$

$x$	$1$	$2$	$3$	$4$
$y$	$9$	$2 \frac{1}{4}$	$1$	$\frac{9}{16}$

Direct & Inverse Proportion (OCR GCSE Maths)

Exam Questions

1. Number Operations & Integers

Number Toolkit

Prime Factors, HCF & LCM

2. Fractions, Decimals & Percentages

Fractions

Percentages

Working with FDP

3. Indices & Surds

Powers, Roots & Standard Form

Surds

4. Approximation & Estimation

Rounding, Estimation & Bounds

Using a Calculator

5. Ratio, Proportion & Rates of Change

Ratio Toolkit

Ratio Problem Solving

Direct & Inverse Proportion

Exchange Rates & Best Buys

Simple & Compound Interest, Growth & Decay

6. Algebra

Algebra Toolkit

Algebraic Roots & Indices

Expanding Brackets

Factorising

Completing the Square

Algebraic Fractions

Rearranging Formulae

Algebraic Proof

Linear Equations

Solving Quadratic Equations

Solving Inequalities

Simultaneous Equations

Iteration

Forming & Solving Equations

Functions

Sequences

7. Graphs of Equations & Functions

Coordinate Geometry

Linear Graphs y = mx + c

Graphing Inequalities

Graphs of Functions

Equation of a Circle

Estimating Gradients & Areas under Graphs

Real-Life Graphs

Transformations of Graphs

8. Basic Geometry

Geometry Toolkit

Angles in Polygons & Parallel Lines

Circle Theorems

9. Congruence & Similarity

Congruence, Similarity & Geometrical Proof

Area & Volume of Similar Shapes

Vectors

Transformations

10. Mensuration

Standard & Compound Units

Bearings, Scale Drawing, Constructions & Loci

Area & Perimeter

Circles, Arcs & Sectors

Volume & Surface Area

Right-Angled Triangles - Pythagoras & Trigonometry

Sine, Cosine Rule & Area of Triangles

3D Pythagoras & Trigonometry

11. Probability

Probability Toolkit

Simple Probability Diagrams

Tree Diagrams

Combined & Conditional Probability

12. Statistics

Statistics Toolkit

Statistical Diagrams

Histograms

Cumulative Frequency & Box Plots

Scatter Graphs & Correlation