Mathematics · Year 9

Lesson 1

Sort numbers into natural numbers, integers, rationals and irrationals, and see how these sets fit together inside the real numbers.

⏱ 18 min · 10 questions

Lesson 2

Trap square roots and cube roots between known values, refine the estimate to one decimal place and check it with a calculator.

⏱ 18 min · 10 questions

Lesson 3

Count and round to significant figures, and choose a sensible level of accuracy for answers calculated from real measurements.

⏱ 18 min · 10 questions

Lesson 4

Extend the index laws to negative exponents, write a⁻ⁿ as 1/aⁿ and evaluate numerical expressions with negative powers.

⏱ 18 min · 11 questions

Lesson 5

Combine every index law, including zero and negative indices, to simplify algebraic expressions with coefficients and several pronumerals.

⏱ 20 min · 11 questions

Lesson 6

Write very large and very small numbers in scientific notation and convert them back to ordinary decimal form.

⏱ 18 min · 11 questions

Lesson 7

Multiply and divide numbers in scientific notation using the index laws and a calculator, then tidy the answer into correct form.

⏱ 20 min · 11 questions

Lesson 8

Use metric prefixes and scientific notation to solve problems about cells, viruses, planets and stars.

⏱ 20 min · 11 questions

Lesson 9

Recognise that every measurement is an estimate, and find the absolute error and the upper and lower limits of a measurement.

⏱ 18 min · 11 questions

Lesson 10

Calculate relative and percentage errors and use them to decide which of two measurements is more accurate.

⏱ 18 min · 11 questions

Lesson 11

Use the formula I = Prn to calculate simple interest earned on savings or charged on loans, including periods given in months or days.

⏱ 18 min · 10 questions

Lesson 12

Rearrange I = Prn to find the principal, rate or time, and compare simple interest loans and savings options to make good decisions.

⏱ 20 min · 12 questions

Lesson 13

Multiply two binomials such as (x + 3)(x − 5) term by term, then collect like terms to simplify the result.

⏱ 18 min · 10 questions

Lesson 14

Recognise and expand perfect squares and differences of two squares using their patterns, and use them for quick mental arithmetic.

⏱ 18 min · 10 questions

Lesson 15

Reverse binomial expansion by finding two numbers with a given sum and product to factorise quadratics like x² + 7x + 12.

⏱ 20 min · 10 questions

Lesson 16

Factorise differences of two squares and perfect squares, and choose the right factorising method for any quadratic expression.

⏱ 20 min · 10 questions

Lesson 17

Measure the steepness of a line segment with rise over run and the gradient formula, and interpret positive, negative, zero and undefined gradients.

⏱ 18 min · 10 questions

Lesson 18

Find the midpoint of a line interval by averaging coordinates, and work backwards to find a missing endpoint.

⏱ 16 min · 10 questions

Lesson 19

Use Pythagoras’ theorem and the distance formula to find exact and rounded distances between points on the Cartesian plane.

⏱ 18 min · 10 questions

Lesson 20

Read the gradient and y-intercept straight from y = mx + c and sketch lines quickly without a table of values.

⏱ 18 min · 11 questions

Lesson 21

Work out the equation of a straight line from its graph, from a point and the gradient, or from two points.

⏱ 20 min · 11 questions

Lesson 22

Explore with a graphing tool how changing m and c moves and turns a line, and use equal gradients to find parallel lines.

⏱ 18 min · 10 questions

Lesson 23

Plot y = x², y = ax² and y = x² + k, and describe how changing a and k changes the width, direction and position of a parabola.

⏱ 20 min · 10 questions

Lesson 24

Tell linear, quadratic and exponential patterns apart using differences and ratios, and choose the right model for a real situation.

⏱ 20 min · 10 questions

Lesson 25

Unfold triangular, trapezoidal and composite right prisms into nets and add the areas of every face to find the total surface area.

⏱ 18 min · 11 questions

Lesson 26

Derive the surface area formula for a cylinder from its net and apply it to closed and open cylinders such as cans, pipes and water tanks.

⏱ 18 min · 10 questions

Lesson 27

Use V = πr²h to find the volume and capacity of cylinders, and rearrange it to find an unknown radius or height.

⏱ 18 min · 10 questions

Lesson 28

Enlarge and reduce shapes by a scale factor, identify what changes and what stays the same, and use scale factors to find unknown lengths.

⏱ 17 min · 11 questions

Lesson 29

Use enlargement to explain similarity, match corresponding sides and angles, and find unknown lengths in similar figures.

⏱ 18 min · 10 questions

Lesson 30

Apply the AAA, SSS, SAS and RHS tests to show two triangles are similar, then use them to solve problems such as finding heights from shadows.

⏱ 19 min · 10 questions

Lesson 31

Follow, test and refine step-by-step compass-and-ruler algorithms for bisecting angles and intervals and constructing perpendiculars.

⏱ 18 min · 10 questions

Lesson 32

Label the opposite, adjacent and hypotenuse sides of a right-angled triangle and use similar triangles to explain why sine, cosine and tangent are fixed for each angle.

⏱ 18 min · 10 questions

Lesson 33

Choose sine, cosine or tangent and use a calculator to find an unknown side length in a right-angled triangle.

⏱ 19 min · 11 questions

Lesson 34

Use inverse sine, cosine and tangent on a calculator to find an unknown angle in a right-angled triangle from two known sides.

⏱ 18 min · 11 questions

Lesson 35

Draw clear diagrams for worded problems involving angles of elevation and depression, then solve them using trigonometry.

⏱ 19 min · 11 questions

Lesson 36

Read and write true and compass bearings, and solve navigation problems using Pythagoras’ theorem and trigonometry.

⏱ 20 min · 11 questions

Lesson 37

Question the surveys, graphs and numbers in news stories and ads to spot misleading claims, weak samples and conclusions the data cannot support.

⏱ 18 min · 10 questions

Lesson 38

Group numerical data into class intervals, draw and read frequency histograms and polygons, and estimate the mean from grouped data.

⏱ 20 min · 10 questions

Lesson 39

Read and build back-to-back stem-and-leaf plots, then use them to compare the centre and spread of two data sets.

⏱ 18 min · 10 questions

Lesson 40

Describe the shape of a distribution and compare data sets using the mean, median and range, choosing the most suitable measure of centre.

⏱ 18 min · 10 questions

Lesson 41

Classify data by type, choose and justify a suitable display, and calculate and interpret sector angles in pie charts.

⏱ 18 min · 10 questions

Lesson 42

Identify bivariate numerical data, plan an investigation into two related variables and recognise sources of bias that could distort the results.

⏱ 18 min · 10 questions

Lesson 43

List every outcome of a two-step experiment using arrays, tables and tree diagrams, and calculate probabilities of compound events.

⏱ 20 min · 10 questions

Lesson 44

Compare two-step probabilities with and without replacement, adjusting the second-stage branches of a tree diagram when items are not returned.

⏱ 20 min · 9 questions

Lesson 45

Use Venn diagrams and two-way tables to find the probability of ‘and’, inclusive ‘or’ and exclusive ‘or’ events.

⏱ 20 min · 10 questions

Lesson 46

Calculate relative frequencies from recorded data to estimate the probability of compound events and predict expected frequencies.

⏱ 18 min · 10 questions

Lesson 47

Design spreadsheet simulations of two-step events and compare the probability of a simple event with related ‘both’ and ‘at least one’ events.

⏱ 20 min · 10 questions

Lesson 48

Work through a complete statistical investigation, choosing displays, calculating summary statistics and judging bias to answer a real-world question.

⏱ 20 min · 10 questions