COVID-19 support: free online GCSE Maths lessons

Areas and perimeters of simple and compound shapes

We’ll be exploring how using areas and perimeters of simple and compound shapes can help with planning out a stage or arena for your large-scale event.

Watch this lesson

- Convert between units of measure within one system, including time and metric units to metric units of length, area
 

- Find the perimeter of rectangles; parallelograms and trapezia; compound shapes
 

- Recall and use the formulae for the area of a rectangle
 

- Find the area of a trapezium and recall the formula
 

- Find the area of a parallelogram
 

- Calculate areas and perimeters of compound shapes made from rectangles.

Volume of cubes, cuboids and right prisms

We’ll be exploring how using volumes of cubes, cuboids and right prisms will help you to plan out a stage or arena for your large-scale event.

Watch this lesson

- Recall and use the formulae for the area of a triangle
 

- Calculate volumes of right prisms and shapes made from cubes and cuboids
 

Surface areas of cuboids and prisms

We’ll be exploring how calculating surface areas and performance areas of cuboids and prisms can help you ensure that a stage or arena space can work best for your large-scale event.

Watch this lesson

- Sketch nets of cuboids and prisms

- Find the surface area of a prism

- Find surface area using rectangles and triangles
 

Circumferences and areas of circles and volumes and surface areas of cylinders

We’ll be exploring how using cylinders and other 3D shapes can help with creating spectacular stage sets for your large-scale event.

Watch this lesson

- Recall and use formulae for the circumference of a circle and the area enclosed by a circle circumference of a circle = 2πr = πd, area of a circle = πr^2

- Use π ≈ 3.142 or use the π button on a calculator

- Give an answer to a question involving the circumference or area of a circle in terms of π

- Find the surface area and volume of a cylinder

Plans and elevations

We’ll be exploring how to interpret and make accurate drawings of triangles and other 2D shapes as well as front and side elevations and plans to help you construct the arena for your large-scale event quickly and accurately. 

Watch this lesson

- Draw sketches of 3D solids
 

- Understand and draw front and side elevations and plans of shapes made from simple solids
 

- Given the front and side elevations and the plan of a solid, draw a sketch of the 3D solid

Forming and solving linear equations

We’ll be exploring how forming and solving linear equations can help you to plan the security for your large-scale event. 

Watch this lesson

- Write expressions and set up simple equations including forming an equation from a word problem

- Solve simple equations including those:
with integer coefficients, in which the unknown appears on either side or on both sides of the equation; with one unknown, with integer or fractional coefficients

- Solve angle or perimeter problems using algebra

Forming and solving linear inequalities

We’ll be exploring how forming and solving linear inequalities will help you make sure your set is not too large for the arena at your large-scale event. 

Watch this lesson

- Solve an inequality such as −3 < 2x +1 < 7 and show the solution set on a number line
 

- Solve two inequalities in x, find the solution sets and compare them to see which value of x
 

- Use the correct notation to show inclusive and exclusive inequalities
 

- Construct inequalities to represent a set shown on a number line

Forming and solving quadratic equations

We’ll be exploring how forming and solving quadratic equations can help you design the best stage for your large-scale event.

Watch this lesson

- Multiply together two algebraic expressions with brackets

- Square a linear expression, e.g. (x + 1)^2

- Factorise quadratic expressions of the form
x^2 + bx + c

- Solve quadratic equations by factorising

Pythagoras’ Theorem in 2D

We’ll be exploring how you can use Pythagoras’ Theorem to quickly, carefully and accurately find the shortest distance to help rescue a stranded vessel.

Watch this lesson

Trigonometric ratios in 2D

We’ll be exploring how you can use the learning from the lesson above and trigonometric ratios to find the ship’s bearing and save the stranded vessel.

Watch this lesson

- Understand, use and recall the trigonometric ratios sine, cosine and tan, and apply them to find angles and lengths in general triangles in 2D figures

- Use the trigonometric ratios to solve 2D problems including angles of elevation and depression
 

Substitution, forming and solving linear equations and simultaneous equations

We’ll be exploring how using substitution, forming linear equations and simultaneous equations and solving them can help you ensure there’s the right number of lifeboats for passengers on the stranded vessel.

Watch this lesson

- Write expressions and set up simple equations including forming an equation from a word problem

- Solve simple equations including those:
with integer coefficients, in which the unknown appears on either side or on both sides of the equation; with one unknown, with integer or fractional coefficients;

- Write simultaneous equations to represent a situation

- Solve simultaneous equations (linear/linear) algebraically and graphically

- Solve simultaneous equations representing a real-life situation, graphically and algebraically, and interpret the solution in the context of the problem
 

Speed, distance and time and converting units

We’ll be exploring how you can use speed, distance and time calculations to work out how long it will take to rescue passengers on the stranded vessel. 

Watch this lesson

- Calculate average speed, distance, time – in miles per hour as well as metric measures

- Change d/t in m/s to a formula in km/h, i.e. d/t × (60 × 60)/1000 – with support
 

Co-ordinates, mid-points of a line, and column vectors

We’ll be exploring how co-ordinates, mid-points of a line, and column vectors can help you plan a round-the-world trip.  

Watch this lesson 

- Identify points with given coordinates and coordinates of a given point in all four quadrants

- Find the coordinates of points identified by geometrical information in 2D (all four quadrants)

- Find the coordinates of the midpoint of a line segment

- Read values from straight-line graphs for real-life situations

- Understand and use column notation in relation to vectors

- Be able to represent information graphically given column vectors

- Calculate using column vectors, and represent graphically, the sum of two vectors, the difference of two vectors and a scalar multiple of a vector

Column vectors and Pythagoras’ Theorem

We’ll be exploring how column vectors and Pythagoras’ Theorem can help you with planning a round-the-world trip. 

Watch this lesson

- Calculate the length of a line segment AB given pairs of points

- Use the trigonometric ratios to solve 2D problems

- Calculate the length of hypotenuse from a column vector

Collecting data, cumulative frequency

We’ll be exploring how collecting and using data and cumulative frequency can help you dig deeper into average screen times. 

Watch this lesson

- Specify the problem and plan:
decide what data to collect and what analysis is needed

- Construct and interpret cumulative frequency tables, cumulative frequency graphs/diagrams and from the graph: estimate frequency greater/less than a given value; find the median and quartile values and interquartile range

Comparing data, box plots

Explore how using box plots and comparing data from students can help you dig deeper into average screen times.

Watch this lesson

- Compare the mean and range of two distributions, or median and interquartile range, as appropriate
 

- Interpret box plots to find median, quartiles, range and interquartile range and draw conclusions

- Produce box plots from raw data and when given quartiles, median and identify any outliers

Smartphone Challenge – using data to make real life decisions

We’ll be exploring how maths can help you choose which phone to buy and why.

Watch this lesson

- Interpret and discuss any data (from tables, charts and graphs)

- Solve word problems involving direct and inverse proportion

- Understand inverse proportion: as x increases, y decreases (inverse graphs done in later unit)
 

Using maths for team success

We’ll be exploring how experimental probability can help you pick your best team.

Watch this lesson

- Interpret and discuss any data (from tables, charts and graphs)

- Find the probability of an event happening using relative frequency

Stock Market Challenge (part 1)

Explore how you can apply your knowledge of percentages increases and decreases to share prices. 

Watch this lesson

- Calculate percentage profit or loss

- Make calculations involving repeated percentage change, not using the formula

- Use compound interest

Stock Market Challenge (part 2)

We’ll be exploring how you can apply your knowledge of percentages increases and decreases to share prices. 

Watch this lesson

- Calculate percentage profit or loss

- Make calculations involving repeated percentage change, not using the formula

- Use compound interest

Using maths to crack the codes

We’ll be exploring how maths influences codes – from the most basic sequence to a sophisticated encryption.

- Substitute numbers into expressions involving brackets and powers

- Recognise odd, even and prime (two digit) numbers
 

- Find the LCM and HCF of two numbers, by listing, Venn diagrams and using prime factors: include finding LCM and HCF given the prime factorisation of two numbers

- Understand that the prime factor decomposition of a positive integer is unique – whichever factor pair you start with – and that every number can be written as a product of two factors

- Solve simple problems using HCF, LCM and prime numbers

Lights. Camera. Action. – Areas and perimeters of simple and compound shapes

We’ll be exploring how using areas and perimeters of simple and compound shapes can help with planning out a stage or arena for your large-scale event. 

Watch this lesson

- Convert between units of measure within one system, including time and metric units to metric units of length, area
 

- Find the perimeter of rectangles; parallelograms and trapezia; compound shapes
 

- Recall and use the formulae for the area of a rectangle
 

- Find the area of a trapezium and recall the formula
 

- Find the area of a parallelogram
 

- Calculate areas and perimeters of compound shapes made from rectangles.

Lights. Camera. Action. – Volumes of cubes, cuboids and right prisms 

We’ll be exploring how using volumes of cubes, cuboids and right prisms will help you to plan out a stage or arena for your large-scale event

- Recall and use the formulae for the area of a triangle
 

- Calculate volumes of right prisms and shapes made from cubes and cuboids

Lights. Camera. Action. – Surface areas of cuboids and prisms

We’ll be exploring how calculating surface areas and performance areas of cuboids and prisms can help you ensure that a stage or arena space can work best for your large-scale event.

- Sketch nets of cuboids and prisms

- Find the surface area of a prism

- Find surface area using rectangles and triangles