Algebra uses letters to stand for numbers. This lets us write rules that work every time.
🔤 Letters as numbers
A variable is a letter that stands for a number we do not know yet. 3x means 3 × x. An expression combines numbers and variables, such as 3x + 2. We can simplify by collecting like terms: 3a + 2a = 5a.
3x means 3 × x. Follow the order of operations: multiply before you add.
📐 Formulae
A formula is a rule using letters. To use one, substitute the numbers and work it out, following the order of operations (brackets first, then multiply, then add).
Area of a rectangle: A = l × w
l = 7, w = 3 → A = 21
Perimeter: P = 2l + 2w
l = 8, w = 5 → P = 16 + 10 = 26
3x is not 3 + x. Writing a number next to a letter means multiply.
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Meaning
What does 3x mean?
No sign means times.
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Simplify
Simplify 3a + 2a.
Same letter.
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Expand
Expand 2(a + 3).
Share the 2.
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Expression
Which of these is an algebraic expression?
Look for a letter.
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Work out 3x + 2 when x = 4.
What is the value?
Enter an exact answer, without rounding.
Substitute x = 4.
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Use A = l × w with l = 7 and w = 3.
What is A?
Enter an exact answer, without rounding.
Multiply.
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Use P = 2l + 2w with l = 8 and w = 5.
What is P?
Enter an exact answer, without rounding.
Double each, then add.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
What is 5n when n = 6?
Question 2 of 5
Simplify 4b + b.
Question 3 of 5
The perimeter of a square with side s is:
Question 4 of 5
What is 2(a + 3) when a = 4?
Question 5 of 5
Which expression means “a number plus 5”?
Lesson 2 · Algebra
⚖️ Solving Linear Equations
An equation is a balance. Whatever you do to one side, you must do to the other.
⚖️ Equations and inverse operations
An equation says two things are equal, for example x + 7 = 12. To solve it, use inverse operations to get the letter alone: the inverse of add is subtract, and the inverse of multiply is divide.
x + 7 = 12 → x = 12 − 7 = 5
3x = 18 → x = 18 ÷ 3 = 6
x ÷ 4 = 3 → x = 3 × 4 = 12
🖼️ See it
An equation is a balance. Undo the adding first, then undo the multiplying, doing the same to both sides.
🔁 Two-step equations
For two-step equations, undo the add or subtract first, then undo the multiply or divide. Always check by substituting your answer back.
2x + 5 = 17
2x = 12
x = 6
check: 2 × 6 + 5 = 17 ✔
Keep the balance. Do the same to both sides.
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Inverse
The inverse operation of adding is:
Opposite.
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Solve
Solve x + 7 = 12.
Subtract 7.
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Solve
Solve 3x = 18.
Divide by 3.
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Balance
To keep an equation balanced you must:
Like a scale.
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Solve x ÷ 4 = 3.
What is x?
Enter an exact answer, without rounding.
Multiply both sides by 4.
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Solve 2x + 5 = 17.
What is x?
Enter an exact answer, without rounding.
Subtract 5, then divide by 2.
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Solve 5x − 4 = 21.
What is x?
Enter an exact answer, without rounding.
Add 4, then divide by 5.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
Solve x − 3 = 10.
Question 2 of 5
Solve 4x = 20.
Question 3 of 5
Solve 3x + 1 = 13.
Question 4 of 5
Solve 3(x + 2) = 21.
Question 5 of 5
How can you check the solution x = 6 to 2x + 5 = 17?
Lesson 3 · Measurement
📦 Volume of Cuboids
Volume is the amount of space inside a 3D shape. We measure it in cubes.
📦 Finding volume
A cuboid is a box shape. Its volume is length × width × height. Volume is measured in cubic units such as cm³ or m³. A cube has all sides equal, so its volume is side × side × side.
l = 5, w = 4, h = 3
V = 5 × 4 × 3 = 60 cm³
Cube with side 2 cm: V = 2 × 2 × 2 = 8 cm³
🖼️ See it
Each layer holds 5 × 4 = 20 one-centimetre cubes, and there are 3 layers.
🥛 Volume and capacity
Capacity is how much a container can hold. 1 cm³ = 1 mL and 1000 cm³ = 1 litre. To find a missing side, divide the volume by the other measurements.
Tank 50 cm × 40 cm × 30 cm = 60 000 cm³ = 60 litres
V = 120, l = 8, w = 5 → h = 120 ÷ 40 = 3
Check the units. All lengths must be in the same unit before you multiply.
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Formula
The volume of a cuboid is:
Three lengths.
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Units
Volume is measured in:
Cubed.
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Capacity
1000 cm³ equals:
Memorise it.
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Cube
A cube has side 2 cm. Which expression gives its volume?
Side cubed.
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A cuboid is 5 cm long, 4 cm wide and 3 cm high.
What is its volume in cm³?
Enter an exact answer, without rounding.
Multiply.
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A cuboid has volume 120 cm³, length 8 cm and width 5 cm.
What is its height in cm?
Enter an exact answer, without rounding.
Divide by l × w.
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A tank measures 50 cm by 40 cm by 30 cm.
How many litres does it hold?
Enter an exact answer, without rounding.
Divide by 1000.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
What is the volume of a 2 cm by 3 cm by 4 cm cuboid?
Question 2 of 5
A cube of side 3 cm has volume:
Question 3 of 5
2 litres equals how many cm³?
Question 4 of 5
Which unit would you use for the volume of a swimming pool?
Question 5 of 5
If the height of a cuboid doubles, its volume:
Lesson 4 · Measurement
🎁 Surface Area
Surface area is the total area of all the faces of a 3D shape, like the amount of wrapping paper needed.
🎁 Adding up the faces
A cuboid has 6 faces in three matching pairs. Find the area of each face, then add them all. Surface area is measured in square units such as cm².
l = 4, w = 3, h = 2
top and bottom: 2 × (4 × 3) = 24
front and back: 2 × (4 × 2) = 16
sides: 2 × (3 × 2) = 12
total = 52 cm²
🖼️ See it
Surface area covers the outside; volume fills the inside.
🧊 Cubes and nets
A net is a 3D shape unfolded flat. A cube has 6 identical square faces, so its surface area is 6 × side². Drawing a net helps you count every face once.
Cube, side 3 cm: face = 9 cm², total = 6 × 9 = 54 cm²
Surface area ≠ volume. One covers the outside; the other fills the inside.
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Faces
How many faces does a cuboid have?
Think of a box.
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Units
Surface area is measured in:
Squared.
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Net
A net is:
Flat pattern.
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Cube
A cube has how many identical square faces?
Six sides.
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A cuboid is 4 cm by 3 cm by 2 cm.
What is its surface area in cm²?
Enter an exact answer, without rounding.
Add the areas of three pairs of faces.
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A cube has a side of 3 cm.
What is its surface area in cm²?
Enter an exact answer, without rounding.
Six equal faces.
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A cuboid is 5 cm by 2 cm by 1 cm.
What is its surface area in cm²?
Enter an exact answer, without rounding.
Find three pairs of faces.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
Surface area of a cube with side 5 cm:
Question 2 of 5
Which would you find using surface area?
Question 3 of 5
A cuboid is 6 by 4 by 2 cm. Its surface area is:
Question 4 of 5
The area of one face of a 4 cm cube is:
Question 5 of 5
A net of a cube has how many squares?
Lesson 5 · Data
📊 Mean, Median, Mode & Range
Averages describe a whole set of data with one number. Each average tells a different story.
📊 Three averages
The mean is the total divided by how many values. The median is the middle value when data is in order. The mode is the most common value. The range is the biggest value minus the smallest.
Put the data in order first. The median is the middle value; the mode is the most common one.
➗ Even number of values
When there is an even number of values, the median is halfway between the two middle ones. To find a missing value, use: total = mean × number of values.
2, 4, 6, 8 → middle values 4 and 6 → median = 5
Mean of 5 numbers is 7 → total = 35
Order the data first before finding the median.
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Mean
The mean of a data set is:
Fair share.
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Median
The median is:
In the middle.
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Mode
The mode of 2, 3, 3, 4, 5 is:
Most frequent.
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Range
The range of 3, 5, 7, 5, 10 is:
Biggest minus smallest.
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Find the mean of 4, 8 and 6.
What is the mean?
Enter an exact answer, without rounding.
Total ÷ 3.
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Find the median of 3, 5, 7, 5, 10.
What is the median?
Enter an exact answer, without rounding.
Order first.
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The mean of 5 numbers is 7.
What is their total?
Enter an exact answer, without rounding.
Mean × number of values.
📝 Lesson quiz · 5 questions
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Question 1 of 5
The median of 2, 4, 6, 8 is:
Question 2 of 5
The mean of 10, 20, 30 and 40 is:
Question 3 of 5
A data set can have more than one:
Question 4 of 5
Which average is easiest to find from a bar chart?
Question 5 of 5
Test scores are 6, 7, 7, 8 and 7. The mode is:
Lesson 6 · Data
🎲 Probability
Probability measures how likely something is to happen, from impossible to certain.
🎲 The probability scale
Probability is a number from 0 (impossible) to 1 (certain). Probability = number of favourable outcomes ÷ total number of possible outcomes. It can be written as a fraction, a decimal or a percentage.
P(heads) = 1/2 = 0.5 = 50%
P(rolling a 6) = 1/6
P(even number on a die) = 3/6 = 1/2
🖼️ See it
Probability goes from 0 (impossible) to 1 (certain). P(roll a 6) = 1/6 and P(heads) = 1/2.
🎒 Using probability
If all outcomes are equally likely, count the ones you want and divide by all of them. The probabilities of all outcomes add up to 1. Over many trials, results get closer to what you expect.
Bag: 3 red, 7 blue → P(red) = 3/10 = 0.3
Roll a die 60 times → expect about 10 sixes
“Likely” is not “certain”. Unlikely events can still happen.
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Scale
An impossible event has probability:
Bottom of the scale.
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Certain
A certain event has probability:
Top of the scale.
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Coin
The probability of getting heads on a fair coin is:
One out of two.
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Die
The probability of rolling an even number on a fair die is:
Count the evens.
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A bag has 3 red and 7 blue counters.
What is the probability of picking a red one, as a decimal?
Enter an exact answer, without rounding.
Favourable ÷ total.
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You roll a fair die 60 times.
About how many sixes do you expect?
Enter an exact answer, without rounding.
Probability × trials.
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A spinner has 8 equal sections and 2 are blue.
What is the probability of blue, as a decimal?
Enter an exact answer, without rounding.
Simplify.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
The probability of picking a red ball from a bag of 4 red and 6 blue balls is:
Question 2 of 5
Which event is impossible?
Question 3 of 5
The probabilities of all outcomes add up to:
Question 4 of 5
If P(rain) = 0.8, rain is:
Question 5 of 5
P(not getting heads) on a coin is:
Lesson 7 · Number
🔢 Factors, Primes, Squares & Cubes
Every whole number is built from smaller numbers multiplied together. Knowing factors and primes makes division, fractions and patterns much easier.
🔢 Factors and multiples
A factor of a number divides into it exactly, with no remainder. Factors come in pairs that multiply to the number. A multiple of a number is in its times table. The highest common factor (HCF) is the biggest factor two numbers share; the lowest common multiple (LCM) is the smallest multiple they share.
Factors of 12: 1 × 12, 2 × 6, 3 × 4 → 1, 2, 3, 4, 6, 12
Multiples of 4: 4, 8, 12, 16, 20, …
HCF of 12 and 18 = 6
LCM of 4 and 6 = 12
🖼️ See it
The factors of 12 are 1, 2, 3, 4, 6 and 12. It has more than two factors, so it is not prime.
⭐ Primes, squares and cubes
A prime number has exactly two factors: 1 and itself. 1 is not prime because it has only one factor, and 2 is the only even prime. A square number is a number times itself (n²); a cube number is a number times itself three times (n³).
Test for a prime by trying to divide by 2, 3, 5 and 7. If none of them work (and the number is below 100), it is prime.
✏️ Quick check · 1 of 7
Prime
Which of these numbers is prime?
Try dividing by 2, 3 and 5.
✏️ Quick check · 2 of 7
Factors
Which list shows all the factors of 12?
Find pairs that multiply to 12.
✏️ Quick check · 3 of 7
Square
Which number is a square number?
Look for n × n.
✏️ Quick check · 4 of 7
One
Why is 1 not a prime number?
Count its factors.
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Find the highest common factor of 12 and 18.
What is the HCF?
Enter an exact answer, without rounding.
List the factors of both numbers.
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Find the lowest common multiple of 4 and 6.
What is the LCM?
Enter an exact answer, without rounding.
List the multiples of both.
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A cube number is n × n × n.
What is 4 cubed (4³)?
Enter an exact answer, without rounding.
Work out 4 × 4 first.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
How many factors does a prime number have?
Question 2 of 5
Which number is a multiple of 7?
Question 3 of 5
What is 5 squared (5²)?
Question 4 of 5
Which is the only even prime number?
Question 5 of 5
Which of these is a cube number?
Lesson 8 · Geometry
📐 Angles in Triangles & Area of Triangles
Three simple angle facts let you find missing angles, and one formula gives the area of any triangle.
📐 Angle facts
Angles on a straight line add up to 180°. Angles around a point add up to 360°. The three angles inside any triangle add up to 180°. An isosceles triangle has two equal sides and two equal angles; an equilateral triangle has three angles of 60°.
Triangle with 40° and 75°: third angle = 180 − 40 − 75 = 65°
Straight line with 110°: other angle = 180 − 110 = 70°
Around a point 120° and 90°: missing = 360 − 210 = 150°
🖼️ See it
Missing angle = 180° minus the two angles you know.The height meets the base at a right angle. The triangle is half of an 8 × 5 rectangle.
🔺 Area of a triangle
A triangle is half of a rectangle with the same base and height, so area = ½ × base × height. The height must be the perpendicular height: measured at right angles to the base, not along a sloping side. Area is in square units such as cm².
base 8 cm, height 5 cm
area = ½ × 8 × 5 = 20 cm²
base 10 cm, height 6 cm → area = 30 cm²
Do not use the sloping side as the height. The height always meets the base at 90°.
✏️ Quick check · 1 of 7
Triangle
The three angles in any triangle add up to:
Half a full turn.
✏️ Quick check · 2 of 7
Straight line
Angles on a straight line add up to:
Half of 360°.
✏️ Quick check · 3 of 7
Height
In the formula ½ × base × height, the height must be:
Think of a right angle.
✏️ Quick check · 4 of 7
Isosceles
An isosceles triangle has:
Iso means equal.
✍️ Type your answer · 5 of 7
A triangle has angles of 40° and 75°.
What is the third angle, in degrees?
Enter an exact answer, without rounding.
°
Subtract both from 180.
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A triangle has a base of 8 cm and a perpendicular height of 5 cm.
What is its area, in cm²?
Enter an exact answer, without rounding.
cm²
Half of base × height.
✍️ Type your answer · 7 of 7
Three angles meet at a point: 120°, 90° and one more.
What is the missing angle, in degrees?
Enter an exact answer, without rounding.
°
Angles around a point add to 360°.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
A right-angled triangle has one angle of 30°. The third angle is:
Question 2 of 5
What is the area of a triangle with base 10 cm and height 6 cm?
Question 3 of 5
Two angles on a straight line are 110° and x. What is x?
Question 4 of 5
Each angle of an equilateral triangle is:
Question 5 of 5
A triangle’s area is half the area of a:
Lesson 9 · Geometry
⭕ Parts of a Circle
Circles are everywhere, from wheels to clocks. Learning the names of their parts helps you draw and measure them.
⭕ Naming the parts
The centre is the point in the middle. The radius goes from the centre to the edge. The diameter goes from edge to edge through the centre, so it is twice the radius. The circumference is the distance all the way round the circle.
radius 7 cm → diameter = 2 × 7 = 14 cm
diameter 18 cm → radius = 18 ÷ 2 = 9 cm
All radii of one circle are the same length.
🖼️ See it
The diameter goes through the centre and is twice the radius. The circumference is a little more than 3 times the diameter.
✏️ Drawing and the circumference
To draw a circle, open your compasses to the radius, put the point on the centre and turn. The circumference is always a little more than 3 times the diameter. The exact number is called π (pi), about 3.14.
diameter 10 cm → circumference ≈ 3.14 × 10 = 31.4 cm
diameter 1 m → circumference ≈ 3.14 m
Check which length you are given. Halve a diameter to get the radius before setting your compasses.
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Radius
The radius of a circle is the distance from:
Half of the way across.
✏️ Quick check · 2 of 7
Diameter
The diameter of a circle is:
Two radii end to end.
✏️ Quick check · 3 of 7
Circumference
The circumference of a circle is:
Circum- means around.
✏️ Quick check · 4 of 7
Compasses
To draw a circle of radius 4 cm you open your compasses to:
Use the radius.
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A circle has a radius of 7 cm.
What is its diameter, in cm?
Enter an exact answer, without rounding.
cm
Double the radius.
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A circle has a diameter of 18 cm.
What is its radius, in cm?
Enter an exact answer, without rounding.
cm
Halve the diameter.
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The circumference is about 3.14 × the diameter.
About how long is the circumference of a circle with diameter 10 cm, in cm?
Enter an exact answer, without rounding.
cm
Multiply by 3.14.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
A wheel has a diameter of 60 cm. Its radius is:
Question 2 of 5
Which line goes from edge to edge through the centre?
Question 3 of 5
A circle has a radius of 2.5 cm. Its diameter is:
Question 4 of 5
The circumference of a circle is a little more than:
Question 5 of 5
All the radii of the same circle are:
Lesson 10 · Geometry
🗺️ Coordinates & Transformations
Coordinates pin down any point on a grid, even below and left of zero. Transformations move shapes around that grid.
🗺️ Four quadrants
A point is written (x, y): go across first, then up or down. The axes cross at the origin (0, 0). Negative x means left of the origin; negative y means below it. The axes split the grid into four quadrants.
(3, 2) → right 3, up 2 (1st quadrant)
(−3, 2) → left 3, up 2 (2nd quadrant)
(−2, −4) → left 2, down 4 (3rd quadrant)
(4, −2) → right 4, down 2 (4th quadrant)
🖼️ See it
Go across first (x), then up or down (y). Negative x is left of the origin; negative y is below it.Each corner is the same distance from the mirror line on the other side: (4, 1) → (−4, 1).
🔁 Translations and reflections
A translation slides every point the same distance: right adds to x, left subtracts, up adds to y, down subtracts. A reflection flips a shape over a mirror line. Reflecting in the y-axis changes the sign of x; reflecting in the x-axis changes the sign of y. Both keep the shape the same size.
(2, 3) translated 4 right, 1 down → (6, 2)
(3, 2) reflected in the y-axis → (−3, 2)
(3, 2) reflected in the x-axis → (3, −2)
Count squares to the mirror line. The image is the same distance on the other side.
✏️ Quick check · 1 of 7
Order
In the coordinates (−3, 5), which number tells you how far across?
Across, then up.
✏️ Quick check · 2 of 7
Quadrant
In which quadrant is the point (4, −2)?
Right and down.
✏️ Quick check · 3 of 7
Reflect
The point (3, 2) is reflected in the y-axis. Where does it go?
Flip left to right.
✏️ Quick check · 4 of 7
Same shape
After a translation, a shape is:
Sliding only.
✍️ Type your answer · 5 of 7
The point (2, 3) is translated 4 right and 1 down.
What is the new x-coordinate?
Enter an exact answer, without rounding.
Moving right adds to x.
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The point (−1, 4) is translated 3 left and 5 down.
What is the new y-coordinate?
Enter an exact answer, without rounding.
Moving down subtracts from y.
✍️ Type your answer · 7 of 7
A rectangle has corners (−2, 1), (3, 1), (3, 4) and (−2, 4).
How wide is it along the x-axis, in units?
Enter an exact answer, without rounding.
Count the squares across.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
The point (0, 0) is called the:
Question 2 of 5
Which point is in the third quadrant?
Question 3 of 5
Reflect (−4, 1) in the x-axis. The image is:
Question 4 of 5
(5, 2) is translated 2 left and 3 up. Where does it land?
Question 5 of 5
A reflected shape is:
Lesson 11 · Data
🥧 Pie Charts & Line Graphs
Pie charts show how a whole is shared out; line graphs show how something changes over time.
🥧 Pie charts
A pie chart is a circle that stands for all the data. Each sector shows one category. A full circle is 360°, so a sector’s angle is its fraction of the total × 360°. Half the data is 180°, a quarter is 90°.
20 pupils: football 10, swimming 5, tennis 5
football 10/20 = 1/2 → 180°
swimming 5/20 = 1/4 → 90°
tennis 5/20 = 1/4 → 90° total 360°
🖼️ See it
Football is 10 out of 20, a half, so it gets 180°. Swimming and tennis are a quarter each: 90°.The line rises until 13:00, then falls. From 9:00 to 13:00 it warms by 8 °C.
📈 Line graphs
A line graph plots values against time and joins the points with straight lines. It shows a trend: going up means increasing, going down means decreasing, flat means no change. Always read the scale on each axis carefully.
9 a.m. 12 °C, 11 a.m. 17 °C, 1 p.m. 20 °C, 3 p.m. 18 °C
warmest at 1 p.m.; rise from 9 a.m. to 1 p.m. = 8 °C
Pie charts compare parts of one whole; they cannot show change over time.
✏️ Quick check · 1 of 7
Pie
A pie chart is best for showing:
Think of slices of one pie.
✏️ Quick check · 2 of 7
Whole
The angles in a pie chart add up to:
A full turn.
✏️ Quick check · 3 of 7
Line
Which data suits a line graph best?
Look for time.
✏️ Quick check · 4 of 7
Half
A sector is exactly half of a pie chart. It shows:
180° out of 360°.
✍️ Type your answer · 5 of 7
In a pie chart of 40 pupils, one sector has an angle of 90°.
How many pupils does it show?
Enter an exact answer, without rounding.
What fraction of 360 is 90?
✍️ Type your answer · 6 of 7
60 people were asked their favourite colour. 20 chose blue.
What angle should the blue sector have, in degrees?
Enter an exact answer, without rounding.
°
Fraction × 360.
✍️ Type your answer · 7 of 7
A line graph shows 12 °C at 9 a.m. and 20 °C at 1 p.m.
By how many degrees did it warm up?
Enter an exact answer, without rounding.
°C
Subtract the readings.
📝 Lesson quiz · 5 questions
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Re-read the lesson, then give it another go.
Question 1 of 5
In a pie chart, a 180° sector shows:
Question 2 of 5
30 pupils: 10 walk to school. What angle is the walking sector?
Question 3 of 5
A line going up on a line graph means the values are:
Question 4 of 5
25% of a class have a cat. The cat sector angle is:
Question 5 of 5
The horizontal axis of a line graph usually shows:
Lesson 12 · Algebra
🔁 Sequences
A sequence is a list of numbers that follows a rule. Spot the rule and you can find any term, even the 100th.
🔁 Term-to-term rules
Each number in a sequence is a term. A term-to-term rule tells you how to get from one term to the next, such as “add 3” or “double”. Find it by looking at the difference between terms.
2, 5, 8, 11, … rule: add 3 → next term 14
50, 44, 38, … rule: subtract 6 → next term 32
3, 6, 12, 24, … rule: double → next term 48
1, 3, 6, 10, … add 2, 3, 4, … (triangular numbers) → 15
🖼️ See it
Each term is 4 more than the one before. The 6th term is 27.
📍 Position-to-term rules
A position-to-term rule uses the term’s position (1st, 2nd, 3rd, …) to work it out directly. This is quicker for terms far along the sequence.
rule: term = 3 × position − 1
position 1 → 2
position 2 → 5
position 10 → 3 × 10 − 1 = 29
Check your rule on the first few terms before using it for a far-away term.
✏️ Quick check · 1 of 7
Rule
What is the term-to-term rule for 4, 9, 14, 19, …?
Find the difference.
✏️ Quick check · 2 of 7
Next
What is the next term of 1, 3, 6, 10, …?
The difference grows by 1.
✏️ Quick check · 3 of 7
Doubling
Which sequence doubles each time?
Multiply by 2.
✏️ Quick check · 4 of 7
Position
The rule is “term = 2 × position + 1”. What is the 1st term?
Use position 1.
✍️ Type your answer · 5 of 7
A sequence starts at 7 and adds 4 each time.
What is the 6th term?
Enter an exact answer, without rounding.
Add 4 five times.
✍️ Type your answer · 6 of 7
The rule is term = 3 × position − 1.
What is the 10th term?
Enter an exact answer, without rounding.
Multiply the position by 3, then subtract 1.
✍️ Type your answer · 7 of 7
A sequence goes 50, 44, 38, 32, …
What is the next term?
Enter an exact answer, without rounding.
Find the difference.
📝 Lesson quiz · 5 questions
0 / 5
Re-read the lesson, then give it another go.
Question 1 of 5
What is the next term in 2, 4, 8, 16, …?
Question 2 of 5
The rule is “add 7” and the first term is 5. The 3rd term is:
Question 3 of 5
Which of these is the sequence of square numbers?
Question 4 of 5
The rule is term = 4 × position. What is the 5th term?
Question 5 of 5
In 30, 27, 24, 21, … the rule is:
Final Challenge
🏆 24-Question Challenge Quiz
Questions from every topic in this course. Pick an answer for each one, then hit Check My Answers.
0 / 24
💪 Keep practicing — go back through the lessons and retake the quiz!
Q1 · Algebraic Expressions & Formulae
Substituting means:
Q2 · Algebraic Expressions & Formulae
Which expression means “a number plus 5”?
Q3 · Solving Linear Equations
To solve y + 9 = 15 you:
Q4 · Solving Linear Equations
How can you check the solution x = 6 to 2x + 5 = 17?
Q5 · Volume of Cuboids
Volume tells us:
Q6 · Volume of Cuboids
If the height of a cuboid doubles, its volume:
Q7 · Surface Area
Surface area adds up the area of:
Q8 · Surface Area
A net of a cube has how many squares?
Q9 · Mean, Median, Mode & Range
The range shows how:
Q10 · Mean, Median, Mode & Range
Test scores are 6, 7, 7, 8 and 7. The mode is:
Q11 · Probability
Probability is always between:
Q12 · Probability
P(not getting heads) on a coin is:
Q13 · Factors, Primes, Squares & Cubes
A factor of a number:
Q14 · Factors, Primes, Squares & Cubes
Which of these is a cube number?
Q15 · Angles in Triangles & Area of Triangles
The angles of a triangle add up to:
Q16 · Angles in Triangles & Area of Triangles
A triangle’s area is half the area of a:
Q17 · Parts of a Circle
The radius is half of the:
Q18 · Parts of a Circle
All the radii of the same circle are:
Q19 · Coordinates & Transformations
In coordinates (x, y), the first number tells you:
Q20 · Coordinates & Transformations
A reflected shape is:
Q21 · Pie Charts & Line Graphs
To work out a pie chart angle you multiply the fraction by:
Q22 · Pie Charts & Line Graphs
The horizontal axis of a line graph usually shows: