Maths Challenge Pack

Welcome! This pack helps you learn maths. It has easy guides, examples, and questions for all ages to try.

How to use this pack

Find your age group using the purple badges. Each section includes a clear explanation of the topic, a worked-out example to show you how it's done, and practice questions to test your skills!

Maths is everywhere. From counting snacks to solving big puzzles, every step helps you get smarter!

Ages 6-7

Topic: Addition within 20

Addition is putting numbers together. We use the plus (+) sign to find a total.

Example: If you have 8 apples and you buy 5 more, how many do you have?

Start at 8 and count forward 5 steps: 9, 10, 11, 12, 13.
The answer is 13.

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Ages 6-7

Topic: Addition within 20

1. What is 7 + 6?

A) 11

B) 13

C) 12

D) 14

2. Which number is even?

A) 3

B) 9

C) 8

D) 15

3. What is 9 + 4?

A) 12

B) 13

C) 14

D) 15

4. Fill in the blank: 12 + ___ = 15

A) 2

B) 3

C) 4

D) 5

5. If you have 11 pens and get 7 more, how many do you have?

A) 17

B) 18

C) 19

D) 20

Ages 8-9

Topic: Fractions (Halves, Thirds, Quarters)

A fraction is a part of a whole. The top number (numerator) tells us how many parts we have. The bottom number (denominator) tells us how many equal parts make the whole.

Example: Which is larger, 1/2 or 1/4?

Think of a pizza. 1/2 is half the pizza. 1/4 is only a small slice. So, 1/2 is larger.

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Ages 8-9

Topic: Fractions (Halves, Thirds, Quarters)

1. What is 1/2 of 20?

A) 5

B) 10

C) 15

D) 2

2. How many cm are in 2 metres?

A) 20cm

B) 200cm

C) 2000cm

D) 2cm

3. What is 1/4 of 12?

A) 2

B) 3

C) 4

D) 6

4. Which fraction is the same as one whole?

A) 1/2

B) 4/4

C) 1/4

D) 3/4

5. What is 1/3 + 1/3?

A) 2/3

B) 1/6

C) 2/6

D) 1/3

Ages 10-11

Topic: BIDMAS (Order of Operations)

When a calculation has many different signs, we must solve it in a specific order: Brackets, Indices, Division/Multiplication, Addition/Subtraction.

Example: 5 + 2 x 3 = ?

Multiplication comes before Addition.
2 x 3 = 6.
5 + 6 = 11.

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Ages 10-11

Topic: BIDMAS (Order of Operations)

1. Solve: (10 - 2) x 5

A) 40

B) 48

C) 10

D) 35

2. Calculate the area of a rectangle that is 8cm long and 5cm wide.

Answer: _______________________

3. Solve: 20 - 4 x 2

A) 32

B) 12

C) 16

D) 8

4. Solve: 3 x (4 + 6)

A) 30

B) 18

C) 24

D) 40

5. What is the value of 2³ + 5?

A) 11

B) 13

C) 15

D) 10

Ages 12-13

Topic: Introduction to Algebra

Algebra uses letters to represent numbers we don't know yet. To "solve" an equation, we want to get the letter on its own on one side of the equals sign.

Example: Solve 2x + 4 = 12

1. Subtract 4 from both sides: 2x = 8
2. Divide by 2: x = 4.

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Ages 12-13

Topic: Introduction to Algebra

1. Simplify: 3a + 2b - a + 4b

A) 4a + 6b

B) 2a + 6b

C) 2a + 2b

D) 4a + 2b

2. If x = 5, what is the value of 3x²?

Answer: _______________________

3. Solve for y: 3y - 5 = 10

Answer: _______________________

4. Factorise: 4x + 8

A) 4(x+2)

B) 2(2x+4)

C) 4x(1+2)

D) 8(x+1)

5. If p = 4 and q = 2, what is 2p + 3q?

A) 12

B) 14

C) 10

D) 16

Ages 14-16

Topic: Pythagoras' Theorem

In a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. The formula is: a² + b² = c².

Example: A triangle has sides of 3cm and 4cm. What is the longest side (hypotenuse)?

3² + 4² = c²
9 + 16 = 25
√25 = 5cm.

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Ages 14-16

Topic: Pythagoras' Theorem

1. Solve the simultaneous equations: 2x + y = 7 and x - y = 2

A) x=3, y=1

B) x=2, y=3

C) x=5, y=-3

D) x=4, y=-1

2. Calculate the length of the diagonal of a rectangle with sides 5m and 12m.

Answer: _______________________

3. A ladder 10m long leans against a wall. The bottom is 6m from the wall. How high up the wall does it reach?

Answer: _______________________

Ages 14-16

Topic: Pythagoras' Theorem

4. Find the length of the side 'c' (hypotenuse) if a = 6 and b = 8.

A) 10

B) 14

C) 12

D) 100

5. Solve the quadratic equation: x² - 5x + 6 = 0

A) x=2, 3

B) x=-2, -3

C) x=1, 6

D) x=-1, -6