Year 7 Algebra Worksheet - Intermediate

Year 7 Algebra worksheet for Year 7 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Algebraintermediate

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Year 7 Algebra: Expressions, Equations and Sequences

Ages 11–12 | Intermediate | UK National Curriculum

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Instructions: Work through each activity, showing clear steps in the answer spaces. Use the algebraic rules you know, and check your answers by substituting them back where possible. Give each answer in its simplest form.

Write and Simplify Expressions

Use letters to represent unknown numbers. In questions 1–3, write an algebraic expression from the words. In questions 4–5, collect like terms and simplify.

1. Write an expression for 7 more than n.

2. Write an expression for 4 times p.

3. Write an expression for the total of x and twice y.

4. Simplify 3a + 5a.

5. Simplify 6m + 2 − 3m + 5.

Substitute into Expressions and Formulae

Replace each letter with the given value, then calculate carefully. Remember that multiplication is usually written without a multiplication sign, so 4a means 4 × a.

1. Find 3x + 4 when x = 5.

2. Find 2a + b when a = 6 and b = 3.

3. Find 5p − 2 when p = 4.

4. The formula for the perimeter of a rectangle is P = 2l + 2w. Find P when l = 7 cm and w = 3 cm.

Solve One-Step Equations

Find the value of x in each equation. Use the inverse operation to undo the operation applied to x, and check your solution in the original equation.

1. x + 8 = 19

2. x − 6 = 13

3. 5x = 35

4. x ÷ 4 = 6

Solve Two-Step Equations

Undo the addition or subtraction first, then undo the multiplication or division. Show your working and check each solution by substituting it into the original equation.

1. 2x + 3 = 15

2. 3x − 4 = 17

3. 4x + 5 = 29

4. 5x − 6 = 24

Generate and Describe Sequences

Write the missing terms in each sequence. For question 4, describe the change from one term to the next using a term-to-term rule.

1. Continue the sequence with the next three terms: 4, 7, 10, 13, ___, ___, ___.

2. Continue the sequence with the next three terms: 30, 26, 22, 18, ___, ___, ___.

3. The sequence starts at 5 and increases by 6 each time. Write the first four terms.

4. State the term-to-term rule for: 2, 6, 10, 14, 18.

Algebra in Context

Translate each situation into an equation, then solve it. Let x stand for the unknown number or quantity. Include the value and units where appropriate.

1. A number increased by 9 is 21. Find the number x.

2. Three identical notebooks cost £12 altogether. Let x be the cost of one notebook in pounds. Write an equation and find x.

3. A taxi fare is £4 plus £2 for each mile. The total fare is £16. Let m be the number of miles. Write an equation and find m.

Answer Key

Activity 1: n + 7 ; 4p ; x + 2y ; 8a ; 3m + 7

Activity 2: 19 ; 15 ; 18 ; 20 cm

Activity 3: x = 11 ; x = 19 ; x = 7 ; x = 24

Activity 4: x = 6 ; x = 7 ; x = 6 ; x = 6

Activity 5: 16, 19, 22 ; 14, 10, 6 ; 5, 11, 17, 23 ; Add 4

Activity 6: x + 9 = 21, x = 12 ; 3x = 12, x = £4 ; 4 + 2m = 16, m = 6 miles