Year 7 Algebra Worksheet - Beginner

Year 7 Algebra worksheet for Year 7 (Key Stage 3 / Year 7-9 (Ages 11-14)). Beginner 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)•Algebrabeginner

9 views

Year 7 Algebra: Build, Substitute, Solve and Sequence

Key Stage 3 · Ages 11–12 · Beginner

Name:

Date:

Score:

Instructions: Work through the activities in order. Use the worked examples and show your steps in the answer spaces. Check that your simplified expressions, substitutions, equation solutions and sequence rules match the question.

Write and Simplify Expressions

Use letters to represent unknown numbers. Remember that 4a means 4 × a. Collect like terms by adding or subtracting the coefficients of terms with the same letter; do not combine unlike terms. For example, 3x + 2x = 5x.

1. Write an algebraic expression for 5 more than n.

2. Simplify 3a + 4a.

3. Simplify 8y − 3y + 2.

4. Simplify 2p + 5 + 3p + 1.

5. Simplify 7m − 2 + m − 4.

Substitute into Expressions

Replace each letter with the given value, then calculate using the correct order of operations. Put the substituted numbers in brackets if that helps you keep track. For example, if x = 3, then 2x + 1 = 2 × 3 + 1 = 7.

1. Find 3a + 2 when a = 4.

2. Find 2b − 5 when b = 6.

3. Find c² + 1 when c = 3.

4. The formula P = 2l + 2w gives the perimeter of a rectangle. Find P when l = 5 cm and w = 3 cm.

Solve One-Step Equations

Find the value of the letter that makes each equation true. Use the inverse operation to undo what has been done to the letter. Check your answer by substituting it back into the original equation.

1. x + 7 = 15

2. y − 4 = 9

3. 5a = 30

4. b ÷ 3 = 6

Solve Two-Step Equations

Undo the addition or subtraction first, then undo the multiplication or division. Keep each step clear and check your solution in the original equation. One example is 2x + 3 = 11: subtract 3, then divide by 2.

1. 2x + 3 = 13

2. 3y − 4 = 11

3. 5a + 2 = 22

4. 4b − 7 = 9

Generate and Describe Sequences

Look at how the terms change from one term to the next. Write the next terms by continuing the same rule. To describe a term-to-term rule, say what operation takes one term to the next.

1. Continue the sequence with the next two terms: 3, 6, 9, 12, ___, ___.

2. Continue the sequence with the next two terms: 20, 17, 14, 11, ___, ___.

3. Write the term-to-term rule for: 4, 9, 14, 19, …

4. A sequence starts at 2 and the term-to-term rule is “multiply by 2”. Write the first five terms.

Answer Key

Activity 1: n + 5 ; 7a ; 5y + 2 ; 5p + 6 ; 8m − 6

Activity 2: 14 ; 7 ; 10 ; 16 cm

Activity 3: x = 8 ; y = 13 ; a = 6 ; b = 18

Activity 4: x = 5 ; y = 5 ; a = 4 ; b = 4

Activity 5: 15, 18 ; 8, 5 ; Add 5 ; 2, 4, 8, 16, 32