Year 8 Algebra Worksheet - Beginner

Year 8 Algebra worksheet for Year 8 (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

8 views

Year 8 Algebra: Expand, Solve and Graph

Ages 12–13 · Beginner · UK National Curriculum

Name:

Date:

Score:

Instructions: Work through each activity in order, showing clear working in the answer spaces. Use the examples and tables to check your method, then apply your algebra skills to the final graph task.

Expand and Factorise

To expand a bracket, multiply the term outside by every term inside: for example, 3(x + 4) = 3x + 12. To factorise, take out the highest common factor: for example, 5x + 15 = 5(x + 3). Complete each expression and show your working.

1. Expand 3(x + 4).

2. Expand 2(3x − 5).

3. Factorise 4x + 20.

4. Factorise 6x − 18.

Solve Equations

Solve each equation by keeping both sides balanced. Collect the x terms on one side and the number terms on the other; when brackets appear, expand them first. Check each solution by substituting it into the original equation.

1. 3x + 5 = 2x + 12

2. 5x − 4 = 2x + 11

3. 2(x + 3) = 14

4. 3(x − 2) = x + 6

Find the nth Term

For a linear sequence, the common difference is the coefficient of n. Find the constant term by comparing the first sequence term with the value of that coefficient when n = 1. Write each rule in the form “nth term = …”.

1. Sequence: 4, 7, 10, 13, … Find the nth term.

2. Sequence: 9, 13, 17, 21, … Find the nth term.

3. Sequence: 12, 10, 8, 6, … Find the nth term.

4. Sequence: 5, 11, 17, 23, … Find the nth term.

Read Gradient and Intercept

In the equation y = mx + c, m is the gradient and c is the y-intercept. Identify both values for each line. The intercept is the value of y when x = 0.

1. y = 2x + 3. Gradient, m = y-intercept, c =

2. y = 4x − 1. Gradient, m = y-intercept, c =

3. y = −x + 5. Gradient, m = y-intercept, c =

4. y = ½x + 2. Gradient, m = y-intercept, c =

Make a Table of Values

Use the pre-filled x-values to calculate each missing y-value from the rule y = 2x + 1. Show your substitutions in the answer spaces. Remember that when x = 0, y is the y-intercept.

x	−1	0	1	2
y

1. When x = −1, calculate y.

2. When x = 0, calculate y.

3. When x = 1, calculate y.

4. When x = 2, calculate y.

Plot and Interpret a Straight-Line Graph

For the rule y = 2x + 1, calculate the coordinates using your table in Activity 5, then plot the points on graph paper and join them with a straight line. Use the plotted line to identify the gradient and y-intercept. The coordinates and interpretation questions are answerable in the spaces provided.

1. Write the four coordinates for x = −1, 0, 1 and 2, in that order.

2. What is the gradient of y = 2x + 1?

3. What is the y-intercept of y = 2x + 1?

4. On your line, what is y when x = 3?

Answer Key

Activity 1: 3x + 12 ; 6x − 10 ; 4(x + 5) ; 6(x − 3)

Activity 2: x = 7 ; x = 5 ; x = 4 ; x = 6

Activity 3: 3n + 1 ; 4n + 5 ; −2n + 14 ; 6n − 1

Activity 4: 1. m = 2, c = 3 ; 2. m = 4, c = −1 ; 3. m = −1, c = 5 ; 4. m = ½, c = 2

Activity 5: 1 ; 1 ; 3 ; 5

Activity 6: (−1, −1), (0, 1), (1, 3), (2, 5) ; gradient 2 ; y-intercept 1 ; y = 7