Year 9 Algebra Worksheet - Beginner

Year 9 Algebra worksheet for Year 9 (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

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Year 9 Algebra: Expand, Solve and Sketch

Ages 13–14 • Beginner • UK National Curriculum

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Instructions: Work through each section, showing clear algebraic steps. Use the boxes for answers and working; check your results by substituting them back into the original equations where possible. For the graph task, use the axes provided in the question description and label key points clearly.

Expand and Simplify Double Brackets

Multiply every term in the first bracket by every term in the second bracket. Then collect like terms. For example, (x + 2)(x + 3) = x² + 5x + 6.

Expand and simplify. Show your working.

1. (x + 2)(x + 4)

2. (x + 3)(x − 2)

3. (x − 1)(x − 5)

4. (2x + 1)(x + 3)

Solve Simultaneous Equations

Find the pair of values that makes both equations true. For the first question, add the equations to eliminate y; then substitute your value into one equation to find y. Check each pair in both equations.

Solve each pair of simultaneous equations. Give your answers as x = … and y = … .

1. x + y = 10

x − y = 2

2. 2x + y = 11

x + y = 7

3. x + 2y = 11

x − y = 2

Solve Linear Inequalities

Solve each inequality as you would solve an equation. Remember to reverse the inequality sign if you multiply or divide both sides by a negative number. State any integer solutions requested.

Solve each inequality.

1. 3x + 2 < 14

2. 5 − 2x ≤ 11

3. 4x − 7 ≥ 9

4. 2x + 1 < 8. Write all integer solutions.

Rearrange Formulae

Make the named letter the subject by performing the same operation on both sides. Undo addition or subtraction first, then multiplication or division. Check your rearrangement by substituting simple values.

Rearrange each formula to make the named letter the subject.

1. y = 3x + 5; make x the subject.

2. P = 2l + 2w; make l the subject.

3. v = u + at; make t the subject.

4. A = bh; make h the subject.

Recognise Quadratic Graphs

A quadratic graph has an x² term and is usually a U-shaped curve or an upside-down U. Use the table of values to recognise the graph, then describe its shape and turning point. For Question 3, make a neat sketch on your own axes, marking the listed coordinates and joining them with a smooth curve.

1. Which equation is quadratic?

2. For y = x², complete the values when x = −2, −1, 0, 1, 2: y = 4, 1, 0, 1, 4. Is the graph U-shaped or upside-down U-shaped?

3. Sketch y = x² − 1 using the points (−2, 3), (−1, 0), (0, −1), (1, 0), (2, 3). Label the turning point.

4. For y = −x² + 4, state whether the graph opens upwards or downwards, and give its turning point.

Answer Key

Activity 1: 1. x² + 6x + 8 ; 2. x² + x − 6 ; 3. x² − 6x + 5 ; 4. 2x² + 7x + 3

Activity 2: 1. x = 6, y = 4 ; 2. x = 4, y = 3 ; 3. x = 5, y = 3

Activity 3: 1. x < 4 ; 2. x ≥ −3 ; 3. x ≥ 4 ; 4. x < 3.5; integer solutions: …, −2, −1, 0, 1, 2, 3

Activity 4: 1. x = (y − 5)/3 ; 2. l = (P − 2w)/2 ; 3. t = (v − u)/a ; 4. h = A/b

Activity 5: 1. y = x² − 4 ; 2. U-shaped ; 3. Smooth U-shaped curve through the given points, with turning point (0, −1) ; 4. Opens downwards; turning point (0, 4)