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Simplifying algebra

Free Printable Simplifying algebra PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 2)

Download free simplifying algebra worksheets (PDF), GCSE maths past paper questions and worked solutions for Simplifying algebra (2F). This is a Grade 2 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, Dr Austin, Maths4EveryOne, Metatutor, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our simplifying algebra revision notes and worked examples with diagrams, try real GCSE past paper simplifying algebra questions with step-by-step solutions, or download a PDF of all simplifying algebra worksheet links.

Free Simplifying algebra PDF Worksheets & Answers

Grade 2 • Topic 2F
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GCSE Maths Grade 2 Revision Notes & Method

Guide to Simplifying algebra: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To simplify by collecting like terms, group terms that have the exact same letter and power (note that x and x2 are not like terms). Always keep the + or − sign immediately in front of each term attached to that term when grouping.

When multiplying algebraic terms, multiply the numbers in front (coefficients) first, then write the letters together in alphabetical order (remembering m × m = m2). When dividing, divide the coefficients and cancel common letters.

Example 1: Simplify:
(a) 5a + 3b − 2a + 4b   (b) 4x2 − 3x + 2x2 − 5x

Solution:

(a) Group the a terms and b terms with their signs:
• (5a − 2a) + (3b + 4b) = 3a + 7b
(b) Group x2 terms and x terms separately:
• (4x2 + 2x2) + (−3x − 5x) = 6x2 − 8x

Example 2: Simplify:
(a) 4p × 3q   (b) 5m × 3m   (c) 18y2 ÷ 6y

Solution:

(a) 4 × 3 = 12, and p × q = pq → 12pq
(b) 5 × 3 = 15, and m × m = m2 → 15m2
(c) 18y26y: 18 ÷ 6 = 3 and y2 ÷ y = y → 3y
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Simplifying algebra Questions & Answers

Past Paper Example 1 GCSE Nov 2023 3F Q13 2 marks
(a) Simplify 8h³ + 14h³ – 2h³ (1) (b) Simplify (9y + 12y) ÷ 3 (1)
(a) Simplify 8h3 + 14h3 - 2h3 [1 mark]
(b) Simplify (9y + 12y) ÷ 3 [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
20h³
Answer (a): 20h3
Part (b) Solution:
21y ÷ 3 = 7y B1
Answer (b): 7y
Past Paper Example 2 GCSE Nov 2017 2F Q3 3 marks
Work out
(a) Simplify 3f × 5g (1) (b) Simplify t × t (1) (c) Simplify (2n + 6n) / 2 (1)
(a) Simplify 3f × 5g [1 mark]
(b) Simplify t × t [1 mark]
(c) Simplify 2n + 6n2 [1 mark]
Worked Solution & Mark Scheme (3 marks)
Part (a) Solution:
3 × 5 × f × g = 15fg B1
Answer (a): 15fg
Part (b) Solution:
t × t = t² B1
Answer (b): t2
Part (c) Solution:
8n ÷ 2 = 4n B1
Answer (c): 4n n
Past Paper Example 3 GCSE Jun 2018 1F Q6 2 marks
(a) Simplify 3 × 4t (1) (b) Simplify 8a – 3a + 2a (1)
(a) Simplify 3 × 4t [1 mark]
(b) Simplify 8a - 3a + 2a [1 mark]
Worked Solution & Mark Scheme (2 marks)
Part (a) Solution:
3 × 4t = 12t B1
Answer (a): 12t
Part (b) Solution:
(8 – 3 + 2)a = 7a B1
Answer (b): 7a

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