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Rearranging (harder)

Free Printable Rearranging (harder) PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 7)

Download free rearranging (harder) worksheets (PDF), GCSE maths past paper questions and worked solutions for Rearranging (harder) (7H). This is a Grade 7 algebra topic from the GCSE questions by topic collection for 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, Maths4Everyone, Corbett Maths, Maths Made Easy, Dr Frost, Naiker Maths, Maths Takeaway, Maths DIY, Dr Austin, Metatutor, E Classroom and PMT, along with past paper question booklets.

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

Free Rearranging (harder) PDF Worksheets & Answers

Grade 7 • Topic 7H
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
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GCSE 9–1 practice booklet & solutions
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Practice Questions & answers
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Textbook Exercise & answers
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MME worksheet & model answers
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GCSE worksheet & solutions
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Exam question booklet & solutions
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GCSE Maths Takeaway exam questions
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Exam-style booklet & solutions
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Practice grid / worksheet & answers
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Topic worksheet & worked solutions
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Online topic notes & examples
 Page
Interactive online lesson & practice
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Grade 7 topics
7A - Surds7B - Bounds
7C - Proportion (harder)7D - Algebraic fractions
7E - The quadratic formula7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs7H - Rearranging (harder)
7J - Functions (harder)7K - Iteration
7L - Area of any triangle7M - The sine rule
7N - The cosine rule7P - Congruent triangles
7Q - 3D pythagoras / trig.7R - Histograms
7S - Conditional probability7T - Exact trig. values (harder)
7U - Area of a segment
GCSE Maths Grade 7 Revision Notes & Method

Guide to Rearranging (harder): Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

When the letter you want to make the subject appears more than once in a formula, follow this standard 4-step method: (1) multiply out any fractions and expand brackets; (2) move all terms containing the target letter to one side and all other terms to the opposite side; (3) factorise out the target letter as a single common factor; (4) divide by the bracket.

If the target letter is trapped inside a square root or power, isolate the root or power term before squaring or taking roots of both sides.

Example 1: Make x the subject of y = 3x + 2x − 4

Solution:

Multiply by (x − 4): y(x − 4) = 3x + 2
Expand bracket: xy − 4y = 3x + 2
Collect x terms on left: xy − 3x = 4y + 2
Factorise out x: x(y − 3) = 4y + 2
Answer: x = 4y + 2y − 3

Example 2: Make m the subject of T = 2√(m + 1m − 3)

Solution:

Square both sides: T2 = 4(m + 1m − 3)
Multiply & expand: T2m − 3T2 = 4m + 4
Collect m terms: m(T2 − 4) = 3T2 + 4
Answer: m = 3T2 + 4T2 − 4
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Rearranging (harder) Questions & Answers

Past Paper Example 1 IGCSE Nov 2023 1H Q15 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
Make n the subject of the formula x = 3p + n3n - 4
Worked Solution & Mark Scheme (3 marks)
x(3n − 4) = 3p + n M1
⇒ 3nx − 4x = 3p + n
⇒ 3nx − n = 3p + 4x M1
⇒ n(3x − 1) = 3p + 4x
⇒ n = (3p + 4x)/(3x − 1). A1
Answer: n = n = 3p + 4x3x - 1
Past Paper Example 2 GCSE Nov 2024 1F Q25 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Make w the subject of the formula y = 3w - 10
Worked Solution & Mark Scheme (2 marks)
y + 10 = 3w M1
⇒ w = (y + 10)/3 A1
Answer: w = w = y + 103
Past Paper Example 3 IGCSE Nov 2024 1F Q11 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
Make d the subject of the formula c = 8d + 5
Worked Solution & Mark Scheme (2 marks)
c − 5 = 8d M1
⇒ d = (c − 5) / 8 A1
Answer: d = d = c - 58

← 7G Trigonometric & exp. Graphs

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