GCSE: Algebra & Solving Linear Equations

Dr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified: 24th August 2013

Algebra Common MishapsEither answer the following or identify the mistake made.

(𝑎+𝑏 )2=𝑎2+2𝑎𝑏+𝑏2

𝑎−𝑏 (𝑐−𝑑 )=𝑎−𝑏𝑐+𝑏𝑑

3𝑎+4𝑏+4

→3 𝑎𝑏

𝑎+3=2𝑛−34

→ 4𝑎+3=2𝑛−3

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(𝑎−𝑏)2=𝑎2−2𝑎𝑏+𝑏2?

Algebraic Simplification Revision

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1

2

3456

7

8

9

10

1213

141516

17

1819

20

3 𝑥 (2 𝑥+5 )=6𝑥2+15 𝑥11 ?

Solving Linear Equations

𝟐𝒂+𝟑 (𝟐−𝟑𝒂 )=𝟑−𝒂

𝒂=𝟏𝟐?

a) b) c) d) e) f) g)

h) i) j) k)

l)

m) n)

o)

x = 2y = -2t=-1y = 5x = -2x = 1

y = -2z = 0x = 7y= -10

x = -2

x=-1

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Solving Linear Equations

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Setting up equationsPeople in the left row work on this:

People in the middle row work on this:

People in in the right row work on this:

Your mum’s age in 6 years time is 3 times as much as it was 6 years ago. How old is your mum?

𝑥

235−3𝑥𝑥−10

The area of the shape is twice its perimeter. Determine

𝟐 𝒙

𝒙

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GCSE Questions

𝑥=39 °?

June 2012

GCSE Questions

𝐴=42m2?

GCSE Questions

𝑥=32?

June 2013

A* Question

𝐴𝑟𝑒𝑎=𝟏𝟏𝒙𝟐?

Exercises

Edexcel GCSE Mathematics Textbook

Page 146 – Exercise 10BQ2, 3, 9, 11-14

Solving Equations involving Fractions

Töten die Fraktionen!!

The first thing you always do whenever you see an equation involving fractions:

Multiply through by the denominator(s), so no fractions!

Solving Equations involving Fractions

16−𝑥4

=1−𝑥 𝑥=−4?

2𝑥−12

−𝑥−53

=54 𝑥=

18?

Solving Equations involving Fractions

𝑥2=𝑥−3 𝑥=6?

3𝑥−42

+2𝑥+15

=8−𝑥3𝑥=2?

Exercises

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2

3

4

5

6

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