GCSE Maths · Higher · Chapter 15: Equations and inequalities · Lesson 1

Linear equations

Grades 4–7About 50 minutesNo calculator44 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Solve $\frac{x}{2} - 6 = 5$ .
[1 mark]
Answer
A2
From chapter 12
A shape of area 16 cm $^{2}$ is enlarged by length scale factor 3. Find the new area.
[1 mark]
Answer
A3
Last lesson
Write $46000$ in standard form.
[1 mark]
Answer
A4
Key Stage 3
How many minutes are in $0.2$ of an hour?
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Solve $\frac{x + 5}{4} = 3$ .

Hint Multiply both sides by 4 first, then undo the

+ 5

Example 2

Solve $4 (x + 2) = 7 x - 13$ .

Hint Expand the bracket. Then collect the

x

terms on the side with more

x

Grades 5–6

C3
Solve $\frac{x + 1}{3} = \frac{x + 9}{5}$ .
[2 marks]
Answer
C4
The equation $3 (x + k) = x + 20$ has the solution $x = 4$ . Work out the value of $k$ .
[2 marks]
Answer
C5
Solve $\frac{x}{3} + \frac{x}{4} = 14$ .
[2 marks]
Answer
C6
Solve $5 x + 3 = 2 x + 8$ . Give your answer as a fraction.
[2 marks]
Answer
C7
The diagram shows three angles on a straight line. Work out the size of the largest angle.
[3 marks]
Not drawn accurately
Answer
C8
The sum of three consecutive odd numbers is $147$ . Work out the largest of the three numbers.
[2 marks]
Answer

Grades 6–7

D1
Max solves $2 x + 9 = 5 x - 6$ . He writes, " $2 x - 5 x = 9 - 6$ , so $- 3 x = 3$ and $x = - 1$ ."
Explain what Max has done wrong, and solve the equation correctly.
[3 marks]
Answer

D2
Gym A charges a joining fee of £40 and then £18 a month. Gym B charges a joining fee of £10 and then £24 a month.
(a)
Write an expression for the cost, in pounds, of Gym A for $m$ months.
[1 mark]
Answer
(b)
Work out the number of months for which the two gyms cost the same.
[3 marks]
Answer
(c)
Ana joins a gym for 12 months. Which gym is cheaper for her, and by how much?
[2 marks]
AnswerGym $\dots\dots$ by £ $\dots\dots$
Total for D2: 6 marks
D3
The rectangle and the equilateral triangle have the same perimeter. Work out the area of the rectangle.
[4 marks]
Not drawn accurately
Answer

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can solve an equation with a fraction, a bracket or the unknown on both sides.
I can write an equation from words or a diagram and solve it.

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