Covers Lessons 8–17: Expanding, factorising and solving equations.
Question 9 3 marks
(a) Expand and simplify: $2(x + 3) + 3(x + 2)$ 2 marks
(b) Factorise: $6x + 9$ 1 mark
(a) $2x + 6 + 3x + 6 = 5x + 12$ [2]
(b) $3(2x + 3)$ [1]
Question 10 3 marks
Solve these equations, showing all working:
(a) $3x + 5 = 20$ 1 mark
(b) $2(x + 4) = 18$ 1 mark
(c) $5x - 3 = 2x + 9$ 1 mark
(a) $3x = 15$, so $x = 5$ [1]
(b) $x + 4 = 9$, so $x = 5$ [1]
(c) $3x = 12$, so $x = 4$ [1]
Question 11 4 marks
Three consecutive numbers add up to 45. Let the first number be $n$.
(a) Write an expression for the sum of the three numbers. 1 mark
(b) Write an equation and solve for $n$. 2 marks
(c) What are the three numbers? 1 mark
(a) $n + (n + 1) + (n + 2)$ or $3n + 3$ [1]
(b) $3n + 3 = 45$ [1]. $3n = 42$, so $n = 14$ [1]
(c) 14, 15, 16 [1]