Covers Lessons 18–20: Index laws and mixed practice from the whole unit.
Question 9 3 marks
(a) Evaluate $2^4$. 1 mark
(b) Simplify $x^3 \times x^5$. 1 mark
(c) Simplify $x^8 \div x^2$. 1 mark
(a) $2^4 = 2 \times 2 \times 2 \times 2 = 16$ [1]
(b) $x^3 \times x^5 = x^{3+5} = x^8$ [1]
(c) $x^8 \div x^2 = x^{8-2} = x^6$ [1]
Question 10 3 marks
Expand and simplify: $3(2x + 1) - 2(x - 4)$
$6x + 3 - 2x + 8$ [2]
$= 4x + 11$ [1]
Question 11 4 marks
(a) Solve $4x - 7 = 2x + 5$. 2 marks
(b) The perimeter of a rectangle is 36 cm. The length is 4 cm more than the width. Find the dimensions. 2 marks
(a) $2x = 12$, so $x = 6$ [2]
(b) Let width = $w$. Length = $w + 4$. $2w + 2(w + 4) = 36$ [1]. $4w + 8 = 36$, $w = 7$ cm, length = 11 cm [1]