Comprehensive assessment covering all 20 lessons. Mixed practice from variables to indices.
Question 16 3 marks
(a) If $a = 3$ and $b = 4$, evaluate $2a + 3b$. 1 mark
(b) Simplify $5x + 3y - 2x + y$. 1 mark
(c) Simplify $3x \times 4x$. 1 mark
(a) $2(3) + 3(4) = 6 + 12 = 18$ [1]
(b) $3x + 4y$ [1]
(c) $12x^2$ [1]
Question 17 4 marks
(a) Expand $4(x + 3)$. 1 mark
(b) Expand and simplify $2(x + 5) + 3(x - 2)$. 2 marks
(c) Factorise $8x + 12$. 1 mark
(a) $4x + 12$ [1]
(b) $2x + 10 + 3x - 6 = 5x + 4$ [2]
(c) $4(2x + 3)$ [1]
Question 18 4 marks
Solve these equations:
(a) $x + 7 = 15$ 1 mark
(b) $3x = 27$ 1 mark
(c) $2x + 5 = 17$ 1 mark
(d) $4x - 3 = 2x + 9$ 1 mark
(a) $x = 8$ [1]
(b) $x = 9$ [1]
(c) $2x = 12$, $x = 6$ [1]
(d) $2x = 12$, $x = 6$ [1]
Question 19 4 marks
(a) Evaluate $3^3$. 1 mark
(b) Simplify $x^4 \times x^6$. 1 mark
(c) Simplify $x^{10} \div x^3$. 1 mark
(d) Simplify $(x^2)^3$. 1 mark
(a) $27$ [1]
(b) $x^{10}$ [1]
(c) $x^7$ [1]
(d) $x^6$ [1]
Question 20 5 marks
A plumber charges a call-out fee of $\$50$ plus $\$40$ per hour.
(a) Write an expression for the total cost $C$ for $h$ hours of work. 1 mark
(b) What is the cost for 3 hours? 1 mark
(c) If the total bill was $\$210$, how many hours did the plumber work? 2 marks
(d) Why can $h$ not be negative in this context? 1 mark
(a) $C = 50 + 40h$ [1]
(b) $C = 50 + 40(3) = 50 + 120 = \$170$ [1]
(c) $210 = 50 + 40h$ [1]. $160 = 40h$, $h = 4$ hours [1]
(d) Time cannot be negative [1]