This quiz covers all 20 lessons of Unit 2. It includes 15 multiple choice questions, 3 short answer questions and 1 extended response. Show all working for full marks.
❓ Multiple Choice (15 questions)
1. Simplify $4x + 3y + 2x - y$.
2. Expand $2(3x + 5)$.
3. Factorise $x^2 - 9$.
4. Solve $x + 8 = 15$.
5. Solve $3x - 7 = 14$.
6. Expand and simplify $(x + 2)(x + 3)$.
7. Solve $\dfrac{x}{4} - 3 = 2$.
8. Solve $-2x + 5 \leq 11$.
9. The 10th term of the sequence 2, 5, 8, 11, ... is:
10. Make $x$ the subject of $y = 2x + 3$.
11. Factorise fully $3x^2 - 12$.
12. Solve $5(x - 2) = 3(x + 4)$.
13. The sum of three consecutive numbers is 72. The smallest number is:
14. Solve $\dfrac{2x + 1}{3} - \dfrac{x - 2}{2} = 4$.
15. A pattern of dots has 6 dots in figure 1, 10 in figure 2, 14 in figure 3. How many in figure 20?
✍ Short Answer (3 questions)
16. Algebra and equations.
(a) Simplify $3(x + 2) - 2(x - 1)$. (2 marks)
(b) Solve $\dfrac{3x - 1}{2} = 7$. (2 marks)
(c) Solve $4 - 3x > 13$. (2 marks)6 MARKS
17. Patterns and formulas.
(a) Find the rule for the nth term of the sequence 8, 13, 18, 23, ... (2 marks)
(b) Using your rule, find the 25th term. (1 mark)
(c) Make $r$ the subject of $C = 2\pi r$. (2 marks)5 MARKS
18. Problem solving.
(a) A rectangle has a length that is 3 cm more than its width. The perimeter is 46 cm. Find the dimensions. (3 marks)
(b) A taxi charges a \$5 flag fall plus \$2.50 per kilometre. If the fare is \$30, how many kilometres did the passenger travel? (2 marks)5 MARKS
✍ Extended Response
19. A gardener plants trees in rows. Row 1 has 5 trees, row 2 has 9 trees, row 3 has 13 trees, and so on, increasing by 4 trees each row.
(a) Find the rule for the number of trees in row $n$. (2 marks)
(b) How many trees are in row 15? (1 mark)
(c) Which row has exactly 45 trees? Show your working. (2 marks)
(d) Explain why it is impossible to have exactly 50 trees in a row. (2 marks)
(e) The gardener wants to plant 200 trees in total across the first $n$ rows. Set up an equation and determine if this is possible. (3 marks)10 MARKS
1. C — $4x + 2x + 3y - y = 6x + 2y.
2. A — $2 \times 3x + 2 \times 5 = 6x + 10.
3. B — Difference of two squares: $(x + 3)(x - 3)$.
4. C — $x = 15 - 8 = 7.
5. A — $3x = 21 \Rightarrow x = 7.
6. B — $x^2 + 3x + 2x + 6 = x^2 + 5x + 6.
7. A — $\dfrac{x}{4} = 5 \Rightarrow x = 20.
8. C — $-2x \leq 6 \Rightarrow x \geq -3 (flip sign).
9. B — $T_n = 3n - 1$. $T_{10} = 30 - 1 = 29.
10. A — $2x = y - 3 \Rightarrow x = \dfrac{y - 3}{2}.
11. C — $3(x^2 - 4) = 3(x + 2)(x - 2).
12. B — $5x - 10 = 3x + 12 \Rightarrow 2x = 22 \Rightarrow x = 11.
13. A — $n + (n+1) + (n+2) = 72 \Rightarrow 3n + 3 = 72 \Rightarrow n = 23.
14. B — Multiply by 6: $2(2x+1) - 3(x-2) = 24 \Rightarrow 4x + 2 - 3x + 6 = 24 \Rightarrow x = 16.
15. C — $T_n = 4n + 2$. $T_{20} = 80 + 2 = 82.
Q16 (6 marks): (a) $3x + 6 - 2x + 2 = x + 8$ [2]. (b) $3x - 1 = 14 \Rightarrow 3x = 15 \Rightarrow x = 5$ [2]. (c) $-3x > 9 \Rightarrow x < -3$ (flip sign) [2].
Q17 (5 marks): (a) Common difference = 5, first term = 8. $T_n = 5n + 3$ [2]. (b) $T_{25} = 5(25) + 3 = 128$ [1]. (c) $r = \dfrac{C}{2\pi}$ [2].
Q18 (5 marks): (a) Let $w$ = width. $2(w + w + 3) = 46 \Rightarrow 2(2w + 3) = 46 \Rightarrow 2w + 3 = 23 \Rightarrow 2w = 20 \Rightarrow w = 10$ cm, length = 13 cm [3]. (b) $5 + 2.5k = 30 \Rightarrow 2.5k = 25 \Rightarrow k = 10$ km [2].
Q19 (10 marks):
(a) Sequence 5, 9, 13, ... (common difference 4). $T_n = 4n + 1$ [2].
(b) $T_{15} = 4(15) + 1 = 60 + 1 = 61$ trees [1].
(c) $4n + 1 = 45 \Rightarrow 4n = 44 \Rightarrow n = 11$. Row 11 has 45 trees [2].
(d) $4n + 1 = 50 \Rightarrow 4n = 49 \Rightarrow n = 12.25$. This is not a whole number, so it is impossible to have exactly 50 trees in a row [2].
(e) Sum of first $n$ terms: $S_n = \dfrac{n}{2}(2a + (n-1)d) = \dfrac{n}{2}(10 + 4(n-1)) = \dfrac{n}{2}(4n + 6) = n(2n + 3) = 200$.
$2n^2 + 3n - 200 = 0$. Using the quadratic formula: $n = \dfrac{-3 + \sqrt{9 + 1600}}{4} = \dfrac{-3 + \sqrt{1609}}{4} = \dfrac{-3 + 40.11}{4} \approx 9.28$.
This is not a whole number, so 200 trees is not possible across a whole number of rows [3].
Tick when you have finished all questions and checked your answers.