This checkpoint assesses your understanding of mixed algebra review, equations review, patterns and generalisation, problem solving and the capstone challenge. It covers Lessons 16–20.
❓ Multiple Choice (10 questions)
1. Simplify $5x + 3y - 2x + y$.
2. Expand $3(x - 4)$.
3. Solve $4x - 7 = 17$.
4. The next term in the sequence 3, 7, 11, 15, ... is:
5. Solve $\dfrac{x + 3}{2} = 5$.
6. Solve $-3x + 5 < 14$.
7. A plumber charges \$50 call-out plus \$40 per hour. For a \$170 bill, the hours worked are:
8. Expand and simplify $(x + 2)(x - 3)$.
9. The rule for the nth term of 5, 9, 13, 17, ... is:
10. Make $x$ the subject of $y = \dfrac{x + 2}{3}$.
✍ Short Answer (4 questions)
11. Simplify the following.
(a) $3a + 5b - a + 2b$ (1 mark)
(b) $2(x + 3) + 3(x - 1)$ (2 marks)3 MARKS
12. Solve the following equations.
(a) $5x - 3 = 22$ (1 mark)
(b) $\dfrac{2x + 1}{3} = 5$ (2 marks)
(c) $4 - 2x \geq 10$ (2 marks)5 MARKS
13. Patterns and formulas.
(a) Find the 20th term of the sequence with rule $T_n = 3n + 7$. (1 mark)
(b) Make $h$ the subject of $A = \dfrac{1}{2}bh$. (2 marks)3 MARKS
14. Word problems.
(a) The sum of three consecutive even numbers is 84. Find the numbers. (3 marks)
(b) A car rental costs \$45 per day plus \$0.25 per km. For a total cost of \$95 and 120 km driven, how many days was the car rented? (2 marks)5 MARKS
1. B — $5x - 2x + 3y + y = 3x + 4y.
2. C — $3 \times x + 3 \times (-4) = 3x - 12.
3. A — $4x = 24 \Rightarrow x = 6.
4. C — Common difference = 4. $15 + 4 = 19.
5. A — $x + 3 = 10 \Rightarrow x = 7.
6. B — $-3x < 9 \Rightarrow x > -3 (flip sign).
7. B — $50 + 40h = 170 \Rightarrow 40h = 120 \Rightarrow h = 3.
8. C — $x^2 - 3x + 2x - 6 = x^2 - x - 6.
9. A — Common difference = 4, first term = 5. $T_n = 4n + 1.
10. B — $3y = x + 2 \Rightarrow x = 3y - 2.
Q11 (3 marks): (a) $3a - a + 5b + 2b = 2a + 7b$ [1]. (b) $2x + 6 + 3x - 3 = 5x + 3$ [2].
Q12 (5 marks): (a) $5x = 25 \Rightarrow x = 5$ [1]. (b) $2x + 1 = 15 \Rightarrow 2x = 14 \Rightarrow x = 7$ [2]. (c) $-2x \geq 6 \Rightarrow x \leq -3$ (flip sign) [2].
Q13 (3 marks): (a) $T_{20} = 3(20) + 7 = 60 + 7 = 67$ [1]. (b) $2A = bh \Rightarrow h = \dfrac{2A}{b}$ [2].
Q14 (5 marks): (a) Let $n$ = first even number: $n + (n+2) + (n+4) = 84 \Rightarrow 3n + 6 = 84 \Rightarrow 3n = 78 \Rightarrow n = 26$. Numbers: 26, 28, 30 [3]. (b) $45d + 0.25(120) = 95 \Rightarrow 45d + 30 = 95 \Rightarrow 45d = 65 \Rightarrow d = 1.44$ days (or 1 day 11 hours) [2].
Tick when you have finished all questions and checked your answers.