This checkpoint assesses your understanding of solving linear equations, inequalities, rearranging formulas and word problems. It covers Lessons 11–15.
❓ Multiple Choice (10 questions)
1. Solve $x + 7 = 15$.
2. Solve $3x = 27$.
3. Solve $2x + 5 = 19$.
4. Solve $4(x - 2) = 24$.
5. Solve $\dfrac{x}{3} + 4 = 9$.
6. Solve $-2x > 10$.
7. Which number line shows $x \leq 3$?
8. Make $x$ the subject of $y = 4x + 3$.
9. Three consecutive numbers sum to $60$. What is the largest number?
10. Solve $3(2x - 1) + 2 = 17$.
✍ Short Answer (4 questions)
11. Solve the following equations.
(a) $x - 9 = 14$ (1 mark)
(b) $5x = 35$ (1 mark)
(c) $\dfrac{x}{4} + 2 = 7$ (1 mark)3 MARKS
12. Solve the following equations.
(a) $3x + 8 = 29$ (1 mark)
(b) $2(x - 3) = 16$ (1 mark)
(c) $5x - 2x + 4 = 25$ (2 marks)4 MARKS
13. Inequalities and formulas.
(a) Solve $-3x + 5 < 20$ and show the solution on a number line. (2 marks)
(b) Make $r$ the subject of $A = \pi r^2$. (2 marks)4 MARKS
14. Word problems.
(a) A rectangle has a length that is $4$ cm more than its width. The perimeter is $36$ cm. Find the dimensions of the rectangle. (3 marks)
(b) A mobile phone plan costs $\$15$ per month plus $\$0.50$ per minute of calls. If the monthly bill is $\$45$, how many minutes of calls were made? (2 marks)5 MARKS
1. A — $x = 15 - 7 = 8.
2. A — $x = 27 \div 3 = 9.
3. A — $2x = 19 - 5 = 14$, so $x = 7.
4. C — $x - 2 = 24 \div 4 = 6$, so $x = 8.
5. B — $\dfrac{x}{3} = 9 - 4 = 5$, so $x = 15.
6. B — Dividing by $-2$ reverses the inequality: $x < -5.
7. B — $x \leq 3$ needs a closed circle at 3 with arrow left.
8. B — $y = 4x + 3 \Rightarrow 4x = y - 3 \Rightarrow x = \dfrac{y - 3}{4}.
9. C — $n + (n+1) + (n+2) = 60 \Rightarrow 3n + 3 = 60 \Rightarrow n = 19$. Largest = $19 + 2 = 21.
10. B — $3(2x - 1) + 2 = 17 \Rightarrow 6x - 3 + 2 = 17 \Rightarrow 6x = 18 \Rightarrow x = 3.
Q11 (3 marks): (a) $x = 14 + 9 = 23$ [1]. (b) $x = 35 \div 5 = 7$ [1]. (c) $\dfrac{x}{4} = 5 \Rightarrow x = 20$ [1].
Q12 (4 marks): (a) $3x = 21 \Rightarrow x = 7$ [1]. (b) $x - 3 = 8 \Rightarrow x = 11$ [1]. (c) $3x + 4 = 25 \Rightarrow 3x = 21 \Rightarrow x = 7$ [2].
Q13 (4 marks): (a) $-3x < 15 \Rightarrow x > -5$ (number line: open circle at $-5$, arrow right) [2]. (b) $r^2 = \dfrac{A}{\pi} \Rightarrow r = \sqrt{\dfrac{A}{\pi}}$ [2].
Q14 (5 marks): (a) Let $w$ = width. $2(w + w + 4) = 36 \Rightarrow 2(2w + 4) = 36 \Rightarrow 2w + 4 = 18 \Rightarrow 2w = 14 \Rightarrow w = 7$ cm, length = $11$ cm [3]. (b) $15 + 0.5m = 45 \Rightarrow 0.5m = 30 \Rightarrow m = 60$ minutes [2].
Tick when you have finished all questions and checked your answers.