Checkpoint 2 of 3 10 MC + 2 Short Answer Lessons 8-14

Checkpoint 2: Linear Equations and Simultaneous Equations

Test your understanding of solving linear equations, working with fractions and formulas, inequalities, word problems, and simultaneous equations using substitution and elimination.

Answer all questions. Use the marking criteria for short answer questions to check your working.

Multiple Choice Questions

2 marks each — 20 marks total

MCQ2 marksL8

Solve $4x - 7 = 13$.

$x = 1.5$ $x = 5$ $x = 4$ $x = 6$

MCQ2 marksL8

Solve $5(x - 3) = 2(x + 6)$.

$x = 3$ $x = 6$ $x = 9$ $x = 7$

MCQ2 marksL9

What is the LCD of $\dfrac{x}{6}$ and $\dfrac{x}{8}$?

14 48 24 2

MCQ2 marksL10

Make $r$ the subject of $V = \dfrac{4}{3}\pi r^3$ (volume of a sphere).

$r = \sqrt[3]{\dfrac{3V}{4\pi}}$ $r = \dfrac{3V}{4\pi}$ $r = \sqrt{\dfrac{3V}{4\pi}}$ $r = \dfrac{V}{\frac{4}{3}\pi}$

MCQ2 marksL11

Solve $-3x + 4 \leq 16$.

$x \leq -4$ $x \geq -4$ $x \leq 4$ $x \geq 4$

MCQ2 marksL11

In interval notation, $x > -2$ is written as:

$[-2, \infty)$ $(-2, \infty)$ $(-\infty, -2)$ $(-\infty, -2]$

MCQ2 marksL12

A number is doubled and 9 is subtracted. The result is 21. What is the number?

6 15 12 10

MCQ2 marksL13

If $y = 3x + 2$ and $2x + y = 14$, what is the value of $x$?

$x = 2$ $x = 3$ $x = 2.4$ $x = 4$

MCQ2 marksL14

To eliminate $y$ from $\begin{cases} 4x + 3y = 17 \\ 2x - 3y = 7 \end{cases}$, you should:

Add the equations Subtract the equations Multiply Equation 2 by 2 Divide Equation 1 by 3

MCQ2 marksL14

The solution to $\begin{cases} 3x + 2y = 12 \\ 3x - 2y = 4 \end{cases}$ is:

$x = 2, y = 3$ $x = \frac{8}{3}, y = 2$ $x = 3, y = 1.5$ $x = 2, y = 2$

Short Answer Questions

Use the marking criteria to check your working

Short Answer5 marks

A gym offers two membership plans. Plan A has a $40 joining fee and costs $15 per week. Plan B has no joining fee and costs $20 per week.

(a) Write an equation for the total cost $C$ of each plan after $w$ weeks. (1 mark)

(b) Find the number of weeks for which both plans cost the same. (2 marks)

Saved

Short Answer5 marks

Solve the following simultaneous equations using an appropriate method. Show all working and check your solution in both equations.

$$\begin{cases} 2x + 3y = 16 \\ 5x - 2y = 3 \end{cases}$$

Saved

Continue to Block C: Linear Relationships →

Return to Unit Hub