Maths Standard Year 11 - Module 1 - Full module review
Formulas and equationsLinear relationshipsMixed practical contextsModel comparison
15 MC5 short answer45 min
0/15
Multiple Choice Score
Answer questions to see your score.
Part A - Multiple Choice
1In $C = 15 + 4k$, what does 4 represent?
Fixed cost
Cost per kilometre
Total cost
Number of kilometres
B. The coefficient of $k$ is the repeated rate: $4 per kilometre.
2Solve $4x + 9 = 37$.
$x=7$
$x=9$
$x=11.5$
$x=28$
A. $4x=28$, so $x=7$.
3A hall costs $80 plus $12 per person. The total is $260. How many people attended?
12
15
20
28
B. $80+12p=260$, so $12p=180$ and $p=15$.
4Rearrange $A = bh$ to make $h$ the subject.
$h=A/b$
$h=Ab$
$h=b/A$
$h=A-b$
A. Divide both sides by $b$.
5Outputs are 9, 14, 19, 24 for inputs 1, 2, 3, 4. Which formula fits?
$y=5x+4$
$y=4x+5$
$y=9x+5$
$y=14x-5$
B. The repeated change is 5, and $4(1)+5=9$.
6A spreadsheet formula =B2*C2+D2 with B2=10, C2=6, D2=15 gives:
31
60
75
150
C. $10 \times 6 + 15 = 75$.
7Use $D = 0.01v^2 + 0.3v$ when $v=50$.
25 m
40 m
65 m
250 m
B. $0.01(2500)+15=40$ m.
8Which ordered pair matches input 3 and output 23?
(23, 3)
(3, 23)
(20, 26)
(3 + 23)
B. Ordered pairs are input first, output second.
9A tank fills from 20 L to 95 L in 5 min. What is the gradient?
15 L/min
19 L/min
23 L/min
75 L/min
A. Change is 75 L over 5 min, so 15 L/min.
10In $S = 120 + 25w$, what is the intercept?
25
120
145
$w$
B. The intercept is the output when $w=0$.
11Which relationship is direct variation?
$C=10+4k$
$y=7x$
$y=7x+3$
$y=12$
B. Direct variation has the form $y=kx$.
12For points $(0,0)$, $(3,21)$ and $(5,35)$, what is $k$ in $y=kx$?
3
5
7
21
C. $k=y/x=21/3=7$.
13At a break-even point:
both models have equal output
both gradients are zero
both starting values are equal
the cheaper starting cost always wins
A. Break-even means the outputs are equal for the same input.
14Solve $35+10h=65+4h$.
$h=3$
$h=5$
$h=6$
$h=10$
B. $6h=30$, so $h=5$.
15Why can the cheaper option change as input increases?
A higher fixed cost may have a lower repeated rate
Starting cost is the only factor
All linear models are direct variation
Break-even points never matter
A. Lower repeated rates become more important for larger inputs.
Part B - Short Answer
1A gym charges $20 joining fee plus $15 per class.
a. Write an equation for total cost $C$ after $c$ classes. 2 marks
b. Find the number of classes if total cost is $95. 2 marks
$C=20+15c$. If $C=95$, then $20+15c=95$, so $15c=75$ and $c=5$ classes.
2A car travels 210 km at 70 km/h. Use $d=st$.
a. Rearrange to make $t$ the subject. 2 marks
b. Find the time. 2 marks
$t=d/s$. So $t=210/70=3$. The time is 3 hours.
3A table has outputs 18, 25, 32, 39 for inputs 0, 1, 2, 3.
a. Write the equation. 2 marks
b. Predict the output for input 6. 2 marks
Intercept is 18 and repeated change is 7, so $y=18+7x$. When $x=6$, $y=60$.
4Plan A costs $20 plus $5 per GB. Plan B costs $50 plus $2 per GB.
a. Find the break-even number of GB. 3 marks
b. State which plan is cheaper above that number. 2 marks
$20+5g=50+2g$, so $3g=30$ and $g=10$. Above 10 GB, Plan B is cheaper because its repeated rate is lower.
5Explain why $C=10+4k$ is linear but not direct variation.
Use the terms fixed cost, origin and direct variation. 3 marks
It is linear because it has a constant repeated change of 4. It is not direct variation because it has a fixed cost of 10, so it does not pass through the origin.
This quiz reviews the full Algebra module. Use missed questions to choose which lessons to revise.