Linear
Identify the gradient and y-intercept of the equation
y = 4x - 7
gradient: 4
y-intercept: -7
Find the y-intercept of the quadratic equation:
y = x^2 - 5x + 9
Write your answer as a coordinate
(0, 9)
Calculate 25% of $360.
$90
Question 1
Answer 1
A straight line passes through the points:
(0, 5) and (2, 9)
Calculate the gradient of the line.
2
Determine whether the point (3, 8) lies on the line:
y = 2x + 2
Show your working
y = 2 x 3 + 2
= 6 + 2
= 8
Yes it does
Expand and simplify:
(x + 6)^2
x^2 + 12x + 36
A salesperson receives a weekly base payment of $250 plus 8% commission on their sales.
If the salesperson sells $3000 worth of products in one week, calculate their total weekly income.
$490
Question 2
Answer 2
Factorise the following expression by grouping:
4a + ab + 12 + 3b
(4 + b)(a + 3)
Calculate the gradient of the line passing through the points:
(-2, 3) (4, 15)
2
Find the x-intercepts of this equation and state them as coordinates:
y = 2x^2 + 10x + 12
(-3, 0)
(-2, 0)
How long must $3000 be invested at 4% per annum simple interest to earn $480 in interest?
4 years
Question 3
Answer 3
Question 6
11 / 18
y = -3x + 12
Sketch the line on a set of axes, labelling the intercepts with their coordinates
x-intercept: (4, 0)
y-intercept: (0,12)
y = -2x^2 + 8x + 10
a. Calculate the coordinates of the turning point
b. State whether the turning point is a maximum or minimum
b. maximum
A worker earns $28 per hour for their regular 35-hour working week.
They are paid double time for any additional hours worked.
In one week, the worker completes 35 regular hours and 5 additional hours.
a. Calculate their total weekly income.
b. Calculate their annual income, assuming they work these hours every week for 52 weeks.
a. $1260
b. $65 520
Question 4
Answer 4
A school hires a venue for $180 and pays an additional $12 per student.
The school charges each student $25 to attend the event.
If 20 students attend, calculate the total profit made by the school.
$80
A school excursion costs $120 to hire a bus, plus $15 per student attending.
a. Write a linear equation for the total cost, C, in terms of the number of students, n
b. If the school has a budget of $570, calculate the maximum number of students who can attend.
a. C = 120 + 15n
b. 30 students
The height of a model rocket is given by:
h = -2t^2 + 12t
where h is the height in metres and t is the time in seconds.
a. Determine when the rocket returns to the ground.
b. Calculate the maximum height reached by the rocket.
c. Find the times when the rocket is 16 metres above the ground.
a. 6 seconds
b. 18 meters
c. 2 and 4 seconds
A person earns $147 000 per year.
Their tax bracket is:
$31 288 plus 37c for each $1 over 135 000
a. Calculate the total annual income tax payable.
b. Calculate the person's annual net income after tax.
a. $35728
b. $111 272Question 5
Answer 5
y = x^2 - 2x - 8
a. Find the x-intercepts.
b. Find the y-intercept.
c. Calculate the coordinates of the turning point.
a. (-2, 0) (4, 0)
b. (0, -8)
c. (1, -9)