Linear and Quadratics
Stats and Probability
Trig and Bearings
Interest
Geometry and Measurement
100
x^2-2x-15=0
x = 5
x = -3
100
Two Sport Captains (1 boy and 1 girl) are to be chosen at random from a group of 11 girls and 6 boys. If Elizabeth and Andrew are in this group, what’s the probability that both of them will be chosen?
1/66
100
A seesaw is 2.4 m long. At its highest point off the ground it makes an angle of 48° with the ground. Write both answers correct to 2 decimal places.
What is the maximum height above the ground of the end of the seesaw?
h = 2.4 × sin(48°) = 1.78 m
100
How much interest is paid on a $9,000 loan over 3 years if the interest rate is 5% p.a.
$1350
100
Find x
x = 139
200
Solve:
3x - 2y = 33
5x + 3y = 17
x = 7
y = -6
200
Tania and Liam wish to start a family, they plan to have 3 children. The chance of any particular child being a boy or girl is equaly likely.
Use a tree diagram to find the probability that they have:
a) 3 children of the same gender
b) at least 2 girls
a) 1/4
b) 1/2
200
A lifesaver is sitting in a 12 m tall tower and sees a swimmer in distress. The angle of depression to the swimmer is 23°. Calculate the horizontal distance, correct to 1 decimal place, the lifesaver must travel to reach the swimmer.
x = 28.3 m
200
$4000 interest is paid on a $25,000 investment after 5 years. Calculate the rate of interest.
3.2%
200
Find the area of the following shape:
A = 10.94m^2
300
Find the equation of the line that passess through the point (4, 7) if it is parallell to
y-2x+5=0
y=2x-1
300
Determine the five-number summary and draw a Box Plot of the following data noting any outliers.
2 5 7 10 12 12 14 15 15 15 18
2, 7, 12, 15, no outliers (any <-5 or >27)
300
A piece of rope is attached to the top of the pole and makes an angle of 50º with the ground.
Find the height of the pole and the length of the rope if the distance from the pole to the rope is 8 m. (2 dp)
Height = 9.53m
Lenght = 12.45m
300
$25,000 principal is invested at 9% pa compounded quarterly
a) find the final Amount of the following investment after 5 years.
b) find the Interest accumulated on the investment.
A = $39012.73
I = $14012.73
300
A circular swimming pool of radius 2.6 m and depth 2.3 m is completely filled with water.
What is the capacity, in litres, of the pool?
π×2.6^2×2.3=48.845" " "m" ^3=48 845 litres
400
Use the quadratic formula given below to solve the quadratic equation
2x^2+3x-5=0
correct to two decimal places.
x = 1
x = -2.5
400
A score was added to the set of scores: 6, 7, 7, 7, 11, 10, 12
The range is now equal to the mode. What score was added?
5 or 13
400
Let x° be the angle of depression from a cliff 50m above sea level to a boat that is 250 horizontally from the cliff.
a) Draw a labelled diagram to represent this situation.
b) Find the angle of depression (ie, the value of x)
11.31°
400
A new TV currently costs $676. What did a similar model cost 5 years ago if the rate of inflation was approximately 8% each year? (Assume the cost of the TV kept pace with inflation.) Give your answer correct to the nearest dollar.
676 = P(1.08)^5
P = $460
400
A cylindrical container of height 18 cm is open at one end. If the radius of the circular end is 10 cm,
what is the external surface area, correct to 2 decimal places?
1445.13cm^3
500
Simplify:
(2x+2)/4-(3-5x)/3
(26x-9)/12
500
A company has two machines that make armchairs.
95% of armchairs produced by Machine A are acceptable.
90% of armchairs produced by Machine B are acceptable.
Machine A produces 40% of the armchairs manufactured at the factory.
An armchair chosen at random is not acceptable. Find the probability that it was produced by Machine A. Give your answer as a fraction in simplest form.
Pr(unac ceptab l e) = 0.4 xx 0.05 + 0.6 xx 0.1 = 0.02 + 0.06 = 0.08
Pr(Mac h i n e A given unac ceptab l e)
=(0.4×0.05)/0.08
=1/4
500
Haley starts from point A and travels 1600 m to point B on a bearing of 55°
and then travels a further 1400 m to point C on a bearing of 125°
a) Draw a clearly labeled diagram of Haley's journey.
b) When Haley arrives at point C, how far is she from point A?
2460m
500
Farmer Jim bought a tractor at the start of 2020 for $78 000. If it is expected to depreciate at 6% p.a. over the next number of years, what will the tractor be worth at the end of 2028?
(depreciation is same as compound interest, but negative)
$44693.59
500
You are given an equilateral triangular based prism. Calculate its Surface Area and volume when all its lengths are 6 cm.
TSA = 139.2 cm^2
V = 93.6cm^3