Algebra
Measurements
Financial Maths
Statistics
Network
100
Solve 5x = 2 - x
x = 1/3
100
Felix’s regular morning coffee order is a macchiato. This is approximately 60mL of coffee, to the nearest mL.
What is the percentage error in this measurement, correct to one significant figure?
±0·8%
100
Tom’s normal rate of pay is $23.75 per hour. In one week he worked 18 hours at the normal rate, 6 hours at time-and-a-half and 2.5 hours at double time. He was also paid a wet weather allowance of $65 for the week.
What were his total earnings for the week?
$825
100
Two coins are tossed 100 times. The results are tabulated below.
What is the experimental probability of tossing a head and a tail?
45/100 = 9/20
100
In the network shown, the number of vertices of even degree is...
3
200
An intravenous drip is delivering 30 drops/min. There are 15 drops/mL and 1·2 L of liquid to be delivered. How long will the drip take to deliver the required dose?
10 hours
200
Yerevan is 3 hours ahead of Lagos. Reykjavik is 4 hours behind Yerevan. What is the time in Reykjavik when it is 3 pm in Lagos?
2 pm
200
Last year, Alex bought 300 shares at $1.75 per share. They are now worth $2.00 per share and Alex receives a dividend of $0.15 per share.
What is the the dividend yield?
7·5%
200
The birth weights of babies born in Australia during 2017 is presented in the following box-and-whisker diagram.
Find the interquartile range.
0.6 kg
200
Find the capacity of the cut shown in the network diagram below.
23
300
Joshua was asked to solve an equation for homework. His solution below has TWO errors.
Which lines DO NOT follow correctly from the previous lines?
Line 2 and Line 3
300
A rectangular swimming pool has two semi-circular sections at each end. The dimensions of the pool are given in the diagram below.
Calculate the perimeter of the pool to the nearest metre.
39 m
300
Isaac has earned a gross annual salary of $102 500 in 2018-19 and his employer has paid $27 500 PAYG tax on his behalf. Isaac has calculated that his total allowable deductions were $1280 for work-related travel, $350 for stationery and $450 for professional subscriptions. Isaac must pay the medicare levy of 2% on his taxable income.
Using the tax table provided by the ATO below, determine how much Isaac’s tax refund or tax liability will be.
Refund = $839.20
300
The stem and leaf plot below shows the number of goals scored by the football teams in the A-League across the 2018/2019 season.
Find the median number of goals scored.
41.5
300
A collection of bushwalking tracks is modelled by the network below. There are six checkpoints labelled A, B, C, D, E and F. Which two of the checkpoints must you start and end at so that a bushwalker could walk along every track exactly once?
A and E
400
The number of seats in a row at a cinema varies inversely with the width of each seat. The present configuration has 42 seats in a row, each of width 47 cm, and this uses up all of the allowed space to comply with safety regulations. The owners of the cinema are considering a refurbishment.
How many seats of width 52 cm can be installed?
37 seats
400
The diagram below represents a property that borders a river.
Use two applications of the trapezoidal rule to estimate the area of the property.
1.235 km2
400
A new start-up company purchases $24 500 worth of office equipment. It is depreciated using the declining balance method at a rate of 18% per annum. Calculate the value of the equipment after 3 years.
$13 508.52
400
A bag contains 7 black balls and 5 white balls. Two balls are selected at random without replacement.
Calculate the probability of selecting two balls of different colours.
35/66
400
Cabins in a national park are to be connected to the power source at P. The weighted graph below shows the distances in metres between certain cabins and the power source.
What is the weight of this minimum spanning tree?
98
500
A surfboard manufacturer has initial costs of $42 500 to set up the factory to produce the surfboards. After the initial set-up costs, every 20 surfboards produced cost a further $2500.
The surfboards are sold to retail outlets for $465 each.
Write down the cost of production C, and the revenue R in terms of n, where n is the number of surfboards manufactured or sold respectively.
C = 42500 + 125n
R = 465n
500
The quadrilateral ABCD represents a block of land, where AB = 40m, BC = 65m, CD = 34m, AD = 54m and ∠BAD is 90◦. This information is shown in the diagram below.
Find the area of the land
2164 m2
500
The table below shows the future value of an annuity of $1 for varying interest rates and time periods. Contributions are made at the beginning of each time period.
What is the minimum quarterly payment into the account, to the nearest dollar, that Hugo needs to make in order to have saved $8000 in 3 years time at 4% p.a. compounded quarterly?
$624.55
500
The maximum daily temperatures during the summer months in Mount Isa are recorded. These maximum temperatures are normally distributed with a mean of 33·8◦C and a standard deviation of 4·1◦C.
What percentage of summer days in Mount Isa would you expect to be between 29·7◦C and 42·0◦C?
81.5%
500
The diagram below shows a weighted network.
Find the maximum flow in the network.
28