Given
- Find integers
and such that (2 marks)
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- State the domain for which
is defined. (2 marks)
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Aussie Maths & Science Teachers: Save your time with SmarterEd
Given
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An object is moving on the
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The diagram shows the front of a tent supported by three vertical poles. The poles are 1.2 m apart. The height of each outer pole is 1.5 m, and the height of the middle pole is 1.8 m. The roof hangs between the poles.
The front of the tent has area
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Two events,
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Consider the discrete probability distribution with random variable
The smallest and largest possible values of
A ship sails 6 km from
size of angle
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A new 200-metre long dam is to be built.
The plan for the new dam shows evenly spaced cross-sectional areas.
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Assuming no wastage, calculate how much rainfall is needed, to the nearest mm, to fill the dam. (2 marks)
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Madison uses the number sentence 15 × 12 = 180 to solve a problem.
Which of the following could be the problem?
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Madison buys 15 showbags. How much does each showbag cost? |
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Madison spends $15 on 180 showbags. How much does she spend? |
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Madison buys 15 showbags that cost $12 each. How many showbags does she buy? |
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Madison buys 12 showbags that cost $15 each. How much does she spend? |
Groucho, Harpo and Zeppo are weighing their grapes.
Harpo's grapes weigh more than Zeppo's, but less than Groucho's grapes.
Which of these could be the weight of Harpo's grapes?
0.11 kg | 0.32 kg | 0.6 kg | 0.7 kg |
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Let
i.
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iii.
In
The process is repeated two more times. Point
Point
The segments
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Let
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ii.
iii.
Alvin is making red cordial.
It is made by mixing water with red concentrate.
Alvin adds 1 litre (L) of water to 75 millilitres (mL) of red concentrate.
How much cordial did Alvin make?
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Sanjeev collected football cards. He had collected 35 cards.
At school, Sanjeev and his friends put all their football cards together.
There was a total of 305 cards.
How many football cards, in total, had Sanjeev's friends collected?
On Monday, Jeremy went to the doctor and was given 24 tablets.
Jeremy was to take 5 tablets each day starting from Monday.
On which day did Jeremy take the last tablet?
Thursday | Friday | Saturday | Sunday |
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On a school camp, each child chose their meal for dinner.
The table shows how many children chose each meal.
Select all the statements that are true.
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More girls than boys chose spaghetti. |
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In total 70 children chose pizza. |
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Less than half the girls chose pizza. |
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In total, there are the same number of girls on the trip as boys. |
Three people,
i.
ii.
iii.
Jarryd buys 3 water bottles for $1.50 each.
He pays for these water bottles with a $10 note.
How much change should Jarryd receive?
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Write a number in the box to make this number sentence true.
Kara deposits an amount of $300 000 into an account which pays compound interest of 4% per annum, added to the account at the end of each year. Immediately after the interest is added, Kara makes a withdrawal for expenses for the coming year. The first withdrawal is
Let
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i. | ||
ii. | ||
iii. | ||
A game involves rolling two six-sided dice, followed by rolling a third six-sided die. To win the game, the number rolled on the third die must lie between the two numbers rolled previously. For example, if the first two dice show 1 and 4, the game can only be won by rolling a 2 or 3 with the third die.
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In triangle
(i)
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(iii)
(iv)
Eight activities,
The network above shows these activities and their usual duration in hours.
The duration of each activity can be reduced by one hour.
To complete this project in 16 hours, the minimum number of activities that must be reduced by one hour each is
A.
B.
C.
D.
A community centre is to be built on the new housing estate.
Nine activities have been identified for this building project.
The directed network below shows the activities and their completion times in weeks.
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The builders of the community centre are able to speed up the project.
Some of the activities can be reduced in time at an additional cost.
The activities that can be reduced in time are
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The owner of the estate is prepared to pay the additional cost to achieve early completion.
The cost of reducing the time of each activity is $5000 per week.
The maximum reduction in time for each one of the five activities,
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A walkway is to be built across the lake.
Eleven activities must be completed for this building project.
The directed network below shows the activities and their completion times in weeks.
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Determine the longest float time, in weeks, on the supervisor’s list. (1 mark)
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A twelfth activity, L, with duration three weeks, is to be added without altering the critical path.
Activity L has an earliest start time of four weeks and a latest start time of five weeks.
Determine the total overall time, in weeks, for the completion of this building project. (1 mark)
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A project has 12 activities. The network below gives the time (in hours) that it takes to complete each activity.
The critical path for this project is
A.
B.
C.
D.
The network below shows the activities and their completion times (in hours) that are needed to complete a project.
The project is to be optimised by reducing the completion time of one activity only.
This will reduce the completion time of the project by a maximum of
A. 1 hour
B. 3 hours
C. 4 hours
D. 5 hours
As an attraction for young children, a miniature railway runs throughout a new housing estate.
The trains travel through stations that are represented by nodes on the directed network diagram below.
The number of seats available for children, between each pair of stations, is indicated beside the corresponding edge.
Cut 1, through the network, is shown in the diagram above.
On one particular train, 10 children set out from the West Terminal.
No new passengers board the train on the journey to the East Terminal.
The rangers at the wildlife park restrict access to the walking tracks through areas where the animals breed.
The edges on the directed network diagram below represent one-way tracks through the breeding areas. The direction of travel on each track is shown by an arrow. The numbers on the edges indicate the maximum number of people who are permitted to walk along each track each day.
One day, all the available walking tracks will be used by students on a school excursion.
The students will start at
Students must remain in the same groups throughout the walk.
A network of tracks connects two car parks in a festival venue to the exit, as shown in the directed graph below.
The arrows show the direction that cars can travel along each of the tracks and the numbers show each track’s capacity in cars per minute.
Four cuts are drawn on the diagram.
The maximum number of cars per minute that will reach the exit is given by the capacity of
A. Cut A
B. Cut B
C. Cut C
D. Cut D
Vehicles from a town can drive onto a freeway along a network of one-way and two-way roads, as shown in the network diagram below.
The numbers indicate the maximum number of vehicles per hour that can travel along each road in this network. The arrows represent the permitted direction of travel.
One of the four dotted lines shown on the diagram is the minimum cut for this network.
The maximum number of vehicles per hour that can travel through this network from the town onto the freeway is
A.
B.
C.
D.
An undirected connected graph has five vertices.
Three of these vertices are of even degree and two of these vertices are of odd degree.
One extra edge is added. It joins two of the existing vertices.
In the resulting graph, it is not possible to have five vertices that are
A. all of even degree.
B. all of equal degree.
C. one of even degree and four of odd degree.
D. four of even degree and one of odd degree.
Hendrix is driving from Bundaberg to Caloundra, a distance of 306 kilometres.
When Hendrix gets to the Sunshine Coast, he has 36 kilometres left.
What distance has Hendrix travelled when he gets to the Sunshine Coast?
kilometres |
Jazz buys 4 avocados for $1.20 each.
He pays for the avocados with a $5 note.
How much change should Jazz receive?
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Sisko is making red cordial for his daughter's birthday party.
Red cordial is made by adding red concentrate with water.
Sisko adds 60 millilitres (mL) of red concentrate to 1 litre (L) of water.
How much red cordial has Sisko made?
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Raphael is 2 years younger than 3 times his sister's age.
If
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Clive and Alvin asked their friends how many books they had read in the past month.
Clive draws a picture graph to show the results for his friends.
Alvin draws a column graph to show the results for his friends.
How many more of Clive's friends read 3-4 books in the last month than Alvin's friends?
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There are 20 raffle tickets, numbered 1 to 20, in a box.
Three prizes are given away by choosing three tickets from the box. One ticket can win one prize only.
The first ticket drawn is number 15 and wins the third prize.
Which of the following is not possible?
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Second prize is won by number 2. |
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First prize is won by a prime number. |
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Second prize is an even number. |
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First prize is won by number 15. |
Kim, Bob and Liz each measure the height of the hedge in their front yards.
Who has the tallest hedge in their front yard?
Kim | Bob | Liz |
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The diagram shows a point
The tangent to the circle at
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i. | ![]() |
ii.
iii.
iv.
A cone is inscribed in a sphere of radius
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The diagram shows two parallel brick walls
A new fence is to be built from
Let
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ii.
iii.
A function is given by
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The figure shown represents a wire frame where
Let
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The rides at the theme park are set up at the beginning of each holiday season.
This project involves activities A to O.
The directed network below shows these activities and their completion times in days.
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i. There are two critical paths. One of the critical paths is A–E–J–L–N.
Write down the other critical path. (1 mark)
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ii. Determine the float time, in days, for activity F. (1 mark)
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Six activities, B, D, G, I, J and L, can all be reduced by one day.
The cost of this crashing is $1000 per activity.
i. What is the minimum number of days in which the project could now be completed? (1 mark)
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ii. What is the minimum cost of completing the project in this time? (1 mark)
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a.
b.i.
b.ii.
c.i.
c.ii.
a.
b.i.
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c.i.
c.ii.
Senior students at a school choose one elective activity in each of the four terms in 2018.
Their choices are communication (
The transition matrix
Let
For the given matrix
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a.
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c. | ||
d. | ||
Alex sends a bill to his customers after repairs are completed.
If a customer does not pay the bill by the due date, interest is charged.
Alex charges interest after the due date at the rate of 1.5% per month on the amount of an unpaid bill.
The interest on this amount will compound monthly.
Marcus paid the full amount one month after the due date.
How much did Marcus pay? (1 mark)
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Alex sent Lily a bill of $428 for repairs to her car.
Lily did not pay the bill by the due date.
Let
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How much interest was Lily charged?
Round your answer to the nearest cent. (1 mark)
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b.
c. | ||