Six men are employed to complete a job in 8 days. After 3 daysâ€™ work, 2 of the men are taken off the job. Find the total time it takes for the job to be completed from start to finish.
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Question 2 of 30
2. Question
It takes Hannah 4 hours to clean her room. When her mother cleans the room it only takes 2 hours. If Hannah started cleaning her room at 3 pm, and her mother started helping her after one hour, what time would they finish?
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Question 3 of 30
3. Question
Donald can complete a job in 20 minutes. If he has been working on the job for 10 minutes, then is joined by Daffy and the job is completed in another 6 minutes, how long would it have taken Daffy to do the job by herself?
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Question 4 of 30
4. Question
Harley Primary School has 240 students. Two-thirds of the students who attend the school play weekend sport. This number equals two-ninth of the number of students who attend the nearby Harley High School. How many students attend the high school?
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Question 5 of 30
5. Question
Julia found a bag of money. When it was unclaimed the police told her she could keep it. She decided to give one-quarter of the money to her parents, one-fifth to her sister and one-eleventh of the remainder to her brother. If her brother received $32, how much did she find?
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Question 6 of 30
6. Question
Students from Year 7, 8 and 9 raised money for a charity. Year 7 students raised one-sixth of the total and Year 9 students raised three-eighths. If Year 8 students contributed $4400, what was raised by Year 9 for the charity?
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Question 7 of 30
7. Question
An alloy consists of 25% nickel, 40% zinc and copper as the remainder. If a block of the alloy consists of 8 kg of zinc, what is the mass of copper in the block?
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Question 8 of 30
8. Question
A paperback has a recommend retail price (RRP). Eric paid $18 for the book at a store offering a 25% discount off RRP, while Jamie bought it from another store with a 35% discount. What was the difference in price?
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Question 9 of 30
9. Question
The manager of Nikkiâ€™s Nuts bought some nuts from a producer. He purchased 30kg of nuts at $4 per kilogram and another 20Â kg of nuts at $5 per kilogram. If the nuts are to be mixed and sold to make a 75% profit, what will be the sale price per kilogram?
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Question 10 of 30
10. Question
All vehicles at Samâ€™s Quality Cars are priced at a profit of 40% on cost price. When Tony bought a car from the dealership he bargained the price down and received a discount of 20% on the sale price. If the dealership still made a profit of $3600 on the sale, what was the original cost of the car for the dealership?
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Question 11 of 30
11. Question
Lanaâ€™s Jewellery store is having a sale. The prices of all diamond rings drop by 20%. On a particular engagement ring the amount of GST drops by $70.40. What is the discounted price of the ring?
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Question 12 of 30
12. Question
There are 28 students on the 8M1 class roll. On a particular day a quarter of the student is absent and 15% of the remainder are helping the principal. What is the ratio of those students present in a class to those who are on the excursion?
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Question 13 of 30
13. Question
The ratio of the populations of Town A and Town B is 5:3 and the ratio of the populations of Town B and Town C is 4:7. If the total population of the three towns is 15900, find the population of each town.
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Question 14 of 30
14. Question
Two maps are drawn for the same area of land. The scale on Map A is 1:8000 while the scale on Map B is 1:12000. Two towns are 24 cm apart on Map A. How far are they apart on Map B?
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Question 15 of 30
15. Question
Elise takes 10 minutes to cycle around a rectangular park at an average speed of 12 km/h. If the ratio of length to width of the park is 3:2, what is the area of the park in hectares?
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Question 16 of 30
16. Question
A train is 1 km long. It travels through a 2-km tunnel at a speed of 60 km/h. From the moment the train enters the tunnel how long will it take before the entire train travels completely through the tunnel?
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Question 17 of 30
17. Question
The average of the ages of three brothers is 13. If the middle-aged boy is 9 years younger than the eldest and 3 years older than the youngest, how old are the boys?
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Question 18 of 30
18. Question
Kateâ€™s grandmother is four times as old as Kate is now. In 6 yearsâ€™ time she will be 2 years older than three times Kateâ€™s age. How old are Kate and her grandmother now?
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Question 19 of 30
19. Question
Find three consecutive odd numbers such that five times the middle number is three more than twice the sum of the first number and the third number.
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Question 20 of 30
20. Question
Jocelyn left the post office at Kalgoorlie at 10 am and travelled east at an average speed of 90 km/h. An hour later Chloe left the post office and travelled west at an average speed of 100 km/h. At what time were they 356 km apart?
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Question 21 of 30
21. Question
Cooper had $10000 to invest. He invested an amount at Sumbank at 8% interest per annum and the rest at another bank at 7% per annum. If his total annual interest was $765, find the amount invested at Sumbank.
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Question 22 of 30
22. Question
On a clock the length of the hour hand is 3 cm shorter than the minute hand. How much further does the minute hand travel compared to the hour hand in 12 hours if the hour hand is 5 cm in length. Give your answer to the nearest centimetre.
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Question 23 of 30
23. Question
ABCD is a parallelogram and M lies on DC where DM=MC. What is the ratio of the area of triangle DBM to the area of the parallelogram ABCD?
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Question 24 of 30
24. Question
Chocolate bars are produced in the shape of a triangular prism. The base of the bar is a right-angled isosceles triangle with two sides 30 mm. Chocolate to produce the bars is melted from a block in the shape of a square-based prism with dimensions 20 cm, 20 cm and 9 cm. If chocolate from the block can make 400 chocolate bars, what is the depth of each bar?
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Question 25 of 30
25. Question
When Lachlan drives to work he picks up his workmate Ryan. Lachlan lives directly 18 km south of Ryan and their workplace is 15 km directly east of Ryanâ€™s house. Lachlan always drives at 40 km/h. How much time would Lachlan save if he did not have to pick up Ryan?
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Question 26 of 30
26. Question
Two yatchs are sailing away from the same buoy. Yatch A is sailing east at 12 km/h and Yatch B is sailing south at 16 km/h. How far apart are the yachts after two and a half hours?
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Question 27 of 30
27. Question
In the first 8 games of her basketball season, Avery scored a mean of 11.5 points. In the ninth game she only scored 4 points. What will she need to score in the tenth game to have an overall mean of 11 points per game?
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Question 28 of 30
28. Question
Kelvin could not remember his scores from 5 history tests marked out of 100. He did remember that the mean was 80, the median was 83, and the mode was 84. If all his scores were whole numbers, what was the lowest score he could have received on any one test?
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Question 29 of 30
29. Question
In a tennis club there are 8 more females and males. If a person is selected from the members of the club, the probability that the person is make is 3/7. How many female members are in the club?
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Question 30 of 30
30. Question
A bag contains red frogs, green frogs and black frogs. There are four times as many red frogs as black frogs and half as many black frogs as green frogs. Anna selected a frog at random from the bag, noted that it was red and ate it. If 34 frogs remain in the bag, what is the chance that the next frog chosen at random will be red?
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Grade 9
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Last week Nathan worked 28 hours at normal pay and 6 hours at time-and-a-half and was paid $794.02. This week he works 30 hours at normal pay and 6 hours at double time. If his pay rate is unchanged, what will be his total pay this week?
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Question 2 of 28
2. Question
The price of a caravan is $60 000. Bruce purchased the caravan by paying a deposit of 20% and the balance on an interest rate of 4% p.a. If the monthly repayments were $960, how many repayments did Bruce have to make?
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Question 3 of 28
3. Question
A car depreciates in value by 18% p.a. in the first 5 years after purchase and then at the rate of 12% p.a. over the following 5 years. Find the value of the car after 10 yeas if it was purchased for $32 000, to the nearest dollar.
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Question 4 of 28
4. Question
From 2002 to 2010, the value of a holiday unit appreciated in price by 4.6% p.a. From 2010 to 2014, the price dropped by 5.3% p.a. What was the value of the holiday unit in 2014, if it was valued at $310 000 in 2002? Give your answer to the nearest thousand.
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Question 5 of 28
5. Question
Two hundred tickets were sold for a concert, with adult tickers being $10 each and children half-price. If there were x adult tickets sold, write an expression for the total value of ticket sales.
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Question 6 of 28
6. Question
Lucas is paid $18 per hour for his part-time job. In one week he worked 14 hours which was a combination of normal time and double time. If he worked 2 hours more at double time than at normal time, how much was he paid for his work?
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Question 7 of 28
7. Question
The cost of framing a rectangular picture is 450 per metre. The length of the picture is 8 cm shorter than twice the width and the total cost of the framing is $67. The picture is to be covered with glass which costs $140 per metre. What is the cost of the glass?
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Question 8 of 28
8. Question
Candice walked from her apartment to the shops at an average speed of 6 km/h. When she arrived she realised that she had forgotten her wallet so she rode a friendâ€™s bike home to get it and then back to the shops at an average speed of 12 km/h. If her total travelling time was 40 minutes how far does she live from the shops?
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Question 9 of 28
9. Question
A man had a goose that laid golden eggs where the number of eggs laid was proportional to the square root of the number of hours the goose slept. When the goose slept for 9 hours, it laid 4 golden eggs. How long did the goose sleep when it laid 2 eggs?
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Question 10 of 28
10. Question
Sean builds boat trailers. He has costs totalling $6000 per month plus $2100 per trailer. He sells the trailer for $3200 each. What is the least number of trailers he must sell if he is to make a profit of at least $10 000 per month?
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Question 11 of 28
11. Question
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Question 12 of 28
12. Question
A group of 166 students attended the regional athletics carnival. The athletes travelled in 10 vehicles, some of them buses and the remainder cars. Each bus could carry 46 students and each car could hold 4 students. Find the number of buses and cars.
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Question 13 of 28
13. Question
Each afternoon Enrico rides the 20km from work to home but one day he got a flat tyre and had to walk the rest of the distance. He rides at an average speed of 30 km/h but walks at 6 km/h. If the entire journey took one hour, how far did he have to walk?
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Question 14 of 28
14. Question
Ethan and Jake are going to race their bikes. Jake leaves at 9:30 am, gets a 45-minute head start and rides at a constant speed of 12km/h. When Ethan starts, he rides at a constant speed of 16 km/h. Draw graphs to represent the distance travelled and find the time when Ethan overtakes Jake.
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Question 15 of 28
15. Question
The square root of 1 less than a certain number is the same as the number subtracted from 7. What is the number?
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Question 16 of 28
16. Question
The dimensions of a square are modified to make a rectangle. Two opposite sides of a square are increased by 6 cm and the other two sides are decreased by 4 cm. The area of the rectangle is the same as the area of the original square. What was the perimeter of the square?
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Question 17 of 28
17. Question
The numerator of a fraction is 4 more than the denominator. If the value of the fraction is 2 less than the value of the denominator, what are the two possible values of the denominator?
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Question 18 of 28
18. Question
When Lachlan drives to work he picks up his workmate Ryan. Lachlan lives directly 18 km south of Ryan and their workplace is 15 km directly easy of Ryanâ€™s house. Lachlan always drives at 40 km/h. How much time, to nearest minute, would Lachlan save if he did not have to pick up Ryan? (Assume there is a direct road from his home to work.)
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Question 19 of 28
19. Question
Two yachts are sailing away from the same buoy. Yacht A is sailing east at 12km/h and Yacht B is sailing south at 16 km/h. When Yacht A has travelled 30km, how far apart are the two yachts?
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Question 20 of 28
20. Question
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Question 21 of 28
21. Question
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Question 22 of 28
22. Question
A cylinder with a diameter of 8 cm and a height of 12 cm is three-quarters filled with warm water. Jack drops ice-blocks measuring 4 cm by 3 cm by 2 cm into the container. How many ice-blocks can be placed into the container before water spills out?
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Question 23 of 28
23. Question
Mia cuts a 4-mm diameter circular hole out of a piece of cardboard and holds the cardboard 45 cm from her eyes so that the moon just fits inside the circle. If the diameter of the moon is 3475 km, how far is the moon from Mia?
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Question 24 of 28
24. Question
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Question 25 of 28
25. Question
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Question 26 of 28
26. Question
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Question 27 of 28
27. Question
Isabella and Madison are playing a game, taking turns rolling two dice. The game is won by the first player to roll a double six. Isabella has the first roll. What is the probability that she wins the game on her second turn, to 2 decimal places?
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Question 28 of 28
28. Question
At a second hand book sale there are 2000 books. There are 800 childrenâ€™s books and the remainder are adultsâ€™ books. Half of the 1100 non-fiction books are for adults. A book is chosen at random. What is the probability that it is fiction, given that it is a childrenâ€™s book?
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Grade 10
Time limit: 0
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Question 1 of 30
1. Question
How long will it take for an amount of money invested at 0.4% per month compound interest to treble in value? Give your answer to the nearest year.
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Question 2 of 30
2. Question
In 2003 a grazing property was worth $890000.Â The value increased for the following 6 years at a rate of 4.2% per annum. After 2009, the value of property dropped by 12% p.a. for the next 3 years due to a severe drought. What was the value of the property in 2012?
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Question 3 of 30
3. Question
Four hundred tickets were sold for a school musical, where adult tickets were $3y each and children were half price. If there were 6x adult tickets sold, write an expression for the total value of ticket sales.
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Question 4 of 30
4. Question
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Question 5 of 30
5. Question
David left home at 7:40pm and walked to a friendâ€™s party at an average speed of 6 km/h. When he arrived at his friendâ€™s home he realised that it was the wrong night, and he ran home at an average speed of 12km/h. If he arrived home at 8:10 pm, how far does he live from his friend?
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Question 6 of 30
6. Question
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Question 7 of 30
7. Question
On fine days Rus rides the 10 km from home to work but this morning he got a flat tyre and had to walk his bike the rest of the distance. He rides at an average speed of 30km/h but walks at 6 km/h. If the entire journey took 10 minutes longer than usual, how far did he ride before he got the puncture?
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Question 8 of 30
8. Question
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Question 9 of 30
9. Question
An aeroplane holds exactly 244 passengers who are charged $25 for the first checked bag and $15 for a second checked bag. On a particular flight every seat was taken and all passengers had either one or two items of checked baggage. How many passengers checked only one bag if the total baggage fees collected was $6820?
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Question 10 of 30
10. Question
Jill knows the square root of six more than her favourite number is the same as the difference between the number and six. Solve an equation to find Jillâ€™s number, if Jillâ€™s number is even.
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Question 11 of 30
11. Question
Every Saturday Jarryd drives a distance of 240 km at a constant x km/h he would reach his destination an hour earlier. Find Jarrydâ€™s usual speed.
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Question 12 of 30
12. Question
Two boats travel at right angles leaving the same dock at the same time. After 1 hour the boats are 20 km apart. If one boat travels 5 km/h faster than the other boat, find the average speed of the slower boat, to the nearest kilometre per hour.
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Question 13 of 30
13. Question
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Question 14 of 30
14. Question
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Question 15 of 30
15. Question
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Question 16 of 30
16. Question
Movie tickets are sold for $15 each and 345 people are willing to buy them. For every $2 increase in price, there are 30 fewer customers. What is the ticket price that will maximise revenue, and how much extra will be collected?
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Question 17 of 30
17. Question
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Question 18 of 30
18. Question
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Question 19 of 30
19. Question
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Question 20 of 30
20. Question
A sphere and a hemisphere have the same radius. What is the ratio of their surface areas?
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Question 21 of 30
21. Question
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Question 22 of 30
22. Question
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Question 23 of 30
23. Question
A cube is completely filled with 8L of water. A solid sphere with diameter 20 cm is placed into the water and sinks to the bottom of the cube. Water spills from the top of the cube. If the sphere is removed, how deep is the water?
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Question 24 of 30
24. Question
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Question 25 of 30
25. Question
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Question 26 of 30
26. Question
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Question 27 of 30
27. Question
The slant heights of two similar cones are 24 cm and 16 cm. What is the radius of the smaller cone if the larger cone has a radius of 8cm? Give your answer to 3 significant figures.
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Question 28 of 30
28. Question
A circle with centre O has a radius OB=12 cm. A perpendicular OC cuts the chord AB at M where OM=4 cm. Find the length of the chord AB, correct to 2 decimal places.
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Question 29 of 30
29. Question
A bag contains five balls numbered 1, 3, 3, 4 and 5. Two balls are selected at random, the first returned before the second is drawn, and the numbers added to give a score. The balls are returned to the bag and the game is played a second time. If the two scores are added, what is the probability that the total will be at least 19?
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Question 30 of 30
30. Question
The probability that A occurs is 0.5. The probability that A occurs given that B occurs is 0.25. The probability that B occurs given that A occurs is 0.2. What is the probability that B occurs?
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Maths Methods 11
Time limit: 0
Quiz Summary
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The cost of parachuting course consists of a change of $250 which covers equipment hire and tuition, and a further expense of $55 per jump. How many jumps could a person doing the course afford if she was prepared to spend to $1000?
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Question 3 of 17
3. Question
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Question 4 of 17
4. Question
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Question 5 of 17
5. Question
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Question 6 of 17
6. Question
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Question 7 of 17
7. Question
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Question 8 of 17
8. Question
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Question 9 of 17
9. Question
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Question 10 of 17
10. Question
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Question 11 of 17
11. Question
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Question 12 of 17
12. Question
A housing loan package offers 8.4% p.a. interest. Fees and charges associated with this product ofÂ $795 are added at the end of each year, after the interest is calculated for that month. Using this package, what monthly payment is needed if $310000 is borrowed over 25 years?
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Question 13 of 17
13. Question
The following data give the marks of 30 students in a physics test.