Assessment

10 620 oranges are to be packed into 45 boxes so that each box contains the same number of oranges. How many oranges will be packed into each box?

I am 35 years old now. In 10 years time, I will be 3 times as old as my son. What will be the age of my son in 20 years time?

A container is 1/3 full of water. If 20 litres are added, then it is 3/4 full. How many litres does the container hold when full?

James buys a new car for $17 500 and after one year it loses 15% of its value. What is its value after 1 year?

Mrs. Chu received her payslip. Her gross wage was $450 and she had to pay 30% of it in tax, and 10% of it into a medicare fund. What was her net wage?

A pair of normal 6-sided dice are rolled. What is the probability of the sum of the 2 numbers to be 5?

Jean had $20 and spent 3/4 of it. How much did she spend?

A car tank when 2/3 full contains 48 litres. What is the capacity of the tank?

How many pieces 0.04 m long can be cut from a piece of timber that is 0.8 m long?

If 40% of a number is 120, find the number.

Find the length of each side of a cube that has a volume of 24389.

Two numbers have a sum of 5 and a product of -24. What are the two numbers?

Find the perimeter of a rectangular block of land 9p metres long and 5q metres wide.

What is 8m subtracted from the product of 2m and 3n?

I think of a number, add 5 to it, multiply this sum by 3 and then subtract 8. The result is 37. What is the number?

Two numbers have a sum of 5 and a product of -24. What are the two numbers?

Find the perimeter of a rectangular block of land 9p metres long and 5q metres wide.

What is 8m subtracted from the product of 2m and 3n?

I think of a number, add 5 to it, multiply this sum by 3 and then subtract 8. The result is 37. What is the number?

From the set of scores 3, 1, 4, 6, 5, 5, 7, 3, 4, 5, 4, 5, 7, the mode is …

Find the range of the scores 4, 3, 5, 1, 2, 8, 7, 10, 6, 9.

A bag contains 3 red, 4 blue and 5 yellow balls. Find the probability of choosing at random a red ball.

What is the difference between the mean and the median of scores 10, 20, 30, 40, 50?

Six men are employed to complete a job in 8 days. After 3 days’ 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.

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?

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?

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?

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?

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?

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?

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?

The manager of Nikki’s Nuts bought some nuts from a producer. He purchased 30kg of nuts at $4 per kilogram and another 20  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?

All vehicles at Sam’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?

Lana’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?

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?

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.

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?

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?

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?

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?

Kate’s grandmother is four times as old as Kate is now. In 6 years’ time she will be 2 years older than three times Kate’s age. How old are Kate and her grandmother now?

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.

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?

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.

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.

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?

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?

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 Ryan’s house. Lachlan always drives at 40 km/h. How much time would Lachlan save if he did not have to pick up Ryan?

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?

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?

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?

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?

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?

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?

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?

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.

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.

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.

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?

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?

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 friend’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?

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?

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?

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.

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?

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.

The square root of 1 less than a certain number is the same as the number subtracted from 7. What is the number?

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?

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?

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 Ryan’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.)

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?

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?

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?

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?

At a second hand book sale there are 2000 books. There are 800 children’s books and the remainder are adults’ 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 children’s book?

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.

In 2003 a grazing property was worth $890000.  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?

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.

David left home at 7:40pm and walked to a friend’s party at an average speed of 6 km/h. When he arrived at his friend’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?

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?

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?

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 Jill’s number, if Jill’s number is even.

Every Saturday Jarryd drives a distance of 240 km at a constant x km/h he would reach his destination an hour earlier. Find Jarryd’s usual speed.

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.

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?

A sphere and a hemisphere have the same radius. What is the ratio of their surface areas?

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?

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.

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.

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?

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?

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?

A housing loan package offers 8.4% p.a. interest. Fees and charges associated with this product of  $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?

The following data give the marks of 30 students in a physics test.

90, 61, 58, 88, 58, 69, 72, 58, 62, 45, 59, 64, 32, 72, 52, 63, 93, 58, 72, 95, 57, 65, 21, 44, 64, 34, 72, 69, 56, 63

The top 10% of students are to be given a certificate of excellence. What mark would be needed to get a certificate?

The following scores were recorded: 2, 6, 9, 1, 3, 5, 6, 7, 8, 2.

For these data find the standard deviation.

If a piece of wire is 80cm long, find the area of the largest rectangle that can be formed by the wire.