wme preliminary mathematics standard exam 2018 · web viewpractice paper 1 preliminary final...

Western MathematicsExams

Practice

Paper 1PRELIMINARYFINAL EXAMINATION

Mathematics Standard

General Instructions

Reading time – 5 minutes

Working time – 2 hours

Write using black pen

Approved calculators may be used

A reference sheet is provided at the back of this paper

In Questions in Section II, show relevant mathematical reasoning and/or calculations

Total marks : 85

Section I – 10 marks (pages 2 – 6)

Attempt Questions 1 – 10

Allow about 15 minutes for this section

Section II – 75 marks (pages 7 – 25)

Attempt Questions 11 – 38

Allow about 1 hour and 45 minutes for this section

Section I

10 marksAttempt Questions 1–10Allow about 15 minutes for this section

Use the multiple-choice answer sheet for Questions 1 – 15

1. Janelle measures the diameter of the screen on her phone to be 145 mm using a ruler marked in 5 mm divisions.

What is the percentage error in her measurement (correct to 2 significant figures)?

(A) 0.25%

(B) 1.7%

(C) 2.5%

(D) 3.4%

2. Fried’s formula (below) is used to give medication dosages for children aged 1-2 years.

A drug called Lederol has an adult dosage of 45 millilitres.

Use the formula to find the dosage of Lederol for a child who is 16 months old (correct to the

nearest millilitre).

(A) 2 ml

(B) 3 ml

(C) 4 ml

(D) 5 ml

3.What is the shaded area, in terms of ?

(A)

(B)

(C)

(D)

4. A clothes dryer is rated at 3000 watts and is used for 2.5 hours per week.

If electricity costs 15 cents per kWh, find the cost of using the dryer for a year.

(A) $58.50

(B) $112.50

(C) $585.00

(D) $1 125.00

5. Oxana sells furniture, which she purchases from a manufacturer.To determine her retail price, she adds 40% to the wholesale price. She must then add 10% GST when selling the furniture.

What would you pay for a bed which costs Oxana $860.00 from the manufacturer?

(A) $910.00

(B) $1 204.00

(C) $1 290.00

(D) $1 324.40

6. Charli is in sales and is paid a weekly retainer of $350.00 plus a commission of 2.5% of weekly sales.

What is her weekly gross pay if her weekly sales were $13 265.00.

(A) $331.63

(B) $615.00

(C) $681.63

(D) $3 666.25

7. Garry is constructing a survey on entertainment options for people in his town.One question from the survey is shown below.

What type of data is being collected by this question?

(A) Categorical, nominal.

(B) Categorical, ordinal.

(C) Quantitative, continuous.

(D) Quantitative, discrete.

8. Julianne draws one card at random from the eight which are shown below.

A1 B4 A7 U2

K9 W8 Q8 A9What is the probability that she draws a card which has an A or a 9, but not both?

(A)

(B)

(C)

(D)

9.Which of the linear functions shown below has a gradient of

(A) (B)

(C) (D)

10. Mei completed eight laps of an oval while training for football.The times for each lap (to the nearest second) are shown below.

68, 55, 52, 48, 54, 54, 56, 65.

What was the mean and standard deviation of the times (correct to 1 decimal place).

(A)

(B)

(C)

(D)


PRELIMINARY FINALEXAMINATION

PRACTICE PAPER 1

Mathematics Standard 2

Section II Answer Booklet

Class and Teacher

Student Number

Student Name

75 marksAttempt Questions 11-36Allow about 1 hour and 45 minutes for this section

Instructions Answer the questions in the spaces provided. These spaces provide guidance for the expected length of response.

Your responses should include relevant mathematical reasoning and/or calculations.

Extra writing space is provided at the back of the booklet. If you use this space, clearly indicate which question you are answering.

Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1

Marks

Question 11 (2 marks)

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2


Barnard’s Star is 5.9630 light years from the Earth.

A light year is a distance of 9.4607×1012 km.

Calculate the distance in kilometres to Barnard’s Star, giving your answer in scientific notation, correct to three significant figures.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2

8 © Western Mathematics Exams 2018


Marks


The Bar chart with a Pareto line below shows the main reason people gave for choosing a restaurant in a survey.

(a) If a restaurant addresses the Quality and Flavour of its meals, what percentage of the people would have their main reason addressed?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(b) What additional reasons would they need to address to ensure they were meeting the needs of 95% of people in the survey?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1



Marks


……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2


Keiran bought a new car exactly three years ago for $48 500. He wants to sell it through a dealer.

The salesman at Trev’s Preloved Cars tells him that it has depreciated by $4 500 every year.

(a) What is the sale price of the car now?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(b) What percentage loss will Keiran make if he sells the car for this price?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1



Marks


A surveyor drew the following diagram of a paddock.

Calculate the area of the paddock.

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

…………………………………………………………………………………………...

2


A parachutist is trying to land on a target which has four sections marked W, X, Y and Z.From experience, he has a 20% probability of missing the target altogether, an 28% probability of landing on section X, a 16% probability of landing on Section W and a 16% probability of landing on Section Y.

(a) What is the probability that he lands on Section Z?

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(b) What is the probability that he lands on Section X or Section Y?

……………………………………………………………………………………………

……………………………………………………………………………………………

1



Marks


Charlotte, who weighs 56 kg, goes to a girl’s night out and consumes 5 standard drinks over a period of 4 hours.

The legal driving limit is a blood alcohol concentration (BAC) of 0.05, for drivers on an unconditional licence.

(a) Use the formula to estimate her BA, and hence, determine if she is over the legal driving limit.

N is the number of standard drinks consumedH is the number of hours of drinkingM is the persons mass in kilograms

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2

(b) To roughly estimate how long it will take for a person’s BAC to reach zero after stopping drinking, this formula can be used:

Where N = the number of hours for BAC to reach zero.

How long after Charlotte stops drinking will it take for her BAC to reach zero? Give your answer to the nearest 10 minutes.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1



Marks

Question 19 (2 marks)The stem and leaf plot shows the number of text messages sent by a group of 25 people in a week.

0 7 91 0 4 72 3 5 6 6 6 83 0 5 7 94 5 6 6 85 2 4 56 6 8 9

Write a five-number summary for the data. …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………...

2


The energy values for the three main component parts of food are

Protein 17 kJ/g

Fat 37 kJ/g

Carbohydrates 17 kJ/g

(a) A hamburger consists of 90 g of protein, 20 g of carbohydrates and 5 g of fat.How many kilojoules would be consumed when eating the hamburger?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1



Marks

(b) Marcella’s daily energy allowance is 8600 kJ.A small bag of chips contains 800 kJ of energy.What percentage of her daily allowance does Marcella consume if she eats a hamburger with a small bag of chips?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(c) Cycling uses 1800 kJ of energy each hour for a person of Marcella’s mass.How many minutes would she need to cycle to burn off the hamburger and chips?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1



Marks


The graph below shows the value of an investment of $12 000 which is invested at 5% pa compound interest.

i.e. The interest is calculated on the principal and is then added to the principal before the next years interest is calculated.

(a) Use the graph to read the value of the investment at the end of 10 years.

……………………………………………………………………………………………

1

(b) Calculate the total amount of interest that is earned on the investment over the 10 years.

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(c) Compare this with the amount of simple interest that would be earned on $12 000 after 10 years.

……………………………………………………………………………………………

……………………………………………………………………………………………

1



Marks


(a) Find the gradient of the line. …………………………………………………………………………………………... …………………………………………………………………………………………...

1

(b) …………………………………………………………………………………………... …………………………………………………………………………………………...

1

(c) On the same graph above, draw the graph of …………………………………………………………………………………………... …………………………………………………………………………………………...

1

(d) Find the point of intersection of the two linear graphs.

…………………………………………………………………………………………...

1



Marks


The sector shown has a radius of 0.5 m and an angle of 120o.

What is the area of the sector in square centimetres?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2


The table below shows the genres of the movies that Eugenie has shortlisted on her streaming service.

(a) What is the relative frequency for the Romance genre?

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(b) If she chooses one movie at random, what id the probability that it is not a Comedy?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1

Question 25 (6 marks)Fergus is on a wage of $22.50 per hour for a normal 40-hour week.Maisie is on an annual salary of $44 720, paid weekly.



Marks

(a) Who would receive the higher weekly gross pay, and how much is the difference?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2

(b) Maisie had allowable tax deductions of $650.00.Use the table below to calculate her income tax due for the year.

Taxable income Tax on this income0 – $18,200 Nil

$18,201 – $37,000 19c for each $1 over $18,200

$37,001 – $80,000 $3,572 plus 32.5c for each $1 over $37,000

$80,001 – $180,000 $17,547 plus 37c for each $1 over $80,000

$180,001 and over $54,547 plus 45c for each $1 over $180,000

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2

(c) Maisie also had to pay a Medicare levy of 2% of her taxable income. Calculate her weekly net pay after her income tax and Medicare levy are deducted.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2



Marks

Question 26 (2 marks)The frequency distribution table below shows the number of calls per hour to a 24/7 hotline over a period of 48 hours.

Number of Calls per hour Frequency

0 31 52 103 54 25 56 107 58 3

Describe the shape of the distribution in terms of skew and symmetry and whether the distribution is uni-modal or bi-modal.

…………………………………………………………………………………………… …………………………………………………………………………………………...

2


The graph shows the cost of purchasing fuel for a car.



Marks

(a) How much would it cost for 30 litres of fuel?

……………………………………………………………………………………………

1

(b) How much fuel could be bought for $70.00?

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(c) Describe how the graph is an example of direct variation.

……………………………………………………………………………………………

……………………………………………………………………………………………

1


Greg has bought a car which has a fuel consumption of 9.5 litres/100km, and which has two scheduled services per year.

The average cost of fuel is $1.45/litre over the year and each scheduled service costs $350.00 plus parts which average $168.00.

(a) Greg drives the car 225 km per week on average. How much would it cost him for fuel for the week?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2

(b) If Greg also purchases 2 tyres which cost $125.00 each, every year.How much should Greg allow in his weekly budget for the running costs of his car.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2



Marks


Leo boards a plane in London at 6 pm on Wednesday 10th September and flies for 22 hours before arriving in Sydney. Given that Sydney’s time zone is ten hours ahead of London’s, what is the local time when he disembarks in Sydney?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2


What is the capacity, in litres, of the cylindrical tank shown?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2




Anna conducts a survey on the number of “friends” that people have on a social media site.There were 160 people who took part in the survey.The box-and-whisker plot below illustrates the results of the survey.

(a) How many people had more than 40 “friends”?

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(b) What was the interquartile range of the data?

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(c) How many people had between 50 and 90 “friends”?

……………………………………………………………………………………………

……………………………………………………………………………………………

2




The train timetable below shows all trains leaving Central on the Cudgegong line between 5:00 pm and 6:00 pm.

Central Station 5:05 pm 5:20 pm 5:35 pm 5:50 pm Pitt St 5:08 pm 5:23 pm 5:37 pm 5:53 pm Barangaroo 5:11 pm 5:26 pm 5:40 pm 5:56 pm Victoria Cross 5:15 pm 5:30 pm 5:44 pm 6:00 pm Crows Nest 5:18 pm 5:33 pm 5:47 pm 6:03 pm Chatswood 5:22 pm 5:37 pm 5:51 pm 6:07 pm North Ryde 5:26 pm 5:41 pm 5:55 pm 6:11 pm Macquarie Park 5:28 pm 5:43 pm 6:13 pm University 5:30 pm 5:45 pm 6:15 pm Epping 5:33 pm 5:48 pm 6:00 pm 6:18 pm Cherrybrook 5:37 pm 5:52 pm 6:04 pm 6:22 pm Castle Hill 5:41 pm 5:56 pm 6:08 pm 6:26 pm Showground 5:44 pm 5:59 pm 6:29 pm Norwest 5:47 pm 6:02 pm 6:13 pm 6:32 pm Bella Vista 5:49 pm 6:04 pm 6:15 pm 6:34 pm Kellyville 5:51 pm 6:06 pm 6:17 pm 6:36 pm Rouse Hill 5:54 pm 6:09 pm 6:20 pm 6:39 pmCudgegong 5:55 pm 6:10 pm 6:21 pm 6:40 pm

(a) Justin wants to leave Pitt St and get to University by 6:00 pm.What is the latest time he could catch the train?

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(b) Ilanah arrives at Barrangaroo station at 5:00 pm and is travelling home to Bella Vista. She needs to stop off at Macquarie Park to run an errand which will take at most 15 minutes. Describe the train journeys that will get her home at the earliest possible time and give this time.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2



Question 33 (4 marks)Missy has 4 songs on her phone. They are by Lily Allen, Ed Sheeran, Justin Timberlake and ZHU.

She puts the phone on random selection mode, but only has time to play two songs before she must leave for class.

(a) Draw a tree diagram to show the possible combinations of the two artists and the order in which they are played.

2

(b) What is the probability that the two songs are by ZHU and Lily Allen in either order?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1

(c) What is the probability that one song is by Ed Sheeran but Justin Timberlake is not included?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1




Mason and Carley are brother and sister who live on a farm which is 25 km from town.

One day they drive separately from their home into town.

Carley’s trip, which took 15 minutes, is shown on the graph below.

(a) At what speed (in km/h) did Carley travel on her way to town? …………………………………………………………………………………………... …………………………………………………………………………………………...

2

(b) Write an equation that would describe the line representing Carley’s trip. …………………………………………………………………………………………... …………………………………………………………………………………………...

1

(c) Mason travelled at 75 km/h. Draw the graph of his trip on the same set of axes. …………………………………………………………………………………………...

1

(d) If they left home at the same time, how many minutes before or after Carley, did Mason arrive in town?

…………………………………………………………………………………………...

1




A paddock has one curved boundary and three straight boundaries.

A surveyor takes the measurements shown.

(a) Use three applications of the Trapezoidal Rule to find the area of the paddock.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

2

(b) Topsoil is to be spread over the paddock to a depth of 5 cm.How many cubic metres of topsoil will be needed?

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

1




Sydney (S) is located at 34o S, 151o E and Johannesburg (J) is at 26o S, 28o E.

(a) The Wallabies rugby team are playing a game which starts at 6 pm on Saturday in Johannesburg. What is the local time in Sydney when the game starts?

…………………………………………………………………………………………...

…………………………………………………………………………………………...

2

(b) The Wallabies fly out of Johannesburg at 10:00 am local time on Sunday on a non-stop flight and arrive in Sydney at 5:28 am on Monday, Sydney time. How many hours were they on the plane?

…………………………………………………………………………………………... …………………………………………………………………………………………...

…………………………………………………………………………………………...

2

End of Examination


Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1Section II Extra writing space

If you use this space, clearly indicate which question you are answering.


2019 Preliminary Final Examination

Mathematics Standard 1Mathematics Standard 2

REFERENCE SHEET


2019 Preliminary Final ExaminationMathematics Standard 2

Name ________________________________ Teacher ________________________

Section I – Multiple Choice Answer Sheet

Allow about 25 minutes for this sectionSelect the alternative A, B, C or D that best answers the question. Fill in the response oval completely.

Sample: 2 + 4 = (A) 2 (B) 6 (C) 8 (D) 9

A B C D

If you think you have made a mistake, put a cross through the incorrect answer and fill in the new answer.

A B C D

If you change your mind and have crossed out what you consider to be the correct answer, then indicate the correct answer by writing the word correct and drawing an arrow as follows.

A B C D

1. A B C D

2. A B C D

3. A B C D

4. A B C D

5. A B C D

6. A B C D

7. A B C D

8. A B C D

9. A B C D

10. A B C D

wme preliminary mathematics standard exam 2018 · web viewpractice paper 1 preliminary final...

Documents