Western Mathematics Exams Practice Paper 1 PRELIMINARY FINAL EXAMINATION Mathematics Standard General Instruction s 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
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WME Preliminary Mathematics Standard Exam 2018 · Web viewPractice Paper 1 PRELIMINARY FINAL EXAMINATION Mathematics Standard General Instructions Reading time – 5 minutes Working
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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)
Western MathematicsExams
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)
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Question 12 (2 marks)
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.
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1
Marks
Question 16 (2 marks)
A surveyor drew the following diagram of a paddock.
Calculate the area of the paddock.
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Question 17 (2 marks)
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?
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(b) What is the probability that he lands on Section X or Section Y?
Write a five-number summary for the data. …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………...
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Question 20 (3 marks)
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?
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 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?
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(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?
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1
Marks
(a) Who would receive the higher weekly gross pay, and how much is the difference?
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(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
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(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.
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1
Marks
(a) How much would it cost for 30 litres of fuel?
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1
(b) How much fuel could be bought for $70.00?
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1
(c) Describe how the graph is an example of direct variation.
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1
Question 28 (4 marks)
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?
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(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.
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1
Marks
Question 29 (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?
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Question 30 (2 marks)
What is the capacity, in litres, of the cylindrical tank shown?
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1
Question 31 (4 marks)
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”?
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(b) What was the interquartile range of the data?
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(c) How many people had between 50 and 90 “friends”?
(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?
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(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.
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1
Question 34 (5 marks)
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? …………………………………………………………………………………………... …………………………………………………………………………………………...
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(b) Write an equation that would describe the line representing Carley’s trip. …………………………………………………………………………………………... …………………………………………………………………………………………...
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(c) Mason travelled at 75 km/h. Draw the graph of his trip on the same set of axes. …………………………………………………………………………………………...
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(d) If they left home at the same time, how many minutes before or after Carley, did Mason arrive in town?
Western Mathematics Exams Preliminary - Standard Mathematics Practice Paper 1
Question 36 (4 marks)
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?
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(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?
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.