Student Number:
______________________
ST PIUS X
COLLEGE
CHATSWOOD
2020 Stage 6
Year 11 Examination
70% of Assessment
Mathematics Standard
General
Instructions
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Total marks:
80
Section I – 10 marks
 Attempt Questions 1-10
 Allow about 15 minutes for this section
Working time - 120 minutes
Write using black pen
NESA approved calculators may be used
A reference sheet is provided at the back of this paper
For questions in Section II, show relevant mathematical reasoning and/or
calculations
Section II – 70 marks
 Attempt all questions
 Allow about 1 hour and 45 minutes for this section
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Year 11 Mathematics Standard
Blank Page
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Year 11 Mathematics Standard
Section I
10 marks
Attempt questions 1 - 10
Allow about 15 minutes for this section
Use the multiple-choice answer sheet for questions 1-10
Leah works a 38-hour week at a rate of $32.88 per hour. If she works at night Leah is paid
a loading of $2.70 per hour. What is Leah’s wage in a week where she works 38 hours of
which 12 are at night?
(A)
$1249.44
(B)
$1281.84
(C)
$1352.12
(D)
$1644.00
The ages of the retirees who live in Adam’s Retirement Village are: 72, 70, 68, 67, 67, 65,
64 and 60. A retiree has moved into the village who is aged 71. What will be the effect on
the ages?
(A)
Mean increases and the standard deviation increases.
(B)
Mean increases and the standard deviation decreases.
(C)
Mean decreases and the standard deviation increases.
(D)
Mean decreases and the standard deviation decreases.
Taxable income
Tax payable
0 - $18 200
Nil
$18 201 - $37 000
Nil + 19 cents for each $1 over $18 200
$37 001 - $87 000
$3572 + 32.5 cents for each $1 over $37 000
$87 001 - $180 000
$19 822 + 37 cents for each $1 over $87 000
$180 001 and over
$54 232 + 45 cents for each $1 over $180 000
Georgia earns $198 000 in a year. Her allowable deductions total $22 000. Using the table
above, which of the following expressions represents her total tax payable?
(A)
$19 822 + $4 000 × 0.37
(B)
$19 822 + $89 000 × 0.37
(C)
$54 232 + $18 000 × 0.45
(D)
$54 232 + $40 000 × 0.45
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Year 11 Mathematics Standard
Ryan makes a dot plot to show the hours spent using the Internet each day by his friends.
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⚫
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0
1
2
3
4
5
6
How many of his friends use the Internet for 3 or more hours each day?
(A)
2
(B)
3
(C)
4
(D)
6
Hudson buys a car for $19 500 and is depreciated at a rate of 15% of its purchase price
each year. What is the salvage value of the car after five years?
(A)
$4875
(B)
$8652
(C)
$14 625
(D)
$16 575
A tablecloth of diameter 80 cm is placed on a table of diameter 120 cm.
What fraction of the table does the tablecloth cover?
1
(B)
(A)
3
4
(C)
(D)
9
2
3
5
9
Which is the correct expression to make v the subject of the formula 𝑢 = 𝑝𝑞 + 𝑣𝑡 2 ?
(A)
𝑡2
𝑣=
𝑢 + 𝑝𝑞
(B)
𝑣=
𝑡2
𝑢 − 𝑝𝑞
(C)
𝑣=
𝑢 + 𝑝𝑞
𝑡2
(D)
𝑣=
𝑢 − 𝑝𝑞
𝑡2
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Year 11 Mathematics Standard
The coordinates of St Petersburg are 60°N, 30°E. What are the coordinates of Oslo if it is
19° west of St Petersburg?
(A) 60𝑜 𝑁, 49𝑜 𝐸
(B) 41𝑜 𝑁, 30𝑜 𝐸
(C) 79𝑜 𝑁, 30𝑜 𝐸
(D) 60𝑜 𝑁, 11𝑜 𝐸
Violet collected information on the type of housing in a new estate. What is the type of
data?
(A) Continuous
(B) Categorical
(C) Discrete
(D) Stratified
10. A line passes through the points (6,0) and (0,3).
What is the equation of the line?
(A)
1
𝑦 =− 𝑥+6
2
(B)
𝑦 = −6𝑥 + 3
(C)
1
𝑦 =− 𝑥+3
2
(D)
𝑦 = 6𝑥 + 3
5
Year 11 Mathematics Standard
Section II
70 marks
Attempt all questions
Allow about 1 hour and 45 minutes for this section
Answer each question in the appropriate writing booklet.
Your responses should include relevant mathematical reasoning and/or calculations.
Question 11
(2 marks)
Marks
The time taken (in seconds) to download ten different videos is shown below:
130, 145, 120, 153, 143, 127, 129, 142, 137, 148, 139, 141.
Calculate correct to two decimal places:
(a)
Mean
1
(b)
Standard Deviation
1
Question 12
(2 marks)
Tyler invests $18,000 in an account paying 5.2% p.a. flat interest over a period of
3 years. What amount is Tyler able to withdraw from his account at the end of
3 years?
6
2
Year 11 Mathematics Standard
Question 13
(3 marks)
Marks
The graph shows the growth in the length of an earthworm.
(a)
When was the initial length of the earthworm?
1
(b)
Calculate the gradient of the line.
1
(c)
What is the equation of this line?
1
Question 14
(1 mark)
Medicine is given as a concentration of 200 mg per 100 mL. What is the dosage rate for this
medicine in g/mL?
7
1
Year 11 Mathematics Standard
Question 15
(2 marks)
Marks
Use the formula 𝑀 = 0.5𝑝2 to find M in standard form, correct to three significant figures, given
that:
(a)
𝑝 = 1.96 × 106
1
(b)
1
𝑝 = 3.5 × 10−4
Question 16
(3 marks)
A water tank is the shape of closed cylinder with a radius of 1.4 m and a height
of 1.9 m.
(a)
Determine the maximum volume of the water tank. Answer correct to three decimal
places.
1
(b)
What is the capacity of the tank to the nearest litre?
1
(c)
Find the surface area of the water tank. Answer correct to two significant figures.
1
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Year 11 Mathematics Standard
Question 17
(4 marks)
Marks
Solve the following equations.
(a)
7𝑥 + 2 = 17 + 4𝑥
1
(b)
6(5𝑚 − 7) = 6𝑚
1
(c)
2𝑎 = 1 +
Question 18
4𝑎
3
2
(2 marks)
A wage sheet of a small business shows one employee’s details.
2
Employee
Rate per hour
Normal hours
Overtime (×2)
Wage
Jill May
$25.00
26
x
$850
Jill worked some overtime hours (double time) that are missing from the wage sheet. Using the
information on the wage sheet, how many hours of overtime did Jill work?
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Year 11 Mathematics Standard
Question 19
(5 marks)
Marks
From a piece of material of length 90cm and width 60cm, a section is the be cut out to be
used as part of a design. The diagram shows the design section ABCE to be cut with
vertical measurements taken at equal intervals across the length of the material.
(a)
Use the Trapezoidal Rule to calculate the area of the section to be used for the design.
(Give your answer correct to 2 decimal places)
3
(b)
What is the area of the off-cut piece left of the material? (Give your answer in correct to 2
decimal places).
2
Question 20
(1 mark)
The pre-GST cost of a mobile phone is $680. What is the GST payable on this mobile phone?
10
1
Year 11 Mathematics Standard
Question 21
(3 marks)
Marks
A movie runs for 198 minutes.
(a)
Convert this time to hours and minutes.
1
(b)
What is the finishing time of the movie if the movie starts at 15:45?
1
(c)
What is the starting time of the movie if the movie finishes at 10:20?
1
Question 22
(2 marks)
The table below shows Jenny’s average water usage per day.
Water usage
L/day
Washing machine
40
Toilet
28
Dishwasher
22
Other
15
(a)
How much water is Jenny using each day?
1
(b)
What percentage of her water usage is for the dishwasher? Answer to the nearest whole
number.
1
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Year 11 Mathematics Standard
Question 23
(4 marks)
Marks
The magazine holder below has four sides and a base. It is open at the top.
(a)
What is the area of the shaded side?
1
(b)
Calculate the surface area of the magazine holder.
1
(c)
The magazine holder is made from heavy duty cardboard. The cost of the cardboard is
$4.29 per square metre. What is the cost of making fifty of these magazine holders?
2
Question 24
(2 marks)
One grain of rice has a mass of 0.00171 grams. Approximately how many grains of rice are
required to make 1.5kgs? (Write your answer in scientific notation with TWO significant
figures).
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2
Year 11 Mathematics Standard
Question 25
(2 marks)
Marks
The graph shows the interest earned over a 4-year period on a lump sum investment.
(a)
If the annual flat rate of interest paid was 5%, what was the amount invested?
Question 26 (2 marks)
Blood alcohol can be estimated using the BAC formula shown below.
𝐵𝐴𝐶Male =
(10𝑁 − 7.5𝐻)
6.8𝑀
Jett weighs 75 kg and consumes five standard drinks in an hour.
What is Jett’s blood alcohol content? Answer correct to two decimal places.
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2
2
Year 11 Mathematics Standard
Question 27
(3 marks)
Marks
Chloe earns a gross wage of $78,000 per annum. She receives 17.5% of 4 weeks normal pay as
holiday loading. (Using 52 weeks per year)
(a)
What is Chloe’s holiday loading?
1
(b)
Chloe has booked an overseas flight for her annual holidays and will be paid
4 weeks normal pay and her holiday loading.
What is Chloe’s gross holiday pay?
1
(c)
What percentage of Chloe’s holiday pay is the holiday loading? Answer correct to the
nearest whole number.
1
Question 28
(2 marks)
A truck was purchased for $21 500 and sold for $8500 after 5 years. Assume straight-line
depreciation. How much does the truck depreciate each year?
Question 29
2
(2 marks)
The mean of five scores is 6. What is the missing score if four of the scores are
3, 5, 5 and 7?
14
2
Year 11 Mathematics Standard
Question 30
(3 marks)
Marks
The cumulative frequency histogram summarises the results of a test.
(a)
How many people completed the test?
1
(b)
What is the frequency of 50%?
1
(c)
Construct a cumulative frequency polygon (or ogive) on this graph.
1
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Year 11 Mathematics Standard
Question 31
(3 marks)
Marks
Jasmine has been offered terms to purchase a car. The price of the car is $22,400 or 35% deposit
and repayments of $90 per week for 4 years.
(a)
What is the amount of the deposit?
1
(b)
Find the total cost of the repayments.
1
(c)
What the cost of purchasing the car on terms?
1
Question 32
(2 marks)
What is the centre angle of a sector with an area of 13.68 m2 and radius of 3.50 m? Answer
correct to the nearest degree.
Question 33
2
(2 marks)
Lucy sells shoes for a retail store and receives wages of $2250 per month plus
4% commission on all her sales. What were her sales in a month if she received a total pay of
$2344?
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2
Year 11 Mathematics Standard
Question 34
(1 mark)
Marks
A car is travelling at a constant speed. It travels 100 km in 4 hours. This situation is described by
the linear equation 𝑑 = 𝑚𝑡 . What is the value of m?
Question 35
(a)
(2 marks)
Complete the following table of values for the equation 𝑦 = 2𝑥 + 1.
x
1
–3
–2
–1
0
1
1
2
y
(b)
Draw the graph of 𝑦 = 2𝑥 + 1. on the number plane below.
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1
Year 11 Mathematics Standard
Question 36
(2 marks)
Marks
A discus was thrown at a World Championships a distance of 74.08 metres.
(a) What is the precision of the reading?
1
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(b) What is the absolute error?
1
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(c) Find the percentage error. Answer correct to three decimal places.
Question 37 (2 marks)
A plane trip from Beijing (UTC +8) to Madrid (UTC +1) takes 15 hours. Dylan leaves Beijing at
7.15 am on the 1st April. What is the date and time Dylan arrives in Madrid?
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1
2
Year 11 Mathematics Standard
Question 38
(2 mark)
The graph above shows the results of a survey given to customers of a city hotel.
Category A represents location, Category B represents cleanliness, C represents Service, D
represents size of room, E represents noise, F represents access to parking and G represent
Other.
(a) Location improved when a new tram stop was built near the hotel. The hotel decides to
work on the category with the next highest number of complaints. If they improve this
category, what percentage of customers would have their complaint resolved?
1
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(b) Which additional category would they need to address to ensure they are satisfying 80%
of their customers?
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Continues over page
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Year 11 Mathematics Standard
Question 39
(3 marks)
A cat ran out onto the road in front of Joni while she was driving home. If Joni has travelled 30km
in half an hour and he reaction time is 0.75.
(a) What is her average speed?
1
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(b) Use the stopping distance (d in km/h) formula below to find Joni’s stopping distance
𝒅=
𝟓𝒗𝒕
𝟏𝟖
+
𝒗𝟐
𝟏𝟕𝟎
Where v is the speed in km/h and d is the reaction time.
2
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End of paper
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Year 11 Mathematics Standard
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