Year 11 General Mathematics

Objective Response Bank
YEAR 11
General Mathematics

Preliminary Course Content

Financial Mathematics
FM1: Earning money
FM2: Investing money
FM3: Taxation
Data Analysis
DA1 and DA2: Statistics in society, data collection and sampling
DA3: Displaying single data sets
DA4: Summary statistics
Measurement
M1: Units of measurement
M2: Applications of area and volume
M3: Similarity of two-dimensional figures
M4: Right-angled triangles
Probability
PB1: The language of chance
PB2: Relative frequency and probability
Algebraic modelling
AM1: Basic algebraic skills
AM2: Modelling linear relationships

Earning money Solutions Main Menu

1  Abbey sells shoes for a retail store and receives wages of $1875 per month plus 4% commission on all her sales. What were her sales in a month if she received a total pay of $1953?
(A) $878.00 / (B) $1946.88
(C) $1950.00 / (D) $2190.12
2  A wage sheet of a small business shows one employee’s details.
Employee / Rate per hour / Normal hours / Overtime (×2) / Wage
Nate Jones / $20.00 / 30 / x / $840
Nate worked some overtime at double time rate which is missing from the wage sheet. Using the information on the wage sheet, how many hours of overtime did Nate work?
(A) 4 / (B) 5
(C) 6 / (D) 8
3  Eliza works for $19.20 per hour for eight hours each day on Thursday and Friday.
On Saturday she works for six hours at time-and-a-half.
How much does Eliza earn in total for Thursday, Friday and Saturday?
(A) $268.80 / (B) $307.20
(C) $480.00 / (D) $691.20
4  Which of the following is the highest pay?
(A) $1442.22 per week
(B) $2884.68 per fortnight
(C) $6247.50 per month
(D) $75 000 per annum
5  Samuel receives a normal hourly rate of $22.60 per hour. What is his pay when he works 8 hours at normal rate and 3 hours are time-and-a-half?
(A) $180.80 / (B) $248.60
(C) $282.50 / (D) $316.40
6  Grace works a 38-hour week at a rate of $26.00 per hour. She receives 17½% of 4 weeks normal pay as holiday loading. What is Grace’s holiday loading?
(A) $172.90 / (B) $691.60
(C) $3952.00 / (D) $4643.60
7  Alexis earns a weekly retainer of $425 plus a commission of 8% on sales. What is her weekly earnings when she made sales of $8620?
(A) $34.00 / (B) $459.00
(C) $689.60 / (D) $1114.60
8  Emma earns a royalty of 15% on net sales. There were $35 850 net sales in the last year. What is Emma’s royalty payment?
(A) $5 377.50 / (B) $30 472.50
(C) $35 850.00 / (D) $41 227.50
9  Henry has a gross weekly wage of $835.12. Henry has deductions of $103.84 for PAYG tax, $33.40 for private health insurance and $5.00 for a charity. What is Henry’s net wage?
(A) $692.88 / (B) $769.68
(C) $900.56 / (D) $977.36
10  A bank charges an account servicing fee of $12 per month, ATM transaction fee of $0.50 and branch enquiry fee of $0.60. What Stella’s banking costs for the past nine months if she made 20 ATM withdrawals and 8 branch enquires?
(A) $108.00 / (B) $109.10
(C) $118.00 / (D) $122.80

Investing money Solutions Main Menu

11  A builder charges a total of $165 to repair a broken window. The Goods and Services Tax (GST) of 10% was included in this total. Which of the following statements is correct?
(A) 90% of $165 was the price of the repair before the GST was added.
(B) The total repair price included $16.50 GST.
(C) The price before adding the GST is $165 ÷ 1.10.
(D) The GST cannot be determined without knowing the original repair cost.
12  Leo invests $1600 for 3 years at 8% p.a. compounding quarterly. How much compound interest will he receive?
(A) $415.54 / (B) $429.19
(C) $2015.54 / (D) $2029.19
13  What is the simple interest on $250 at 5.5% p.a. for 2 years?
(A) $25.00 / (B) $27.50
(C) $34.70 / (D) $275.00
14  Sebastian invests $4 000 at 10% p.a. simple interest. How many years will it take for Liam’s investment to double in value?
(A) 8 years / (B) 9 years
(C) 10 years / (D) 11 years
15  Using the graph what is the interest after years?
(A) $40
(B) $50
(C) $60
(D) $100
16  Willow invests $70 000 at 7% p.a. interest compounding annually. What is the amount owed after 5 years? (Answer to the nearest dollar)
(A) $$28 179 / (B) $74 900
(C) $94 500 / (D) $98 179
17  What is the simple interest rate when $8000 increases to $8600 over 3 years?
(A) 2.5% p.a. / (B) 3% p.a.
(C) 6% p.a. / (D) 7.5% p.a.
18  What is the interest earned for 3 years on $6000 at 9% p.a. interest compounding monthly? (Answer to the nearest dollar)
(A) $1770 / (B) $1852
(C) $7770 / (D) $7852
19  Abigail brought 800 shares at a market value of $10.20 each. Brokerage costs incurred were $38 including GST. What is the total cost of purchasing the shares?
(A) $48.20 / (B) $8160
(C) $8198 / (D) $30 400
20  A painting was bought for $460 000 and appreciated at the rate of 7% p.a. What will be the value of the painting after 4 years? (Answer to the nearest dollar).
(A) $473 016 / (B) $492 200
(C) $588 800 / (D) $602 966

Taxation Solutions Main Menu

21  Ryder is landscape gardener and entitled to the following tax deductions: union fees of $484, donations of $720, equipment cost of $860, and car expenses of $1455. What is Ryder’s total allowable tax deduction?
(A) $484 / (B) $860
(C) $1455 / (D) $3519
22  Audrey has an allowable deduction of $4690. What is her taxable income if her gross annual salary is $43 720
(A) $39 030 / (B) $43 720
(C) $48 410 / (D) $90 620
23  Edward has a taxable income of $53 684. What is his Medicare levy? (Assuming the Medicare levy is calculated at a rate of 1.5% of the taxable income).
(A) $80.53 / (B) $805.26
(C) $8052.60 / (D) $80 526
24  Lola is a librarian who has a taxable income of $69 410. The tax payable on the first $30000 is $3 600 and the balance was taxed at a marginal rate of 30%.
How much does Lola have to pay in tax?
(A) $3 600 / (B) $15 423
(C) $30 000 / (D) $24 423
25  Lilly has an allowable deduction of $8460. What is her taxable income if her gross annual salary is $56 140
(A) $47 680 / (B) $56 140
(C) $64 600 / (D) Unknown
26  Caleb has a taxable income of $45 680. The tax payable on the first $30 000 is $3 600 and the balance was taxed at a marginal rate of 30%. How much does Caleb have to pay in tax?
(A) $3 600 / (B) $4 704
(C) $8 304 / (D) $37 376
27  The rate of the Medicare levy is 1.5% of the taxable income. What is the taxable income if the Medicare levy was $989.70? Answer correct to the nearest dollar.
(A) $15 / (B) $1485
(C) $6 598 / (D) $65 980
28  The pre-GST cost of a mobile phone is $360. What is the GST payable on this phone?
(A) $15 / (B) $30
(C) $36 / (D) $45
29  A cost of repairing a fence (including GST) comes to $495. What is the GST component?
(A) $39.00 / (B) $45.00
(C) $49.50 / (D) $50.00
30  A MP3 player costs 115 Euros after a 21% VAT has been added. What was the price without VAT? Answer to the nearest cent.
(A) 90.85 Euros
(B) 94.00 Euros
(C) 95.04 Euros
(D) 96.74 Euros

Statistics and society, data collection and sampling Solutions Main Menu

31  For the scores 20, 22, 22, 14, 19, 22, 20, 21, 24 and 12 consider the following statements.
I The median is greater than the mean.
II The mode is less than the median.
(A) Both statement I and II are true.
(B) Both statement I and II are false.
(C) Statement I is false and statement II is true
(D) Statement I is true and statement II is false
32  What type of data is information collected on the type of motor vehicle?
(A) Discrete / (B) Continuous
(C) Categorical / (D) Stratified
33  A survey required the participants to write down their age last birthday.
Which of the following terms best describes this data?
(A) Categorical / (B) Continuous
(C) Discrete / (D) Stratified
34  A country has 30% of the population between the ages of 20 and 30. How many people aged between 20 and 30 should be included in a sample of 250 people?
(A) 30 / (B) 45
(C) 60 / (D) 75
35  In a grocery store every fifth bottle of milk is checked for a used-by-date.
What is this method of sampling?
(A) Census / (B) Random
(C) Stratified / (D) Systematic
36  ‘Do you agree? Yes/No’. What is the classification for this data?
(A) Categorical / (B) Continuous
(C) Discrete / (D) Text
37  Which of the following is an example of a random sample?
(A) First ten shoppers in the store.
(B) Ten shoppers who used EFT.
(C) Ten shoppers drawn from a box.
(D) Ten shoppers who spent the most.
38  Four boys and four girls randomly selected from a surf club. How would you describe this type of sample?
(A) Quantitative / (B) Random
(C) Stratified / (D) Systematic
39  Which one of these is an example of categorical data?
(A) The age of a student.
(B) The length of a playground.
(C) The colour of a wall.
(D) The capacity of a swimming pool.
40  Source of data obtained by interviewing people.
(A) Primary / (B) Observing
(C) Secondary / (D) Survey

Displaying single data sets Solutions Main Menu

41  What is the class centre for the class 85-89? / Class / Frequency / Cumulative Frequency
80-84 / 2
85-89 / 4
90-94 / 3
95-99 / 6
(A) 4
(B) 85
(C) 87
(D) 89
42  What is the cumulative frequency of class 95-99 for the above table?
(A) 6 / (B) 9
(C) 15 / (D) 99
43  What is the total number of marks? /
(A) 50
(B) 100
(C) 150
(D) 200
44  What is the frequency of 40 in the above graph?
(A) 0 / (B) 10
(C) 40 / (D) 100
45  A, B, C and D represent the answers to a survey question. If 300 people completed the survey how many people selected answer D /
(A) 10
(B) 30
(C) 270
(D) 300
46  What is the size of the angle used for C in the sector graph?
(A) 18º / (B) 36º
(C) 54º / (D) 72º
47  Find the range of this data: 3, 4, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10
(A) 4.5 / (B) 5
(C) 5.5 / (D) 7
48  A radar chart is constructed with 10 sectors. What is the size of the angle in each sector?
(A) 10 / (B) 18
(C) 30 / (D) 36
49  A box-and-whisker plot has a lower extreme of 17, lower quartile of 24, median of 30, upper quartile of 35 and upper extreme of 39. What is the range of data?
(A) 9 / (B) 18
(C) 22 / (D) 30
50  Find the interquartile range of this data: 15, 15, 16, 14, 12, 18, 20, 22, 52, 28
(A) 7 / (B) 10
(C) 15 / (D) 22

Summary statistics Solutions Main Menu

51  What is the mode for these scores 7, 4, 4, 7, 5, 4, 3, 1, 6, 5, 3, 5 and 5?
(A) 4 / (B) 4.5
(C) 5 / (D) 6
52  Zachary spends the following amounts each day: $5.30, $4.40, $4.50, $5.00, $3.80, $4.80. What is the median?
(A) $4.10 / (B) $4.40
(C) $4.65 / (D) $4.75
53  What is the median of the data in this table? / Score / Frequency / fx
1 / 8
2 / 5
3 / 5
4 / 3
5 / 3
(A) 1
(B) 2
(C) 2.5
(D) 4
54  What is the mean of the data in the above table?
(A) 1 / (B) 2
(C) 2.5 / (D) 4
55  What is the population standard deviation of 19, 6, 11, 15, 13, 14, 10 and 21?
(A) 4.5 / (B) 4.8
(C) 8 / (D) 13.6
56  What is the mode of 7, 15, 5, 9, 10, 11, 12, 7 and 14?
(A) 5 / (B) 7
(C) 10 / (D) 14
57  What is the class centre of 30-35?
(A) 32 / (B) 32.5
(C) 33 / (D) 33.5
58  The mean of five scores is 4. What is the missing score if four of the scores are 2, 5, 5 and 7?
(A) 1 / (B) 2
(C) 4 / (D) 5
59  What is the mode of the data in this table? / Score / Frequency
1 / 3
2 / 4
3 / 2
4 / 6
5 / 7
6 / 3
(A) 3
(B) 4
(C) 5
(D) 7
60  What is the population standard deviation of the data in the above table?
(A) 1.49 / (B) 1.52
(C) 1.58 / (D) 1.61

Units of measurement Solutions Main Menu

61  The number of significant figures in the number 0.00206 is:
(A) 2 / (B) 3
(C) 4 / (D) 5
62  Hugo has planted red and white rose bushes in the ratio 2:3. How many white rose bushes are there if he planted at total of 30 rose bushes?
(A) 6 / (B) 12
(C) 18 / (D) 20
63  What is 425 000 written with two significant figures?
(A) 42 / (B) 43
(C) / (D) 430 000
64  What is the new price when $60 is increased by 20% then decreased by 20%?
(A) $38.40 / (B) $57.60
(C) $60.00 / (D) $86.40
65  Arrange the numbers , and in ascending order.
(A) , ,
(B) , ,
(C) , ,
(D) , ,
66  A four litre tin of paint is made using a mixture of blue, white and green paint in the ratio 3:5:2. How much blue paint is needed per tin?
(A) 300 mL / (B) 900 mL
(C) 1200 mL / (D) 2000 mL
67  The concentration of salt in liquid A is 20g per 100 mL and the concentration of salt in liquid B is 40g per 100 mL. What is the concentration of salt when 150 mL of liquid A is mixed with 250 mL of liquid B?
(A) 30g per 100 mL
(B) 32.5g per 100 mL
(C) 37.5g per 100 mL
(D) 60g per 100 mL
68  Ava made a drink by mixing water with cordial in the ratio 5:2. What amount of water is required if she used 2.5 L of cordial?
(A) 2 L / (B) 2.5 L
(C) 5 L / (D) 6.25 L
69  Chloe’s car uses 8 L of fuel to travel 25 km. How far can it travel on 20 L of fuel?
(A) 6.25 km / (B) 50 km
(C) 60 km / (D) 62.5 km
70  A plane travels at an average speed of 750 km/h. How far will it travel in 5 hours?
(A) 150 km / (B) 750 km
(C) 755 km / (D) 3750 km

Applications of area and volume Solutions Main Menu