Maths Quest 11 Standard General Mathematics 1
Trigonometry WorkSHEET 7.1 Name: _________________________
1 Find the values of unknown marked sides
correct to 2 decimal places.
4
2 Find the value of angle correct to 1 decimal
place.
2
3 A ladder 6 m long rests against a vertical wall
and forms an angle of 40° to the horizontal
ground. How high up the wall does the ladder
reach, correct to 2 decimal places?
2
Maths Quest 11 Standard General Mathematics 2
4 A large heavy drum is pushed 3.5 m up an
inclined plane. If the inclined plane rises 2 m
vertically, find the angle the inclined plane
makes with the horizontal.
2
5 A child 1.08 m tall flies a kite with 100 m of
released string which makes an angle of 70°
with the horizontal. How high is the kite
flying?
3
6 The angle of depression of a boat from a cliff
60 m high is 10°. How far (to the nearest
metre), is the boat from the base of the cliff?
2
Maths Quest 11 Standard General Mathematics 1
Financial arithmetic WorkSHEET 9.1 Name: ___________________________
1 If $3200 is invested for 9 months at 5% p.a.,
calculate:
(a) the amount of simple interest earned
(b) the total amount at the end of the term.
2
2 How long will it take to earn $500 simple
interest by investing $8500 at 4.25%?
2
3 Johnny invested $60 000 in Ski International
debentures. He earned 6.5% p.a., which is paid
quarterly.
(a) How much interest will he earn over 5
years?
(b) How much interest will he earn each
quarter?
3
Maths Quest 11 Standard General Mathematics 2
4 Two banks pay simple interest on short-term
deposits. Bank A pays 6% p.a. over 4 years and
Bank B pays 6.5% p.a. over 3.5 years.
Calculate the difference between each bank’s
final payout if $5000 was invested into each
account.
3
5 Determine the principal invested in a term
deposit that accumulates $2060 in simple
interest after 6 months at a rate of 5.5% p.a. (to
the nearest dollar).
3
Maths Quest 11 Standard General Mathematics 3
6 Kim has $18 000 to invest for 2 years. She has
the following options:
(a) A term deposit at 4.5% compounded
annually.
(b) Shares, paying a dividend rate of 1.12%
per quarter.
(c) A building society account, paying a return
of 0.38% per month.
(d) A business venture with guaranteed return
of 0.01% daily.
Advise Kim which option to take if all the
investments are equally secure.
9
7 Jack and Jill bought a house for $120 000 in an
area where the house prices rise on average 3%
per year. They decided to hold on to their house
until its value is $220 000. How many years
should Jack and Jill wait until they sell their
current house?
3
Maths Quest 11 Standard General Mathematics 4
8 (a) Calculate the compound interest on term
deposit of $10 000 at the rate of 6% p.a. for
3 years when investment is compounded
(i) annually
(ii) semi-annually
(iii) quarterly
(iv) monthly
(v) daily.
(b) Which is the best investment option?
11
Maths Quest 11 Standard General Mathematics 5
9 The painting Elisa bought for $560 from an art
exhibition appreciates (increases in value) by
15% p.a. If this rate of appreciation continued,
determine the value of the painting after
25 years.
2
10 An iPod is priced at $499 at the beginning of
2005.
(a) If the inflation rate is 4.2% p.a., estimate
the cost of the iPod at the beginning of
2006.
(b) The government predicts inflation to fall to
3.1% in 2006. Estimate the cost of the iPod
at the beginning of 2007.
4
Maths Quest 11 Standard General Mathematics 1
Financial arithmetic WorkSHEET 9.2 Name: ___________________________
1 Kelly invests $5000 at 3% simple interest for
10 months. Calculate:
(a) the amount of simple interest earned
(b) the total amount at the end of the term.
3
2 How much time will it take for Peter to earn
$1000 simple interest if he invests $5000 at the
rate of 3.2% p.a.?
2
Maths Quest 11 Standard General Mathematics 2
3 Karen has $20 000 to invest for 12
3 years. She
considers the following options:
(a) a term deposit at 4.25% compounded
annually
(b) shares, paying a dividend rate of 1.25% per
quarter
(c) a building society account, paying a return
of 0.45% per month
(d) a business venture with a guaranteed return
of 0.02% daily.
Advise Karen which option to take if all the
investments are equally secure.
9
4 Kay and Jim bought a house for $150 000 in an
area where the house prices rise on average 5%
per year. They decided to hold on to their house
until its value is $200 000. How many years
should Kay and Jim wait until they sell their
current house?
2
Maths Quest 11 Standard General Mathematics 3
5 The passbook page below shows all the
transactions for the month of September.
Date Credit Debit Balance
4 Sept. $80 $429.13
12 Sept. $534.12
15 Sept. $541.60
26 Sept. $534.12
28 Sept. $18.40
(a) Calculate the balance after each transaction
and enter your results in the table.
(b) Calculate the total credits for the month of
September.
(c) Calculate the total debits for the month of
September.
(d) Find the interest that will be earned in
September if the bank pays 3.75% p.a.
simple interest on the minimum monthly
balance.
Maths Quest 11 Standard General Mathematics 4
6 Use the passbook page from question 5 to find
the interest that will be earned in September if
the bank pays 3.75% p.a. simple interest on the
minimum daily balance.
7
7 For a ‘55 days interest free’ credit card,
calculate the amount of interest charged on an
outstanding balance of $872.25 which was
repaid 10 days after the due date, given that the
first purchase was made on the first day of the
30-day statement period and the annual
percentage interest rate was 15.75%. (Assume
that no other purchases were made after the end
of the statement.)
4
Maths Quest 11 Standard General Mathematics 5
8 The minimum balance owing on a credit card
account is taken to be the larger of $25 or 1.5%
of the outstanding balance. Any excess above
the card limit must also be included in the
payment. Calculate the minimum balance due
on a credit account with a limit of $1400 if the
closing balance was:
(a) $1440
(b) $1280
(c) $860
3
Maths Quest 11 Standard General Mathematics 6
9 An ‘up to 55 days interest-free period’ credit
card was used for purchases which, after the
30-day interval, totalled $1400.
(a) Find the minimum amount due if the
current credit limit on this card is $2000
and the bank requires the larger of $25 or
1.5% of the outstanding balance. Any
excess above the card limit must also be
included in the payment.
(b) If the balance was paid 10 days after the
due date (which was 25 days from the
statement date), what was the interest at
16% p.a. from the start of the 30-day
interval?
5
10 A personal loan of $6000, borrowed at 15%
p.a. calculated on a reducing monthly balance,
is to be repaid in monthly instalments of $150
each. Determine the amount still owed at the
end of the second month
5
Maths Quest 11 Standard General Mathematics 1
Univariate data WorkSHEET 1.1 Name: ___________________________
1 A sample of people were asked: ‘Do you
support capital punishment?’ Their responses
were divided into three categories: Yes, No and
Unsure. The results were as follows:
Y U Y Y N
N Y Y Y Y
Y Y U N N
Y N U N Y
Y Y Y Y Y
Y N N Y U (a) Construct a frequency distribution table for
the data.
(b) Represent the information using a bar
graph.
2
2 This question refers to information given in
question 1:
(a) How many people were in favour of
capital punishment?
(b) What was the relative frequency of people
in favour of capital punishment?
(c) What was the percentage who were in
favour?
(d) What type of data does this question
illustrate?
2
Maths Quest 11 Standard General Mathematics 2
3 A restaurant owner surveyed his customers
about how they liked the taste of the Christmas
Day Special meal. The results are shown
below:
delicious great fine fine
delicious great delicious delicious
delicious delicious great great
great fine great delicious
great delicious fine fine
(a) Construct a dotplot of the data.
(b) How many customers found the meal
delicious?
3
4 This question refers to the data in question 3:
(a) What percentage of the customers found
the meal delicious?
(b) What type of data does this illustrate?
4
5 Explain what is meant by discrete data and
continuous data.
2
6 The following data gives the lengths in
centimetres of 25 red finned trout caught in
Lake Eildon in Victoria.
17.3 19.6 20 21.6 21.7
17.6 19.6 20.3 21.1 21.7
18.3 19.4 20.5 20.9 22.8
18.4 19.2 20.6 20.9 22.9
18.8 19.2 20.6 20.8 23.7 Represent the data on a frequency distribution
table.
2
Maths Quest 11 Standard General Mathematics 3
7 (a) Using the result in question 6, draw a
histogram of the data.
(b) Add a frequency polygon to the histogram.
3
8 This grouped frequency table gives the number
of ‘salmon cods’ caught by a fisherman on
25 fishing trips.
Number of
salmon cods
Frequency
f
20–24 1
25–29 2
30–34 4
35–39 4
40–44 6
45–50 8 (a) Draw a histogram of the data.
(b) Add a polygon to the histogram.
(c) State the skew.
4
Maths Quest 11 Standard General Mathematics 4
9 The test marks of 30 students are shown below: Test
mark
Frequency
f
40– 3
50– 4
60– 5
70– 8
80– 7
90– 3 (a) What does 60 mean in the table?
(b) Copy the above table and add a
cumulative frequency column.
(c) How many students had marks less than
70?
4
10 (a) Using the result in the previous question,
represent the data using an ogive.
(b) How many students obtained a mark
below 80?
3
Maths Quest 11 Standard General Mathematics 1
Univariate data WORKSHEET 1.2 Name: ___________________________
1 The following frequency table shows the sizes
of fish caught by a fisherman on 25 occasions.
Size of fish
Frequency
f
25–29 2
30–34 6
35–39 7
40–44 5
45–49 3
50–55 2 (a) Draw a histogram of the data.
(b) Add a frequency polygon to the
histogram.
(c) Describe the distribution.
3
2 Copy the table in the question above and add a
cumulative frequency column.
2
Maths Quest 11 Standard General Mathematics 2
3 (a) Using the cumulative frequency table
obtained in the question above, represent
the data using an ogive.
(b) How many fish were less than 40 cm?
3
4 The masses of 30 women were measured and
recorded as below.
Weight
(kg)
Frequency
f
60– 4
65– 7
70– 6
75– 8
80– 3
85– 1
90– 1
(a) What is meant by 75– in the table?
(b) Copy the table and add a cumulative
frequency column.
3
Maths Quest 11 Standard General Mathematics 3
5 (a) Represent the data in the question above
using an ogive.
(b) How many women weigh less than
70 kg?
3
6 The following data give the amount of weekly
pocket money given to a student for 8 weeks:
$5.80, $6.40, $5.00, $6.50, $6.80, $5.90, $6.80,
$5.20.
(a) Find the mean of the pocket money.
(b) Find the median of the pocket money.
(c) Find the mode of the pocket money.
4
Maths Quest 11 Standard General Mathematics 4
7 This frequency table shows the sick days taken
by the workers in a factory in a month.
Number
of sick
days
Frequency
f
0 8
1 6
2 4
3 2
4 4
5 3
6 3 (a) Find the mean number of sick days per
worker.
(b) Find the median number of sick days per
worker.
(c) Find the mode for the number of sick days.
5
Maths Quest 11 Standard General Mathematics 5
8 This grouped frequency table shows the area of
farm lots in hectares.
Area (ha) Frequency
30– 3
40– 2
50– 8
60– 6
70– 3
80– 1
90– 2
(a) Add the midpoint, x, frequency times
midpoint, f x, and cumulative frequency
columns to the table. Write the sum of the f
and f x columns.
(b) Find the mean area of the farm lot.
(c) Find the median area of the farm.
(d) Find the mode.
5
9 The number of goals scored by a team is shown
below.
5, 4, 4, 7, 5, 9, 12, 14, 16, 16.
(a) Find the lower quartile.
(b) Find the upper quartile.
(c) Find the interquartile range
2
10 Use your calculator to find the standard
deviation of the set of outcomes when a six-
sided die is rolled as shown below.
1, 2, 3, 4, 5, 6
State your answer correct to 2 decimal places.
1
Maths Quest 11 Standard General Mathematics 1
Bivariate data WorkSHEET 4.1 Name: ___________________________
1 The table shows the number of Icy-poles sold
and the temperature of the day recorded by a
shopkeeper.
Daily temperature
(°C)
Number of Icy-
poles sold
14 250
10 200
22 365
26 500
30 630
20 420
18 320
12 280
8 220
6 150
(a) Plot the data upon a scatterplot.
(b) State the type of correlation shown by the
scatterplot and draw a suitable conclusion
from it.
3
Maths Quest 11 Standard General Mathematics 2
2 The table below shows mass and height for
men and women aged from 18 years onwards.
Height
(cm)
Mass
(kg)
150 50
160 57
170 65
180 72
190 81
200 90
(a) Construct a scatterplot showing this data.
(b) State the type of correlation shown by the
scatterplot and draw a suitable
conclusion.
3
Maths Quest 11 Standard General Mathematics 3
3 A potato farmer records the yield in kilograms
and the length in metres of 10 commercial
potato plots as shown.
Length
(m)
Yield
(kg)
10 220
6 250
16 400
2 25
13 500
7 430
4 120
12 350
5 310
8 280
(a) Construct a scatterplot to illustrate this
data.
(b) State the type of correlation shown by the
scatterplot and draw a suitable
conclusion.
3
Maths Quest 11 Standard General Mathematics 4
4 The heights of 15 Year-10 students from Clever
High were compared with the lengths of their
ulnas (the bone that extends from the elbow to
the centre of the wrist bone). The results are
shown below.
Ulna (cm) Heights (cm)
26 170
28 174
25 178
25 167
24 166
23 164
25 176
26 177
25 170
27 172
25 183
26 175
(a) Which measurement is independent (put
on the x-axis)?
(b) Construct a scatterplot of height against
ulna length.
(c) State the type of correlation and draw a
suitable conclusion.
4
Maths Quest 11 Standard General Mathematics 5
5 The temperature (°C) and rainfall (mm) over
2 weeks during the month of April in
Melbourne is shown below.
Temperature
(°C)Rainfall (mm)
5 3
16 5
20 8
10 9
14 6
8 7
18 8
13 7
9 6
17 7
7 4
14 10
4 2
3 1
(a) Which is the independent variable (put on
the x-axis)?
(b) Construct a scatterplot of rainfall against
temperature.
(c) State the type of correlation and draw a
suitable conclusion.
4
Maths Quest 11 Standard General Mathematics 6
6 This table shows the hearing test scores of
people of different ages:
Age Hearing test score
55.0 2.5
40.0 3.8
35.0 4.0
30.0 3.9
42.0 2.5
48.0 3.2
50.0 2.2
48.0 1.8
32.0 3.0
45.0 2.0
30.0 4.0
56.0 1.8
(a) Which is the independent variable (put on
the x-axis)?
(b) Construct a scatterplot showing hearing
test score against age.
(c) Find the correlation coefficient and
interpret your result.
(a) 3
Maths Quest 11 Standard General Mathematics 7
7 The table below shows the average monthly
temperature and average occupancy rate of
motel rooms in a rural locality. Average
temperature (°C)
Number of room
nights occupied
25 45
20 40
30 50
18 47
12 40
6 28
7 20
8 16
18 25
20 30
23 48
26 50
(a) Which is the independent variable?
(b) Find the correlation coefficient and
interpret your result.
4
Maths Quest 11 Standard General Mathematics 1
Bivariate data WorkSHEET 4.2 Name: ___________________________
1 The table shows average weekly earnings and
median house prices each quarter over the last
3 years.
Average weekly
earnings ($)
Median
house prices
($)
620 150 000
618 144 000
625 140 000
622 144 000
627 130 000
630 120 000
628 136 000
632 140 000
635 120 000
636 100 000
638 130 000
636 134 000
(a) Which is the independent variable?
(b) Construct a scatterplot.
(c) Draw a suitable conclusion from the
scatterplot.
4
2 Use the calculator to calculate the correlation
coefficient of the data in question 1. Interpret
your result.
3
Maths Quest 11 Standard General Mathematics 2
3 The table shows the daily temperature (°C) and
rainfall (mm) during the month of February for
15 wet days.
Temperature
(°C)
Rainfall
(mm)
30 3
32 25
28 20
30 27
25 10
26 8
28 15
33 35
29 33
25 19
24 15
28 26
31 28
35 30
33 28
(a) Which is the independent variable?
(b) Construct a scatterplot of rainfall against
temperature and draw a suitable
conclusion.
3
4 Use the results of question 3 to calculate the
correlation and draw a conclusion.
3
Maths Quest 11 Standard General Mathematics 3
5 The travelling times of full-time Victorian
university students using public transport is
being investigated. The time taken for a one-
way trip (in minutes) is recorded along with the
distance travelled (in kilometres).
Distance travelled
(km)Time (minutes)
15 50
30 30
20 30
15 45
20 25
14 30
20 40
15 42
16 20
17 30
12 15
20 20
35 25
20 35
10 15
(a) Which is the independent variable?
(b) Construct a scatterplot of time against
distance travelled.
3
6 Use the data in question 5 to calculate the
correlation coefficient. Interpret your result.
3
Maths Quest 11 Standard General Mathematics 4
7 This table shows the number of crab traps
dropped into the sea by a fishing crew, and the
number of crabs caught over a period of
10 days. The maximum number of crab traps
legally allowed by the fisheries department was
47 per licence.
Number
of crab
traps used
Number of
crabs
caught
25 10
40 32
45 12
40 8
38 15
35 20
42 18
44 14
39 7
46 5
(a) Which is the independent variable?
(b) Construct a scatterplot of the number of
crabs caught against the number of nets
used. Interpret your results.
3
(c) Use the data to calculate the correlation
coefficient and draw a conclusion.
3
Maths Quest 11 Standard General Mathematics 5
8 Find the equation of a straight line that joins the
points (2, 5) and (3, 1).
2
9 A forensic scientist wished to establish the
height of adult females from the length of their
ulnas. She measured the heights of 10 skeletons
and the length of the ulna in each. Her results
are shown below.
Length of ulna
(cm)
Height of
skeleton (cm)
24 160
22 156
25 160
20 150
25 163
23 162
26 165
24 156
21 155
25 164 (a) Which is the independent variable?
(b) Construct a scatterplot showing height of
skeleton against length of ulna.
(c) Find the calculator to find the equation of
the line of best-fit using the least square
method.
6
Maths Quest 11 Standard General Mathematics 6
10 Use the 3-median method to find the equation
of the regression line for the data in question 9.
3