General Maths Exam Revision Semester 2 - 2015

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


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


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


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


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


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


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


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


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


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.


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


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


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


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


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


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


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


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


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


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


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


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


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


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.


scatterplot and draw a suitable

conclusion.

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.


scatterplot and draw a suitable

conclusion.

3


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


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


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


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


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


(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


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


(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


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


(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


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


(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


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


10 Use the 3-median method to find the equation

of the regression line for the data in question 9.

3

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General Maths Exam Revision Semester 2 - 2015