Name: ____________________ Class: __________( ) Date: __________

Junior Secondary Foundation Topics Supplement

3. Approximation, Errors, Percentages

Exercise 3A Conventional Questions  Exam Tips

1. (a) Round off 218.594 to the nearest integer.
(b) Round up 218.594 to 2 decimal places. 1. (b), (c)
Note the difference between rounding
(c) Round down 218.594 to 2 significant figures. up and rounding down. Do not mix up
the meanings of 2 decimal places and
2 significant figures.

2. Peter wants to buy the following tourism products from a travel agent:
Product Unit price Quantity needed
Air ticket
$3 388 per ticket 4 tickets
(tax included)
Accommodation
$1 820 per night 5 nights
(family room)
Travel insurance $273 per set 3 sets

(a) By rounding up the unit price of each product to the nearest $100, 2. (a) Remember to write down the
unit of the answer.
estimate the total amount that Peter should pay.
Explain (b) If Peter has only $24 000, does he have enough money to buy all
the products needed? Use the result of (a) to explain your answer.

3. The length and width of a piece of rectangular land are measured as

11.0 m and 8.4 m respectively. If the two measurements are correct to
the nearest 0.2 m, find the percentage error in calculating the perimeter
of the land correct to the nearest 0.01%.

4. In the figure, ABCDEF is a six-sided polygonal cardboard, where all the

measurements are correct to the nearest mm.
A B
6 mm
E
F 15 mm
9 mm

D 18 mm C

(a) Find the maximum absolute error of the measurements. 4. (a) Do not write the maximum
absolute error in the form of
(b) Find the least possible area of the cardboard. ±x mm.
4. (b) The least possible area is not the
Explain (c) Kelvin claims that the area of the cardboard can be greater than area of the cardboard calculated
from the given measurements.
349 mm2. Do you agree? Explain your answer.

© Oxford University Press 2012 W03-1

 Name: ____________________ Class: __________( ) Date: __________
5. (a) The weight of a piece of iron sheet is measured as 400 g correct to
the nearest 10 g. Find the least possible weight of the iron sheet.
(b) The weight of another piece of iron sheet is measured as 3.0 kg
correct to the nearest 0.1 kg.
Explain (i) Is it possible that the actual weight of this iron sheet is greater
than 3 080 g? Explain your answer.
Explain (ii) Is it possible to cut this iron sheet into 8 pieces of smaller iron 5. (b)(ii) Use the results of (a) and
(b)(i).
sheets, with each weight measured as 400 g correct to the
nearest 10 g? Explain your answer.

Explain 6. The volume of juice in a bottle is measured as 3 000 cm3 correct to the
nearest 100 cm3. Sally wants to pour n glasses of juice from the bottle
such that the volume of juice in each glass is measured as 150 cm3
correct to the nearest 10 cm3. Sally claims that at most 21 glasses of
juice can be obtained. Do you agree? Explain your answer.

7. Jenny deposits $6 000 in a bank at an interest rate of 2% per annum.

Find the simple interest received after 8 months.

8. A sum of $35 000 is deposited at an interest rate of 5% per annum for 8. Divide the interest rate per annum
by 4 to obtain the interest rate per
3 years, compounded quarterly. Find the amount correct to the nearest quarter.
dollar.

9. In a mathematics test, the score of Carmen is 10% lower than that of

Paul. It is given that the score of Carmen is 90.
(a) Find the score of Paul. 9. (a) In setting up an equation, any
symbol(s) used should be
Explain (b) The score of Tom is 10% higher than that of Carmen. Who has the defined.
highest score? Explain your answer.

10. In an online game, Nancy has 200 houses. The number of houses owned
by Karen is 20% more than that owned by Nancy.
(a) Find the number of houses owned by Karen.
Explain (b) If Karen gives a certain number of her houses to Nancy, will the 10. (b) Note that the number of houses
is an integer.
number of houses owned by Nancy be twice that owned by Karen?
Explain your answer.

11. In a shop, the marked price of a wallet is $648. It is given that the
marked price of the wallet is 35% higher than the cost.
(a) Find the cost of the wallet.
(b) If the wallet is sold at $456, find the loss per cent.
Explain (c) If the wallet is sold at a discount of 30% on its marked price, will
the shop make a loss? Explain your answer.

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 Name: ____________________ Class: __________( ) Date: __________
12. In a shop, the cost of a dining table A is $1 800. If a dining table A is
sold at a discount of 10% on its marked price, then the profit per cent is
25%.
1 800
(a) Find the marked price of a dining table A. 12. (a) Do not use $ as the
1 + 25%
Explain (b) With the shop owner’s special offer, a customer buys the first selling price.

dining table at a discount of 15% and the second dining table at a

discount of 30% on their marked prices. If a customer buys two
dining tables A, will the shop owner make a profit? Explain your
answer.

13. There are 525 male employees in a company. The number of male
employees is 25% more than that of female employees.
(a) Find the total number of employees in the company.
(b) There are 756 employees with university degrees in the company.
(i) Find the percentage of employees with university degrees in
the company.
Explain (ii) There are 68% of the male employees with university degrees 13. (b)(ii) Find the number of male
employees with university
in the company. Is the number of female employees with degrees and the number of
female employees with
university degrees less than the number of male employees university degrees. Then
make a comparison.
with university degrees? Explain your answer.

14. In the current financial year of a city, the amount of salaries tax charged
for a citizen is calculated according to the rules in the table below:
The net chargeable income is Net chargeable income Rate
equal to the net total income On the first $35 000 2%
minus the sum of allowances. On the next $35 000 8%
On the next $35 000 k%
Remainder 20%
(a) In the current financial year, the net chargeable income of a citizen
is $95 000. According to the rates in the table, the citizen’s salaries
tax payable is $7 000. Find the value of k.
Explain (b) John is a citizen in the city. In the current financial year, the net 14. (b) Find John’s salaries tax payable
and the amount obtained from
total income and the sum of allowances of John are $384 000 and each deposit. Then, make a
comparison.
$126 000 respectively. To pay his salaries tax, John deposits
$32 000 in a bank 12 months before the due day of paying salaries
tax at an interest rate of 3.6% per annum, compounded monthly.
He also deposits $5 000 in a bank 6 months before the due day of
paying salaries tax at an interest rate of 3.36% per annum,
compounded monthly. Based on the total amount obtained from the
two deposits, will John have enough money to pay his salaries tax
on the due day? Explain your answer.

© Oxford University Press 2012 W03-3

Name: ____________________ Class: __________( ) Date: __________

Junior Secondary Foundation Topics Supplement

3. Approximation, Errors, Percentages

Exercise 3B MC Questions 5. The length of a side of a square is measured as

1. 0.012 559 98 = 15 cm correct to the nearest cm. Find the least
A. 0.012 6 (correct to 3 decimal places). possible area of the square.
B. 0.012 6 (correct to 5 decimal places). A. 210.25 cm2
C. 0.012 6 (correct to 3 significant figures). B. 224.75 cm2
D. 0.012 6 (correct to 4 significant figures). C. 225 cm2
D. 240.25 cm2
2. If 2.855 7 < x < 2.856 4, which of the
following must be true? 6. The lengths of the four sides of a trapezium are
2.9(correct
A. x = 2.9 (corr. to
to 22 significant
sig. fig.) figures) measured as 4.1 cm, 4.1 cm, 5.2 cm and
B. x = 2.85 (correct to 3 significant figures) 10.8 cm respectively. If these measurements
C. x = 2.856 (correct to 4 significant figures) are correct to the nearest 0.1 cm, find the
D. x = 2.856 0 (correct to 5 significant relative error in calculating the perimeter of the
figures) trapezium.
1
A.
484
3. 5 235.251 8 =
1
A. 5 230 (correct to the nearest ten). B.
242
B. 5 240 (rounded down to 3 significant 1
C.
figures). 121
2
C. 5 235.2 (correct to 5 significant figures). D.
121
D. 5 235.26 (rounded up to 2 decimal
places). 7. The length of a long piece of ribbon is
measured as 20 m correct to the nearest m. If
4. The figure shows the positions of four real the ribbon is cut into n pieces such that the
numbers w, x, y and z on the number line. length of each shorter piece is measured as
Which of the following is the best estimate of 18 cm correct to the nearest cm, find the
w – (xy – z)? greatest possible value of n.
w x y z
A. 110
–6 0 6 B. 117
A. –14 C. 118
B. –6 D. 123
C. 2
D. 8

© Oxford University Press 2012 W03-4

Name: ____________________ Class: __________( ) Date: __________
8. If the monthly savings of Raymond are 12. Jane sold two jackets for $450 each. She
decreased from $1 500 to $1 250, then the gained 25% on one and lost 25% on the other.
percentage decrease in the monthly savings is After the two transactions, Jane
1 A. lost $150.
A. 9 % . C. 20%.
11 B. lost $60.
2 1
B. 16 % . D. 83 % . C. gained $60.
3 3
D. had no gain and no loss.
9. A sum of $20 000 is deposited at an interest
rate of 3% per annum for 4 years, compounded 13. If the population of city A is 25% more than
half-yearly. Find the interest correct to the the population of city B, then the population of
nearest dollar. city B is

A. $2 400 C. $2 530 A. 20% less than the population of city A.

B. $2 510 D. $2 547 B. 25% less than the population of city A.
C. 75% less than the population of city A.
10. Steven buys a flat for $2 500 000. He then sells D. 80% less than the population of city A.
the flat to Sammi at a loss of 15%. At what
price should Sammi sell the flat in order to 14. If the base and the height of a parallelogram
make a profit of 15%? are decreased by 20% and increased by k%

A. $1 806 250 C. $2 500 000 respectively so that its area is decreased by

B. $2 443 750 D. $3 306 250 10%, find the value of k.

A. 7.5 C. 12.5
11. In the current financial year of a city, the B. 10 D. 15
amount of salaries tax charged for a citizen is
calculated according to the following rules: 15. In a school, 60% of the students are boys. If

Net chargeable income Rate 48% of the girls and 54% of the boys fail a

On the first $38 000 3% mathematics examination, then the percentage

of students who pass the mathematics
On the next $38 000 7%
examination is
On the next $38 000 12%
A. 46.8%. C. 51.6%.
Remainder 18%
B. 48.4%. D. 53.2%.
Benny is a citizen in the city. In the current
financial year, the net chargeable income of
16. The marked price of a mobile phone is $5 000.
Benny is $120 000. Find his salaries
If the mobile phone is sold at a discount of
tax payable.
30% on its marked price, then the loss per cent
A. $8 360 C. $10 460
is 12.5%. What should the discount per cent be
B. $9 440 D. $15 200
if the profit is $750?
A. 5% C. 15%
B. 6.25% D. 18.75%

© Oxford University Press 2012 W03-5