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Class : F3___ No.___ Name ___________________________________ Teacher ____________

Form 3 Mathematics

Easter Holiday Revision Exercise PART 1 SECTION A Answer ALL questions and write your answers in the spaces provided.

1. Factorize 121 x2y2.

(2 marks)

2. Factorize 5m 42 + 2m2.

(3 marks)

3. (a) Without using a calculator, find the value of 72 ÷ 7

0 and express the

answer as a fraction.

(b) Simplify (p3q2)1, where p ≠ 0 and q ≠ 0, and express the answer with positive indices.

(4 marks)

4. Solve the inequality 5(x 3) < 3(3 x).

(3 marks)

5. $3 200 is deposited in a bank at an interest rate of 5 % p.a. compounded yearly.

Find the amount and compound interest received after 4 years.

(Give the answers correct to the nearest dollar.) (4 marks)

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6. The value of a bottle of red wine is $3 500. If its value increases by 4% every year, what will its value be

after 10 years? (Give the answer correct to the nearest $10.)

(2 marks)

7. The sum of a father’s age and his son’s age is not greater than 35. If the father’s age is x, and is 6 times of

his son’s age, find the range of x.

(4 marks)

8. A card is drawn at random from a pack of 52 playing cards. What is the probability that the card drawn is

(a) a black queen? (b) a picture card?

(5 marks)

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9. A dice is thrown a number of times. The results are as follows:

Outcome 1 2 3 4 5 6

Frequency 23 15 10 25 13 34

(a) What is the total number of dice throws?

(b) Find the experimental probability of getting the number 6.

(c) Find the experimental probability of getting a number smaller than 4.

(6 marks)

10. Three cities run for election of the best city. Here are their marks for different aspects.

Aspect City

Weight A B C

Civilization 7 8 5 3

Environmental protection 8 6 7 3

Transportation 9 8 8 2

Economy 6 5 4 2

(a) Find the weighted mean mark of each city.

(b) If the city getting the highest weighted mean mark wins the election and becomes the best city,

which city wins the election?

(7 marks)

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11. In the figure, △ABC is an isosceles triangle and BAD = CAD. Prove that

(a) △ABD △ACD,

(b) △BCD is an isosceles triangle.

(6 marks)

12. The weights of 8 packets of potato chips are as follows:

30 g, 32 g, 28 g, 38 g, 42 g, 42 g, 36 g, 40 g

(a) Find (i) the mean of these weights.

(ii) the median of these weights.

(iii) the mode of these weights.

(b) If the datum 36 g is deleted, which average(s) in (a) remain(s) unchanged?

(10 marks)

A

B

D

C

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13. (a) Represent 1 × 24 + 0 × 23 + 1 × 2 + 1 × 22 + 0 × 1 as a binary number.

(b) Represent 13 × 162 + 5 × 16 + 7 × 1 as a hexadecimal number.

(2 marks)

SECTION B (52 marks) Answer ALL questions and write your answers in the spaces provided.

14. (a) Factorize 12a2 3a 9. (b) Using the answer in (a), factorize 12(b 1)2 3(b 1) 9.

(7 marks)

15. Find the value of each of the following expressions and express the answer in scientific notation.

(a) 4 780 000 000 + 220 000 000 (b) 2 001 000.0

104.0000 6 72

(9 marks)

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16. The table below shows the salaries tax rates.

Net chargeable income Rate

On the first $40 000 2 %

On the next $40 000 7 %

On the next $40 000 12 %

Remainder 17 %

Last year, Hugo’s average monthly income was $20 000 and his salaries tax payable was $8 400. If his

average monthly income increases by 5 % this year and he has allowances of $120 000, find

(a) his salaries tax payable this year.

(b) the percentage change in his salaries tax payable, correct to 3 significant figures.

(9 marks)

17. Derek buys y bottles of soya milk for $6 each and (y 2) bottles of milk for $9 each. If he has $150 only,

find the greatest possible value of y.

(7 marks)

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18. Form a three-digit number from the digits 3, 5 and 6 (digits cannot be repeated). Use a tree diagram to

find the probabilities of the following events.

(a) An odd number is formed.

(b) A number that is divisible by 5 is formed. (7 marks)

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19. The following are the results of an intelligence quotient (IQ) test of the employees

in an organization:

89 92 120 114 90 78 86 93 107 112

124 88 109 105 92 97 112 123 105 117

125 114 79 100 108 98 100 86 112 102

(a) Construct a frequency distribution table with class intervals 7079, 8089, etc. for the data.

(b) Using the table in (a), find the mean of the IQs of these employees.

(c) Using the table in (a), find the modal class of the IQs of these employees. (6 marks)

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20. In the figure, AD = BD, BDE = ADE and AC // ED.

Prove that AB is an altitude of △ABC.

(7 marks)

A

E

B D

C

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PART 2

Choose the best answer for each question.

1.

6. 11. 16. 21. 26.

2.

7. 12. 17. 22. 27.

3.

8. 13. 18. 23. 28.

4.

9. 14. 19. 24. 29.

5.

10. 15. 20. 25. 30.

1. If k is positive, which of the following represents the solutions of x k?

A.

B.

C.

D.

2. xx23

A. x33 .

B. 223 x .

C. x33

1.

D. 223

1x

.

3. Factorize 25 + 10h + h2.

A. (5 + h)2

B. (5 h)2

k 0

k 0

0 k

0 k

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C. 5(5 + h)2

D. 5(5 h)2

4. The solution of 123

34

x

x is

A. 9

7x . B.

9

7x . C.

3

1x . D.

3

1x .

5. Find the 1st and 3rd quartiles (Q1 and Q3) of the following data.

9, 5, 18, 20, 10, 8, 3

A. Q1 = 3, Q3 = 18

B. Q1 = 5, Q3 = 10

C. Q1 = 5, Q3 = 18

D. Q1 = 8, Q3 = 10

6. A point Q is selected randomly on the rope XY 15 cm in length. Find the probability that the length of

QY is less than 12 cm.

A. 5

4

B. 5

2

C. 5

1

D. 15

1

7. The following cumulative frequency polygon shows the distribution of ages of 80 employees:

15 cm

X Y Q

12

10

20

30

40

50

60

70

80

0

Cu

mu

lati

ve

freq

uen

cy

90

20 25 30 35 40 45 50

Age

55

Ages of 80 employees

Find the 80th percentile (P80) of the ages of these

80 employees.

A. 34

B. 36

C. 38

D. 50.5

8. The weight of 2 × 108 grains of pollen is 50 g. Find the weight of a grain of pollen.

A. 2.5 × 108 g

B. 2.5 × 107 g

C. 4 × 107 g

D. 4 × 108 g

9. The rateable value of a flat is $720 000. If the rates percentage charge is 5 % each year, find the rates

payable in a quarter of a year.

A. $36 000

B. $24 000

C. $18 000

D. $9 000

10. The base of a triangle is increased from 15 cm to 18 cm, but its height is decreased

by 10 % from 12 cm. Find the percentage change in the area of the triangle.

A. 8 %

B. +8 %

C. +10 %

D. +12 %

11. A bag contains 5 white balls, 4 yellow balls and 6 green balls. A ball is drawn from the bag randomly

for 30 times, and the ball drawn is put back into the bag each time. Find the expected number of times

of getting a yellow ball.

A. 12

13

B. 10

C. 9

D. 8

12. Tim has lunch at a fast food restaurant. The probabilities and prices of the set lunches that he can

choose are as follows.

Set lunch Probability Price

A 0.2 $30

B 0.15 $36

C 0.4 $35

D 0.25 $40

Find the expected value of Tim’s expenditure on lunch.

A. $32.8

B. $35.25

C. $35.4

D. $40

13. Which of the following is not a factor of x4 81?

A. x 3

B. x + 3

C. x 9

D. x2 + 9

14. If x 0, 2

2 44

xx

A.

22

xx .

B.

22

xx .

C.

xx

xx

22.

D.

2

1)2(

xx .

15. Factorize (m + n)2 6(m + n) + 9.

A. (m n + 3)2

B. (m + n 3)2

C. (m + n + 3)(m + n 3)

D. (m n + 3)(m + n 3)

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16. If a 0 and x is a positive integer, which of the following must be true?

A. ax = ax

B. x

x

aa

3

13

C. x

x

a

aa

22)(

D. (ax)2 = (ax)2

17. If a 0 and b 0, which of the following must be true?

I. a b 0

II. 011

ba

III. 0a

b

b

a

A. III only

B. I and II only

C. II and III only

D. I, II and III

18. If x is an integer and 2x + 5 13 3x, find the smallest value of x.

A. 0

B. 1

C. 2

D. 3

19. Two eggs are drawn randomly from a box of 3 chicken eggs and 2 duck eggs. The probability of getting

2 chicken eggs is

A. 10

1.

B. 10

3.

C. 5

1.

D. 5

3.

20. The depreciation rate of a computer is 12 % per year. What is the percentage decrease in its value after 2

years?

A. 22.56 %

B. 24 %

C. 25 %

D. 77.44 %

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21. A sum of money is deposited in a bank at an interest rate of 8 % p.a. compounded half-yearly. What is

the minimum number of years for the amount to exceed two times of the principal?

A. 7 years

B. 8 years

C. 9 years

D. 10 years

22. The figure shows a target in the shape of an equilateral triangle of side 20 cm.

It is formed by several equilateral triangles. Connie throws a dart at random and it hits the target. Find

the probability that the dart hits the shaded region.

20 cm

A. 16

1

B. 8

1

C. 4

1

D. 3

1

23. The table below shows the distribution of the monthly salaries of the employees

in a company.

Monthly salary ($) 8 000 8 800 10 500 13 000 22 000 280 000

Number of employees 3 5 8 5 3 1

Which of the following is/are more appropriate to reflect the real situation?

I. The average monthly salary of the employees is greater than $22 000.

II. The median is a suitable average.

III. $15 692 is a suitable average.

A. II only

B. III only

C. I and II only

D. I, II and III

24. In the figure, BA AC, AE = EC and AB // ED.

Which of the following may not be true?

A. DE AC

B. AD = AB

C. AD = CD

D. AD is a median of △ABC.

A

B D

C

E

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25. The table below shows the original prices, number of people ordering per day

and the percentage increases in price of 4 set meals in a fast food restaurant.

Set meal A B C D

Original price $36 $40 $50 $60

Number of people ordering per day 125 85 60 30

Percentage increase in price 10 % 6 % 3 % 1 %

Which of the following is/are more appropriate to reflect the real situation?

I. The average percentage increase in price is 5 %.

II. The percentage increase in sales is 6 %.

III. The percentage increase in sales is 12 %.

A. I only

B. II only

C. I and II only

D. I and III only

26. Factorize x3 125.

A. (x 5)(x2 + 5x + 25)

B. (x + 5)(x2 5x + 25)

C. (x 25)(x2 + x + 5)

D. (x + 25)(x2 x + 5)

27. Each of the following cases lists the lengths of three line segments. Which set of the line segments can

form a triangle?

A. 4.7 cm, 4.7 cm, 9.4 cm

B. 5 cm, 6 cm, 12 cm

C. 8.5 cm, 9.5 cm, 20 cm

D. 10 cm, 15 cm, 18 cm

28. Which of the following numbers has/have the same value as 15310?

I. 100110002 II. 100110012 III. 9916

A. I only

B. II only

C. I and II only

D. II and III only

29. If △ABC is an acute-angled triangle, which of the following points must lie

inside △ABC?

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I. The centroid of △ABC

II. The circumcentre of △ABC

III. The orthocentre of △ABC

A. I only

B. III only

C. I and II only

D. I, II and III

30. In the figure, AY and BZ are the angle bisectors of BAC and ABC respectively. They intersect at P.

CP is extended to meet AB at X. Which of the following must be true?

A

B C Y

X Z

P

I. AP = BP = CP

II. CX bisects ACB.

III. △AXP △AZP

A. I only

B. II only

C. I and III only

D. I, II and III