Term Exam Paper Kit
Introduction
Mathematics in Action (Second Edition) – Term Exam Paper Kit is written in accordance with each volume (1A, 1B, 2A, 2B, 3A and 3B) of the Mathematics in Action (Second Edition) series. It is specially designed to help teachers prepare term examination papers.
This Term Exam Paper Kit consists of two examination papers - Paper 1 and Paper 2. The details are as follows:
No. of questions / No. of Extra questions provided / Suggestedsolutions / Marking scheme
Paper 1 / Section A
Short questions / 10 / – / ü
(numerical answers only)
Section B
Long questions / 10 / 10 / ü / ü
Section C
Harder long questions / 3 / – / ü / ü
Paper 2 / Multiple choice questions* / 40 / 10 / ü
Extra questions for both Paper 1 and Paper 2 are provided for greater flexibility. In addition, corresponding extra questions for Section B and C can help teachers develop their own examination papers easily. Suggested solutions and Marking scheme are provided for all of the questions in Section B and C.
The soft copy of the questions is available on teacher’s website.
F. 2 First Term Examination
Mathematics (Paper 1)
Name: Class: No.:
Time Allowed: 75 minutes
This paper consists of 3 sections. Write your answers in the spaces provided.
Total Marks: 100
Section A (20 marks)
Answer ALL questions in this section. Each question carries 2 marks.
Working steps are NOT required in this section.
1. It is given that a : b = 3 : 2 and a : c = 6 : 1. Find the ratio
a : b : c.
2. If a length of 5 cm on the map represents an actual
distance of 4 km, express the scale of the map in the
form 1 : n.
3. Expand
4. Factorize
5. Simplify .
6. Factorize .
7. In 2009, the population of Town A was 1 132 000,
correct to the nearest 500. Find the percentage error
of this number, correct to 3 significant figures.
8. In the figure, △ABC and △ADE are two equilateral
triangles. Find ∠CDE.
______
9. In the figure, find x + y + z.
10. The diagram below shows the sales of a certain brand of toilet roll in 2009 and 2010.
(a) What is the ratio of the sales of toilet roll
in 2009 and 2010?
(b) Does the diagram mislead readers?
Section B (50 marks)
Answer ALL questions in this section. Each question carries 5 marks.
Working steps MUST be shown in answering questions in this section.
11. ABC oats are sold in packets of different sizes as shown in the figure.
(a) By comparing the price of each gram of oats, which package is more economical to customers? Explain briefly.
(b) The manufacturer decides to change the price of the ‘Large Packet’ so that both the packets are equally economical to customers. Find the new price of each ‘Large Packet’.
12. In a glass of lemon tea of volume 350 mL, the ratio of lemon juice to tea is 2 : 5.
(a) Find the volume of the lemon juice.
(b) If 50 mL of lemon juice is added to the lemon tea, find the new ratio of lemon juice to tea in the glass.
13. If where A, B and C are constants. Find the values of A, B and C.
14. Consider the formula
(a) Make y the subject of the formula.
(b) Find the value of y when .
15. (a) Factorize (3x + 7y)2 - (3x - 7y)2.
(b) Hence, or otherwise, simplify
16. (a) Factorize
(b) Simplify
17. The length and width of a school hall are measured to be 24.0 m and 14.5 m respectively, correct to the nearest 0.5 m.
(a) Find the maximum absolute error of the measurements.
(b) Find the upper limits of the actual length and width of the hall.
(c) Find the maximum area of the hall, correct to 3 significant figures.
18. In the figure, AEC, BED and BCF are straight lines. BA = BC. Find the values of x and y.
19. In the figure, ADE and BCE are straight lines.
(a) Find ∠BAC.
(b) Is △ABC an equilateral triangle? Explain your answer.
20. The following frequency polygon shows the time that S2A students spent on completing their art model.
The table below shows the time spent by S2B students.
Class mark (min) / 79.5 / 89.5 / 99.5 / 109.5 / 119.5Frequency / 4 / 8 / 10 / 5 / 13
(a) On the above figure, draw a frequency polygon to present the data in the table.
(b) Students in which class spend more time on completing their art model in general? Explain your answer.
(c) If students have to finish the art model within 104.5 minutes, how many S2B students cannot meet the requirement?
Section C (30 marks)
Answer ALL questions in this section. Each question carries 10 marks.
Working steps MUST be shown in answering questions in this section.
21. (a) Prove that each of the following is an identity.
(i)
(ii)
(4 marks)
(b) Let .
(i) By putting a = 9.99 and b = 0.01 into (a)(ii), find the exact value of S without using a calculator.
(ii) Mary estimates the value of S by first rounding off 9.99 and 0.01 to 1 decimal place. Find Mary’s estimate and its absolute error.
(6 marks)
22. The figure shows a regular pentagon ABCDE. EA and BC produced intersect at F.
(a) (i) Find ∠CDE.
(ii) Find ∠AEC.
(5 marks)
(b) (i) Is △CEF an isosceles triangle? Explain your answer.
(ii) Find ∠EFC.
(3 marks)
(c) If some more identical pentagons are put side by side to the figure to form a closed ring, find the number of pentagons required.
(2 marks)
23. The following table shows the body temperatures (°C) of 40 students.
Body temperature (°C) / 35.0 - 35.9 / 36.0 - 36.9 / 37.0 - 37.9 / 38.0 - 38.9 / 39.0 - 39.9Frequency / 3 / 10 / 19 / 6 / 2
(a) (i) Complete the following table.
Body temperature below (°C) / 34.95Cumulative frequency
(ii) Draw a cumulative frequency polygon to present the data.
(5 marks)
(b) Find (i) the 20th percentile,
(ii) the upper quartile.
(2 marks)
(c) If a student with body temperatures between 35.55°C and 37.55°C are regarded as normal, what is the percentage of students who are not normal?
(3 marks)
-- End of paper --
F.2 First Term Examination
Mathematics (Paper 1 - Extra Questions)
Section B (Each question carries 5 marks)
1. It is given that .
(a) Find x : y.
(b) Hence, if x : z = 5 : 3, find x : y : z.
2. In the figure, ABCD and PQRS are two similar trapeziums.
(a) Find the value of x.
(b) It is given that the perimeter of ABCD is 30. Find the perimeter of PQRS.
3. (a) Expand (m + n)(m - n).
(b) Using the result of (a), expand (m2 + m - 1)(m2 - m + 1).
4. A man buys 30 oranges at $x each and 42 lemons at $y each. He packs 5 oranges and 7 lemons into a box and sells each box of fruit for $(8x + 9y). After selling all the boxes of fruit, he gets a profit of $P.
(a) Express x in terms of P and y.
(b) Find x if y = 1.5 and P = 72.
5. (a) Factorize .
(b) Hence, factorize .
6. Refer to the following figure.
(a) Find the measured length of the pencil.
(b) Find the percentage error of the measured length of the pencil.
7. The figure shows the test report for English, Chinese and Mathematics tests that Peter took. However, part of the report was torn as shown on the right.
Assume all marks are integers.
(a) If Peter’s total marks is 230, correct to the nearest ten, find the upper limit and the lower limit of the marks of Mathematics test.
(b) Peter estimates that the marks he got should be the lower limit found in (a). After checking, his actual marks is 85. Find the relative error of his estimation in fraction.
8. In the figure, ACE and BCD are straight lines.
(a) Find a and b.
(b) Is △ABD an isosceles triangle? Explain your answer.
9. In a regular n-sided polygon, the size of an interior angle is nine times that of an exterior angle. Find the value of n.
12 24 11 12 1317 6 15 13 6
8 28 21 20 19
6 9 20 14 8
10. The monthly overtime record (correct to the nearest h) of 20 employees in a certain company in a month is listed on the right.
(a) Complete the frequency distribution table below.
Time (h) / Class mark (h) / Frequency6 - 10
(b) Draw a frequency curve to present the data in (a).
- End of paper --
F.2 First Term Examination
Mathematics (Paper 2)
Time Allowed: 75 minutes
*********************************************************************
Instructions:
(I) There are 40 questions in this paper and each question carries equal mark. Answer ALL questions and mark your answers on the multiple choice answer sheet provided.
(II) The diagrams in this paper are not drawn to scale.
*********************************************************************
1. A motorcycle travels 243 km in 180 minutes. Find its speed.
A. 1.35 km/ h
B. 13.5 km/ h
C. 40.5 km/ h
D. 81 km/ h
2. Given that 15 : (x - 2) = 3 : 5, find the value of x.
A. 13
B. 17
C. 23
D. 27
3. If , =
A. 1 : 2.
B. 3 : 4.
C. 2 : 3.
D. 3 : 2.
4. Given that 5x = 6y and y : z = 3 :4, find x : z.
A. 5 : 3
B. 5 : 4
C. 3 : 10
D. 9 : 10
5. In a triangle, the three interior angles are in the ratio 2 : 3 : 4. What is the size of the largest angle in the triangle?
A. 60°
B. 80°
C. 100°
D. 140°
6. In the figure, BC is longer than AB by 1 cm. BC : CD = 7 : 10. If CD = 5 cm, find
AB : BC : AD.
A. 5 : 7 : 10
B. 5 : 7 : 22
C. 6 : 7 : 10
D. 6 : 7 : 23
7. In the figure, ABCD and PQRS are two similar quadrilaterals.
Find r and s.
A. r = 12, s = 5
B. r = 15, s = 5
C. r = 12, s = 6
D. r = 15, s = 6
8. Which of the following are identities?
I.
II.
III.
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
9. If , where A and B are constants, then
A. A = -2, B = -2.
B. A = -2, B = 2.
C. A = 2, B = -2.
D. A = 2, B = 2.
10. Which of the following expressions have a factor a - b?
I. am - bm
II. a2 - b2
III. a2 + ab - 2b2
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
11. Factorize 16pqr - 6prs + 4ps.
A. 2(8pqr - 3prs + 2ps)
B. p(16qr - 6rs + 4s)
C. 2p(8qr - 3rs + 2s)
D. 2r(8pr - 3rs + 2p)
12. If the side of a square is x + 2y, its area is
A. x2 + 2y2.
B. x2 + 4y2.
C. x2 + 2xy + 2y2.
D. x2 + 4xy + 4y2.
13.
A.
B.
C.
D.
14. Simplify
A.
B.
C.
D. 3
15. Simplify
A. -3x
B. 3x
C. 3(x - 1)
D.
16. Simplify
A. 0
B.
C.
D.
17. Given a formula , if a = 2, b = 3 and , find the value of c.
A. 6
B. 7
C. 8
D. 9
18. If , then x =
A. .
B. –.
C. .
D. –.
19. Factorize x2 - 7x + 10.
A. (x - 1)(x - 10)
B. (x + 1)(x + 10)
C. (x + 2)(x + 5)
D. (x - 2)(x - 5)
20. Factorize 4x2 + 19x + 12.
A. (x + 2)(4x + 6)
B. (x + 4)(4x + 3)
C. (2x + 6)(2x + 2)
D. (2x + 4)(2x + 3)
21. The L.C.M. of 4x + 6y and 6x2 - xy - 15y2 is
A. (4x + 6y)(6x2 - xy - 15y2).
B. 2(2x + 3y)(3x - 5y).
C. 2(2x + 3y)(3x + 5y).
D. 2(2x + 3y)(2x - 3y)(3x + 5y).
22. x3 + 27y3 =
A. (x + 3y)3
B. (x + 3y)(x2 - 3xy + 9y2)
C. (x - 3y)(x2 + 3xy + 9y2)
D. (x - 3y)(x2 + 9xy + 9y2)
23. Express 0.025 46 m in mm and round off the result correct to 2 significant figures.
A. 3 mm
B. 25 mm
C. 25.5 mm
D. 255 mm
24. How many ‘0’s are significant figure in 0.030 028 0?
A. 2
B. 3
C. 4
D. 5
25. In an election, the vote is 579 795. When the vote is rounded off correct to 3 significant figures, the absolute error is
A. 795.
B. 205.
C. 5.
D. 0.035.
26. The lettuce in a hamburger weighs 50 g, correct to the nearest g. Which of the following is NOT a possible weight of the lettuce?
A. 49.049 g
B. 49.51 g
C. 50.01 g
D. 50.45 g
27. Find the percentage error when the number 625 is rounded off to 1 significant figure.
A. 4%
B.
C.
D.
28. In the figure, find the value of d.
A. 30°
B. 50°
C. 60°
D. 70°
29. Find ∠ABC in the figure.
A. 24°
B. 48°
C. 57°
D. 66°
30. In the figure, △ABD is an equilateral triangle and ADC is a straight line. Find ∠BCD.
A. 25°
B. 30°
C. 35°
D. 40°
31. In the figure, BCDE is a straight line. Find ∠ADE.
A. 117°
B. 127°
C. 133°
D. 143°
32. In the figure, find a.
A. 40°
B. 50°
C. 60°
D. 70°
33. If each interior angle of a regular n-sided polygon is 140°, then n =
A. 7.
B. 8.
C. 9.
D. 10.
34. In the figure, ∠BAE =
A. 20°.
B. 24°.
C. 84°.
D. 100°.
35. The table below shows Mr Chan’s monthly expenditure.