1 - Mathematics in Action (Second Edition)
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 |Suggested |Marking scheme |
| | | |questions provided |solutions | |
|Paper 1 |Section A |10 |– |( | |
| |Short questions | | |(numerical answers | |
| | | | |only) | |
| |Section B |10 |10 |( |( |
| |Long questions | | | | |
| |Section C |3 |– |( |( |
| |Harder long questions | | | | |
|Paper 2 |Multiple choice questions* |40 |10 |( | |
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 [pic]
4. Factorize [pic]
5. Simplify [pic].
6. Factorize [pic].
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.
[pic] ___________________
9. In the figure, find x + y + z.
[pic]
10. The diagram below shows the sales of a certain brand of toilet roll in 2009 and 2010.
[pic]
(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 [pic] where A, B and C are constants. Find the values of A, B and C.
14. Consider the formula [pic]
(a) Make y the subject of the formula.
(b) Find the value of y when [pic].
15. (a) Factorize (3x + 7y)2 ( (3x ( 7y)2.
(b) Hence, or otherwise, simplify [pic]
16. (a) Factorize [pic]
(b) Simplify [pic]
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.
[pic]
The table below shows the time spent by S2B students.
|Class mark (min) |79.5 |89.5 |99.5 |109.5 |119.5 |
|Frequency |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) [pic]
(ii) [pic]
(4 marks)
(b) Let [pic].
(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 ( 39.9 |
|Frequency |3 |10 |19 |6 |2 |
(a) (i) Complete the following table.
|Body temperature below |34.95 | | | | | |
|((C) | | | | | | |
|Cumulative frequency | | | | | | |
(ii) Draw a cumulative frequency polygon to present the data.
[pic]
(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 [pic].
(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 [pic].
(b) Hence, factorize [pic].
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 13 |
|17 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) |Frequency |
|6 ( 10 | | |
| | | |
| | | |
| | | |
| | | |
(b) Draw a frequency curve to present the data in (a).
[pic]
( 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 [pic], [pic]=
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. [pic]
II. [pic]
III. [pic]
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
9. If [pic], 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. [pic]
A. [pic]
B. [pic]
C. [pic]
D. [pic]
14. Simplify [pic]
A. [pic]
B. [pic]
C. [pic]
D. 3
15. Simplify [pic]
A. (3x
B. 3x
C. 3(x ( 1)
D. [pic]
16. Simplify [pic]
A. 0
B. [pic]
C. [pic]
D. [pic]
17. Given a formula [pic], if a = 2, b = 3 and [pic], find the value of c.
A. 6
B. 7
C. 8
D. 9
18. If [pic], then x =
A. [pic].
B. –[pic].
C. [pic].
D. –[pic].
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. [pic]
C. [pic]
D. [pic]
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.
|Item |Food |Travel |Savings |Others |
|Expenditure |5500 |1000 |3500 |3000 |
Mr Chan wants to present the percentage of each item. Which of the following statistical diagrams should he use?
A. bar chart
B. pie chart
C. broken-line graph
D. scatter diagram
36. The table below shows the time that a group of students spend on playing video games per week.
|Time less than (hour) |0.5 |3.5 |6.5 |9.5 |12.5 |15.5 |
|Cumulative frequency |0 |40 |100 |150 |195 |200 |
Find the percentage of students who spend between 3.5 hours and 12.5 hours per week on playing video games.
A. 25%
B. 50%
C. 77.5%
D. 97.5%
37. The diagram shows the result of S2A and S2B students in a Mathematics test.
[pic]
Which of the following statements is/are correct?
I. S2B students perform better than S2A students in general.
II. No students in S2A and S2B got a mark lower than 35.
III. The diagram shows 2 cumulative frequency curves.
A. II only
B. I and II only
C. II and III only
D. I, II and III
The following cumulative frequency curve shows the scores of a group of contestants in a singing contest.
[pic]
Refer to the above graph, answer Q38 and Q39.
38. How many contestants have scores 20.5 or above?
A. 4
B. 6
C. 34
D. 36
39. Which of the following are correct?
I. There are 40 contestants in the singing contest.
II. The 30th percentile is 18.
III. The difference between the marks corresponding to the upper quartile and the lower quartile is 10.
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
40. The following cumulative frequency polygon shows the IQ scores of 100 students.
[pic]
If the top 10% of students will attend an intelligent competition, what is the lowest IQ score for a student to attend the competition?
A. 111.5
B. 114.5
C. 119.5
D. 124.5
(( End of paper ((
F.2 First Term Examination
Mathematics (Paper 2 - Extra Questions)
1. The figure shows the floor plan of a flat. The length and the width of the plan are 4 cm and
3 cm respectively. If the actual length of the flat is 8 m, find the actual area of the flat.
A. 6 m2
B. 12 m2
C. 24 m2
D. 48 m2
2. Which of the following expressions CANNOT be factorized?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
3. If x2 – 12x – k is a perfect square expression, what is the value of k?
A. –36
B. –6
C. 6
D. 36
4. Simplify[pic]
A. [pic]
B. [pic]
C. [pic]
D. [pic]
5. Factorize p2 ( 2pq ( 3q2 ( p + 3q.
A. (p + 3q)(p ( q + 1)
B. (p + 3q)(p ( q ( 1)
C. (p ( 3q)(p + q ( 1)
D. (p ( 3q)(p + q + 1)
6. The lengths of pencil A and pencil B are measured to be 10.1 cm and 12.5 cm respectively, correct to the nearest 0.1 cm. The largest possible difference between the lengths of pencil A
and B is
A. 2.3.
B. 2.4.
C. 2.45.
D. 2.5.
7. The measured weight of a parcel is 500 g and its relative error is 0.001. The maximum absolute error of the measurement is
A. 1 g.
B. 0.5 g.
C. 0.05 g.
D. 0.000 002 g.
8. In the figure, O is the centre and AOB is a diameter of the circle.
If (BCO = 50(, find x.
A. 100(
B. 110(
C. 120(
D. 130(
9. In the figure, ADC is a straight line. Which of the following is / are isosceles triangle(s)?
I. △ADB
II. △BDC
III. △ABC
A. I only
B. I and II only
C. I and III only
D. I, II and III
10. The frequency polygon below shows the sales of iPhones at different prices last month.
[pic]
Suppose the corresponding class intervals of the above frequency polygon are $3000 ( $3999, $4000 ( $4999, ... Find the class interval with the highest frequency.
A. $4000 ( $4999
B. $5000 ( $5999
C. $6000 ( $6999
D. $7000 ( $7999
(( End of paper ((
F.2 First Term Examination
Mathematics (Paper 1)
Suggested Solutions and Marking Scheme
*******************************************************************
General Instructions:
(1) Marks will not be deducted for wrong spelling.
(2) 1 mark will be deducted for poor expression or poor presentation.
Maximum of 2 marks will be deducted in Section B and C.
(3) 1 mark will be deducted for wrong / no unit.
Maximum of 1 mark will be deducted for the whole paper.
*******************************************************************
Section A (20 marks)
|Question |Answer |Marks |Remarks |
|1 |6 : 4 : 1 |2 | |
|2 |1 : 80 000 |2 | |
|3 |36x2 ( 60xy + 25y2 |2 | |
|4 |(p ( 4)(q + 3) |2 | |
|5 |[pic] |2 | |
|6 |(x + 2)(7x ( 9) |2 | |
|7 |0.0221% |2 | |
|8 |30( |2 | |
|9 |180( |2 | |
|10 |(a) 3 : 4 |1 | |
| |(b) yes |1 | |
Suggested solutions Marks Remarks
Section B (50 marks)
11. (a) Price of each gram of oats for the ‘Small Packet’
[pic]
[pic] 1
Price of each gram of oats for the ‘Large Packet’
[pic]
[pic] 1
∵ $0.08/g < $0.09/g
∴ ‘Small Packet’ is more economical
to customers.
(b) Let $P be the required new price of each ‘Large Packet’.
[pic] 1
∴ The new price of each ‘Large Packet’
is $96. 1
12. (a) The volume of the lemon juice
[pic] 1
[pic]
[pic] 1
(b) The new volume of the lemon juice
[pic]
[pic] 1
The new volume of the tea
[pic]
[pic] 1
The new ratio of lemon juice to tea in the glass
[pic]
[pic] 1
Suggested solutions Marks Remarks
13. [pic] 1
∴ [pic] 1
By comparing the like terms, we have
[pic] 1
[pic] 1
[pic] 1
14. (a) [pic]
[pic] 1
[pic] 1
[pic]
[pic] 1
(b) When [pic]
[pic]
[pic] 1
[pic] 1
Suggested solutions Marks Remarks
15. (a) [pic]
[pic] 1
[pic]
[pic] 1
[pic] 1
(b) [pic]
[pic]
[pic] 1
[pic] 1
16. (a) [pic] [pic] 2
(b) [pic]
[pic]
[pic] 1
[pic] 1
[pic] 1
17. (a) Maximum absolute error
[pic]
[pic] 1
Suggested solutions Marks Remarks
(b) Upper limit of the actual length
[pic]
[pic] 1
Upper limit of the actual width
[pic]
[pic] 1
(c) Maximum area of the school hall
[pic] 1
[pic] (cor. to 3 sig. fig.) 1
18. ∵ BC = BA
∴ ∠BCA = ∠BAC (base ∠s, isos. △)
= y 1
In △CDE,
[pic] (∠ sum of △)
[pic] 1
[pic] (adj. ∠s on st. line)
[pic] 1
∠AEB = ∠CED (vert. opp. ∠s)
= 90° 1
In △ABE,
[pic] (∠ sum of △)
[pic]
[pic] 1
19. (a) ∵ AC = CE
∴ ∠CAE = ∠CEA (base ∠s, isos. △)
= 30° 1
[pic] (int. ∠s, BA // CD)
[pic]
[pic]
[pic] 1
Suggested solutions Marks Remarks
(b) [pic] (ext. ∠ of △)
[pic] 1
In △ABC,
[pic] (∠ sum of △)
[pic]
[pic] 1
∵ [pic]
∴ AC = AB = BC
∴ △ABC is an equilateral triangle.
20. (a) [pic]
1 for correct line segments
(b) Since the frequency polygon for S2B
students lies to the right of that for S2A
students, S2B students spend more time
on completing their art model in general. 1
(c) Number of S2B students who cannot meet the requirement
= 5 + 13
= 18
Suggested solutions Marks Remarks
Section C (30 marks)
21. (a) (i) [pic]
[pic] 1
∴ L.H.S. = R.H.S.
∴ [pic] is an
identity.
(ii) [pic] 1
[pic] (from (a))
∴ L.H.S. = R.H.S.
∴ [pic] is
an identity
(b) (i) Put a = 9.99 and b = 0.01 into (a)(ii), we have
(9.99)3 + (0.01)3
= (9.99 + 0.01)3 ( 3(9.99)(0.01)(9.99 + 0.01)
= 103 ( 3(9.99)(0.01)(10)
= 1000 ( 2.997
= 997 003
∴ S = [pic]
(ii) ∵ 9.99 = 10.0 (cor. to 1 d.p.) 1
0.01 = 0.0 (cor. to 1 d.p.) 1
∴ Mary’s estimate = 10.03 + 0.03
= 1000 1
∴ Absolute error = 1000 ( 997.003
= 2.997 1
Suggested solutions Marks Remarks
22. (a) (i) The sum of all interior angles of ABCDE
[pic] (∠ sum of polygon)
[pic] 1 deduct 1 mark for no/wrong
∵ All the interior angles of ABCDE are reason
equal.
∴ [pic]
[pic] 1
(ii) ∵ CD = DE
∴ [pic] (base. ∠s, isos. △) 1
In △CDE,
[pic] (∠ sum of △)
[pic]
[pic] 1
[pic]
[pic]
[pic]
[pic] 1
(b) (i) [pic]
[pic]
[pic]
[pic]
∵ [pic] = 72° 1
∴ FC = FE (sides opp. equal ∠s)
∴ △CEF is an isosceles triangle.
(ii) In △CEF,
[pic] (∠ sum of △)
[pic]
[pic] 1
(c) Let n be the number of pentagons in the closed ring.
[pic] (∠s at a pt.) 1 Accept any other correct method
[pic]
∴ The number of pentagons in the closed 1
ring is 10.
Suggested solutions Marks Remarks
|23. |(a) |(i) |Body temperature below |34.95 |
| | | |((C) | |
| | |6 ( 10 |8 |6 |
| | |11 ( 15 |13 |7 |
| | |16 ( 20 |18 |4 |
| | |21 ( 25 |23 |2 |
| | |26 ( 30 |28 |1 |
2 deduct 0.5 marks for each mistakes
(b) [pic]
1 Correct labels on the x-axis and y-axis
1 Correct title
1 Joining the points
Answers
F.2 First Term Examination
Mathematics (Paper 2)*
1. D
2. D
3. C
4. D
5. B
6. B
7. A
8. C
9. B
10. D
11. C
12. D
13. C
14. B
15. A
16. C
17. B
18. C
19. D
20. B
21. B
22. B
23. B
24. B
25. B
26. A
27. A
28. D
29. B
30. B
31. B
32. B
33. C
34. C
35. B
36. C
37. B
38. A
39. B
40. C
F.2 First Term Examination
Mathematics (Paper 2 – Extra Questions)*
1. D
2. A
3. A
4. D
5. C
6. D
7. B
8. A
9. D
10. B
*: The soft copy of the suggested solutions is available on our website.
S2 Second 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. Write down the solution of the simultaneous equations [pic] from their graphs as shown.
[pic]
______________________
2. Simplify [pic] and express your answer with positive indices. ______________________
3. Express the number –0.003 509 in scientific notation. ______________________
4. In the figure, CDE is a straight line. Is BA // CF? Give the reason.
______________________
5. Which of the following are rational numbers?
[pic], [pic], [pic], –( ______________________
6. Express [pic] in its simplest form. ______________________
7. In the figure, find BD.
[pic] ______________________
8. The following figure is formed by a circle and a semi-circle. Find the area of the figure in terms of π.
[pic] ______________________
9. If the base radius and the height of a cylinder are 4 cm and 5 cm respectively, find the volume of the cylinder in terms of (. ______________________
10. Find the acute angle ( if tan ( = cos 25( + sin 75(. (Give your answer correct to 3 significant figures.) ______________________
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. Solve the following simultaneous equations.
(a) [pic] (b) [pic]
12. In a shop, the total selling price of 15 oranges and 10 apples is $60. Mrs. Chan paid $65 to buy 10 oranges and 15 apples.
(a) Let $x and $y be the selling prices of each orange and apple respectively. Set up a pair of simultaneous linear equations in two unknowns.
(b) Find the selling prices of each orange and apple.
13. The following shows the lengths of Great Wall of China, Tsing Ma Bridge and Mandy’s hand span.
| |Great Wall of China |Tsing Ma Bridge |Mandy’s hand span |
|Length (mm) |885 180 000 000 |149 000 000 |118 |
(a) Express each of the above lengths (in mm) in scientific notation.
(b) (i) How many times is the length of the Great Wall of China to that of Tsing Ma Bridge? Give your answer correct to 3 significant figures.
(ii) How many times is the length of the Great Wall of China to that of Mandy’s hand span? Give your answer correct to 3 significant figures.
14. (a) Convert B7D16 into a denary number.
(b) Convert 4410 into a binary number.
15. In the figure, ADB is a straight line. Find, correct to 3 significant figures,
(a) CD and (A,
(b) area of △ADC.
16. Refer to the figure on the right.
(a) Find EC.
(b) Is △CDE a right-angled triangle? Give the reason.
17. Refer to the figure on the right.
(a) Prove that △ABF ~ △DEC.
(b) If △ACF ( △EDC, prove that AF2 = BF ( CF.
18. (a) Express [pic] and [pic] in their simplest forms.
(b) Hence, simplify [pic].
19. In the figure, PQR is a semi-circle centred at O. Find, correct to 3 significant figures,
(a) the radius of the semi-circle PQR,
(b) the total area of the figure.
20. A cylindrical glass of base radius 5 cm and height 12 cm is fully-filled with water.
(a) Find the volume of water in the glass in terms of π.
(b) Some water is poured from this glass into another cylindrical glass of base radius 4 cm and height 15 cm until the new glass is half-filled. Find the depth of water remained in the original glass.
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. In the figure, the centre of the arc ADE is O.
(a) Find (BAC and (ACD.
(b) Find the length of arc AD. (Give your answer in surd form.)
(c) Find the perimeter of the shaded region. (Give your answer in surd form.)
22. Refer to the figure on the right. QPT is a straight line.
(a) Find (RPS.
(b) Find RS, correct to the nearest integer.
(c) Find (RSP, correct to 1 decimal place.
23. In the figure, OA(B(C( is formed by rotating OABC about O such that OC( coincides with OA.
(a) (i) Join AC and A(C(. Prove that
△AOC ( △A(OC(.
(ii) Find (AOC and (BCO.
(b) Suppose CO is produced to B(. By considering (B(OC(, prove that
OC: BC [pic] : 1.
( End of paper (
S2 Second Term Examination
Mathematics (Paper 1 - Extra Questions)
Section B (Each question carries 5 marks)
1. Simplify [pic] and express your answer with positive indices.
2. In the figure, the area of △BCD is 96 cm2.
(a) Find BC.
(b) Determine whether △ABC is a right-angled triangle. Explain briefly.
3. The figure shows a solid whose cross-section is a sector.
(a) Find the volume of the solid in terms of π.
(b) Find the total surface area of the solid in terms of π.
4. Refer to the figure on the right.
(a) Find AD.
(b) Find BC.
5. A wire of length 10 cm is bent into sector OAB as shown in the figure. Find, correct to 3 significant figures,
(a) (AOB,
(b) the area of sector OAB.
6. (a) Simplify [pic].
(b) Using the result of (a), find the value of [pic] without using a calculator.
7. Refer to the figure.
(a) Find x.
(b) Is AB // ED? Give the reason.
8. Jason and Yvonne have a total amount of $360. If Yvonne gives $80 to Jason, she will have 80% the amount Jason has. Find the original amounts Jason and Yvonne have respectively.
9. In the figure, AE and BD intersect at C.
(a) Find a and b.
(b) Prove that △ADB is an isosceles triangle.
10. In the figure, BCD is a straight line and
AB = BC = CA = CD = 10.
(a) Prove that △ABD is a right-angled triangle.
(b) Find the length of AD in surd form and express it in its simplest form.
S2 Second 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. Which of the following points lie on the graph of x + 3y = 4?
A. (–2, 2)
B. (–1, –1)
C. (0, 1)
D. (1, –1)
2. The figure on the right shows the graphs of 2x + y = –4 and x – 2y = 3.
Which of the following is the solution of both the two equations?
A. x = 1, y = 2
B. x = 1, y = –2
C. x = –1, y = 2
D. x = –1, y = –2
3. Solve the simultaneous equations [pic].
A. x = –5, y = 10
B. x = 1, y = –4
C. x = 5, y = 0
D. x = 25, y = 20
4. Solve the simultaneous equations 4x – 3y – 1 = 5x – 4y = 0.
A. x = 5, y = 4
B. x = 4, y = 5
C. x = –4, y = 5
D. x = –5, y = 4
5. Nick is 5 years older than Jerry. If the sum of their ages is 45, how old is Nick?
A. 15 years old
B. 20 years old
C. 25 years old
D. 30 years old
6. Simplify [pic].
A. xy
B. [pic]
C. [pic]
D. [pic]
7. Simplify [pic].
A. [pic]
B. [pic]
C. [pic]
D. [pic]
8. Simplify [pic].
A. 32n
B. 3n
C. 2
D. 3
9. Express the number 0.000 005 72 in scientific notation.
A. 0.572 ( 10–5
B. 5.72 ( 10–5
C. 5.72 ( 10–6
D. 5.72–6
10. A light year is the distance travelled by light in a year. If the speed of light is 3 ( 108 m/s and 1 year = 365 days, then 1 light year =
A. 9.4608 ( 1012 km.
B. 1.098 ( 1011 km.
C. 2.592 ( 1010 km.
D. 6.570 ( 109 km.
11. What is the place value of the underlined digit 1 in the number 111012?
A. 1
B. 22
C. 23
D. 24
12. Which of the following has the largest value?
A. 10010
B. 1A716
C. 110001102
D. F516
13. Refer to the figure on the right. Which of the following is / are isosceles triangle(s)?
I. △ADB
II. △BCD
III. △ABC
A. I only
B. II only
C. I and III only
D. I, II and III
14. In the figure, AB = AC and BC = DC = DA. Find (BAC.
A. 30(
B. 36(
C. 64(
D. 72(
15. In the figure, AE and CD intersect at F. Which of the following must be correct?
I. △ABE ~ △CBD
II. △ADF ~ △CEF
III. BD = BE
A. I only
B. I and II only
C. II and III only
D. I, II and III
16. In the figure, ADBE is a straight line. If △ABC ( △DEF, which of the following must be correct?
I. AC // DF
II. BC // EF
III. AD = BE
A. I only
B. I and II only
C. II and III only
D. I, II and III
17. Refer to the figure on the right. Which of the following must be correct?
I. AB // CD
II. CD // EF
III. BC // FG
A. I only
B. I and II only
C. II and III only
D. I, II and III
18. In the figure, ADB and CED are straight lines. Which of the following must be correct?
I. △ADE ~ △CDA
II. △CEA ~ △CDB
III. △ACD ~ △ABC
A. I only
B. I and II only
C. I and III only
D. II and III only
19. Which of the following is NOT a rational number?
A. [pic]
B. [pic]
C. [pic]
D. [pic]
20. Simplify the expression [pic].
A. 0
B. [pic]
C. [pic]
D. [pic]
21. Simplify the expression [pic].
A. 5 B. 15
C. [pic] D. [pic]
22. Simplify the expression [pic].
A. [pic] B. 0.6
C. [pic] D. [pic]
23. Simplify [pic].
A. [pic]
B. [pic]
C. [pic]
D. [pic]
24. In the figure, find the length of AD.
A. 28 cm
B. 32 cm
C. 39 cm
D. 47 cm
25. The figure shows 3 squares ABDE, ACHI and BFGC, and a right-angled triangle ABC. If the area of ACHI is 20 cm2 and that of AEDB is 45 cm2, what is the area of the whole shaded region AEDBFGCHI?
A. 130 cm2
B. 145 cm2
C. 160 cm2
D. Cannot be determined
26. The figure shows 2 right-angled triangles ABC and ABD with sides as shown. Which of the following is true?
A. a + b = c + d
B. a – c = b – d
C. (a – c)(a + c) = (d – b)(d + b)
D. (a + b)2 = (c + d)2
27. If the area of a square is a cm2, what is the length of its diagonal?
A. [pic] cm
B. [pic] cm
C. [pic] cm
D. [pic] cm
28. If a and b are positive numbers, which of the following can be the lengths of the sides of a right-angled triangle?
I. 8a, 17a, 15a
II. [pic], [pic], [pic]
III. [pic], [pic], [pic]
A. I only
B. II only
C. I and II only
D. I and III only
29. In the figure, the ratio of the diameters of the larger semi-circle to that of the smaller semi-circle is 4 : 3. Find the area of the figure.
A. 100( cm2
B. 200( cm2
C. (28( + 96) cm2
D. (50( + 96) cm2
30. In the figure, O is the centre of the sector AOB. Find the area of the sector, correct to 3 significant figures.
A. 5.24 cm2
B. 7.85 cm2
C. 13.6 cm2
D. 20.4 cm2
31. In the figure, O is the centre of the circle. Find the perimeter of the shaded region, correct to 2 decimal places.
A. 1.14 cm
B. 4.57 cm
C. 5.97 cm
D. 8.89 cm
32. The figure shows 2 identical circles. Find the area of the shaded region in terms of (.
A. 4( cm2
B. 8( cm2
C. 4(3 – () cm2
D. 8(4 – () cm2
33. The radius and the capacity of a cylindrical glass are 6 cm and 576( cm3 respectively. At the beginning, it is half filled with water. Now 9 identical marbles, each of volume 5( cm3, are put into the glass. If the marbles are completely immersed in water and water does not overflow, find the new depth of water in the glass.
A. 1.25 cm
B. 5.25 cm
C. 9.25 cm
D. 16.25 cm
34. A metal cube of side 5 cm is melted and recast to form a cylinder of height of 3 cm. What is the base radius of the cylinder? Give your answer correct to 3 significant figures.
A. 3.64 cm
B. 4.42 cm
C. 6.45 cm
D. 13.3 cm
35. The figure shows a rolling pin made of 3 wooden cylinders. The length and the base diameter of the 2 identical handles at both sides are 10 cm and 2 cm respectively, while the length and the base diameter of the middle cylinder are 30 cm and 8 cm respectively. Find the total surface area of the rolling pin.
A. 310( cm2
B. 312( cm2
C. 314( cm2
D. 316( cm2
36. In △PQR, PQ = 5 cm, PR = 10 cm and (Q = 90(. Find (R.
A. 30(
B. 45(
C. 60(
D. 75(
37. Find sin ( in the figure.
A. 0.75
B. 0.45
C. [pic]
D. [pic]
38. Refer to the figure on the right. Find (ABC correct to
3 decimal places.
A. 41.4(
B. 48.6(
C. 101(
D. 109(
39. Refer to the figure on the right. Find the length of PQ, correct to 3 sigificant figures.
A. 4.62
B. 10.9
C. 13.9
D. 18.9
40. In the figure, O is the centre of the circle. Find the length of PQ, correct to 2 decimal places.
A. 0.87
B. 1.15
C. 1.73
D. 2.00
S2 Second Term Examination
Mathematics (Paper 2 - Extra Questions)
1. Solve the simultaneous equations [pic].
A. x = –2, y = –8
B. x = –2, y = 8
C. x = 2, y = –8
D. x = 2, y = 8
2. It is given that the tens digit of a 2-digit number is 1 smaller than the units digit. If the sum of the two digits is 11, what is the 2-digit number?
A. 45
B. 56
C. 65
D. 67
3. Simplify the expression [pic].
A. y–8
B. y–4
C. xy–2
D. x4y–8
4. Arrange the following number in descending order.
1001002 3010 B016
A. B016, 3010, 1001002
B. B016, 1001002, 3010
C. 1001002, B016, 3010
D. 1001002, 3010, B016
5. In the figure, PQRS and QUT are straight lines. Which of the following must be correct?
I. △UST is an isosceles triangle.
II. △URS is an isosceles triangle.
III. (RSU = (TSU
A. I only
B. I and II only
C. II and III only
D. I, II and III
6. Simplify [pic].
A. [pic]
B. [pic]
C. [pic]
D. [pic]
7. Find the area of the trapezium in the figure.
A. 12.5 cm2
B. 34 cm2
C. 48 cm2
D. 61.5 cm2
8. The figure shows two arcs AB and CD, with a common centre O. Arc AB = 60( cm, arc CD = 48( cm and
OB = 40 cm. Find the length of BD.
A. 8 cm
B. 10 cm
C. 16 cm
D. 20 cm
9. The figure shows a hollow cylindrical pipe. If the thickness of the pipe is 2 cm, what is the volume of the pipe?
[pic]
A. 144( cm3
B. 240( cm3
C. 280( cm3
D. 480( cm3
10. Find (DBA in the figure, correct to 3 significant figures.
A. 13.2(
B. 21.7(
C. 26.3(
D. 37.5(
S2 First Term Examination
Mathematics (Paper 1)
Suggested Solutions and Marking Scheme
*******************************************************************
General Instructions:
(1) Marks will not be deducted for wrong spelling.
(2) 1 mark will be deducted for poor expression or poor presentation.
Maximum of 2 marks will be deducted in Section B and C.
(3) 1 mark will be deducted for wrong / no unit.
Maximum of 1 mark will be deducted for the whole paper.
*******************************************************************
Section A (20 marks)
|Question |Answer |Marks |Remarks |
|1 |x = 3, y = 0 |2 | |
|2 |a3 |2 | |
|3 |(3.509 ( 10(3 |2 | |
|4 |Yes, int. (s supp. |2 | |
|5 |[pic], [pic] |2 | |
|6 |[pic] |2 | |
|7 |6 cm |2 | |
|8 |16( cm2 |2 | |
|9 |80( cm3 |2 | |
|10 |61.9( |2 | |
Suggested solutions Marks Remarks
Section B (50 marks)
11. (a) [pic] [pic]
From (1), we have
[pic] [pic]
By substituting (3) into (2), we have
[pic]
By substituting y ’ 3 into (3), we have
[pic]
∴ The solution is x ’ (2, y ’ 3. 1
(b) [pic] [pic]
From (1), we have
[pic] 0.5
From (2), we have
[pic] [pic] 0.5
(3) ( 2 :
[pic] [pic]
(4) – (5):
[pic]
By substituting x = (8 into (3), we have
[pic]
∴ The solution is x = (8, y = (5.2. 1
Suggested solutions Marks Remarks
12. (a) [pic] [pic]
or [pic] [pic]
(b) (1) ( 2 :
[pic] [pic] 0.5
(2) ( 3:
[pic] [pic] 0.5
(4) – (3):
[pic]
By substituting y = 3 into (1), we have
[pic]
∴ The selling prices of each orange and apple are
$2 and $3 respectively. 1
13. (a) Length of Great Wall of China
[pic] 1
Length of Tsing Ma Bridge
[pic] 1
Length of Mandy’s hand span
[pic] 1
(b) (i) 8.8518 ( 1011 ( 1.49 ( 108 0.5
= (8.8518 ( 1.49) ( 1011( 8
= 5.94 ( 103 (cor. to 3 sig. fig.)
∴ The length of the Great Wall of China
is 5.94 ( 103 times that of Tsing Ma Bridge. 0.5
(ii) 8.8518 ( 1011 ( 1.18 ( 102 0.5
= (8.8518 ( 1.18) ( 1011( 2
= 7.50 ( 109 (cor. to 3 sig. fig.)
∴ The length of the Great Wall of China
is 7.50 ( 109 times that of Mandy’s hand span. 0.5
Suggested solutions Marks Remarks
14. (a) [pic] [pic]
(b) 2 44 remainder
2 22 ...... 0
2 11 ...... 0
2 5 ...... 1
2 2 ...... 1
2 1 ...... 0
0 ...... 1
2 Method marks
∴ [pic] 1
15. (a) In △BCD,
[pic] 0.5
[pic] 0.5
In △ABC,
[pic] 0.5
[pic] 0.5
(b) In △ABC,
[pic] 0.5
In △BCD,
[pic] 0.5
∴ [pic]
Suggested solutions Marks Remarks
∴ Area of △ACD
[pic]
[pic] 1
[pic] 1
16. (a) In △ABC,
[pic] [pic]
∴ [pic] [pic]
(b) In △CDE,
[pic]
∵ CD2 + DE2 = EC2 1
∴ △CDE is a right-angled triangle. 1
(converse of Pyth. theorem) deduct 1 mark for
incorrect / missing
reason
17. (a) In △ABF and △DEC,
[pic] alt. (s, AB // ED 0.5
[pic] alt. (s, AF // DC 0.5
[pic] [pic] 0.5
∴ △ABF ~ △EDC AAA 1
Suggested solutions Marks Remarks
(b) ∵ △ACF ( △EDC given
∴ AF = EC and CF = DC corr. sides, ( △s 0.5
∵ △ABF ~ △DEC proved in (a)
∴ [pic] corr. sides, ~ △s 0.5
[pic] 0.5
[pic] proved
∴ [pic] 1
18. (a) [pic] 1
[pic] 1
(b) [pic] (from (a)) 1
[pic]
[pic] 1
[pic]
[pic] 1
19. (a) In △PQR,
[pic] 0.5
Suggested solutions Marks Remarks
∴ Radius of the semi-circle PQR
[pic] 1
(b) In △PQR,
[pic] 0.5
∴ Area of the figure
’ area of the semi-circle ( area of △PQR
[pic]
[pic] 1+1
[pic] 1
20. (a) Volume of water in the glass
[pic] 1
(b) Volume of water in the new glass
[pic] 1
Volume of water remained in the
original glass
= (300( ( 120() cm3
= 180( cm3 1
Suggested solutions Marks Remarks
Let d cm be the depth of water remained
in the original glass.
[pic] 1
∴ The depth of water remained in the
original glass is 7.2 cm. 1
Section C (30 marks)
21. (a) In △ABC,
[pic] 0.5
[pic] 1
∵ CD = CA (radii)
∴ [pic] (base (s, isos. △) 0.5
∴ [pic] (( sum of △) 1
(b) [pic] 1
[pic] 1
(c) [pic] 1
[pic] 1
[pic] 1
Suggested solutions Marks Remarks
∵ △ACD is an equilateral triangle.
∴ AD = [pic]
∴ [pic] 1
[pic] 1
22. (a) [pic] ((s at a pt.) 0.5
In △PQR,
[pic] 0.5
∵ [pic] 1
(b) [pic] 0.5
In △SPT,
[pic]
[pic] 1
[pic]
[pic] 1
Suggested solutions Marks Remarks
Draw a perpendicular line from R and meet ST at X
such that RX ( ST. 0.5
In △RSX,
[pic] 0.5
[pic] 0.5
∴ [pic] 1
(c) [pic] 1
[pic] 1
∴ [pic] 1
23. (a) (i) Since [pic]is formed by rotating
OABC about O.
∴ [pic]
and [pic] 1
In [pic]
[pic] [pic]
∴ [pic] SAS 1
Suggested solutions Marks Remarks
(ii) ∵ [pic] (proved in (a)(i))
and [pic] 0.5
((s at a pt.)
∴ [pic] 1
∴ [pic] 1
(b) [pic] alt. (s, C(B( // OA( 0.5
[pic] corr. (s, C(O // BC 0.5
In △B(OC(,
i.e. [pic] 1
[pic] Pyth. theorem 0.5
[pic]
i.e. [pic] [pic]
∴ [pic]
i.e. [pic] 1
S2 Second Term Examination
Mathematics (Paper I ( Extra Questions)
Suggested Solutions and Marking Scheme
Suggested solutions Marks Remarks
Section B (Each question carries 5 marks.)
1. [pic]
[pic] 1
[pic] 1
[pic] 1
[pic] 1
[pic] 1
2. (a) Let CD ’ x cm.
∵ Area of △BCD ’ 96 cm2
∴ [pic] 1
[pic]
[pic]
[pic] 1
[pic] 1
b) In △ABC,
[pic] 1
[pic]
∵ [pic]
∴ △ABC is a right-angled triangle.
(converse of Pyth. theorem) 1 deduct 1 mark for
incorrect / missing
reason
Suggested solutions Marks Remarks
3. (a) Volume of the solid
[pic] 1
[pic] 1
(b) Area of the curved surface
[pic]
[pic] 1
Area of the two bases
[pic]
[pic] 1
Area of the two rectangles
[pic]
∴ Total surface area of the solid
[pic] 0.5
[pic] 0.5
4. (a) In △ACD,
[pic] 0.5
[pic] 0.5
(b) [pic]
[pic] 1
In △ACD,
[pic]
[pic] 1
Suggested solutions Marks Remarks
In △BCD,
[pic]
[pic] 1
[pic] 1
5. (a) Let (AOB ’ (.
[pic] 1 + 1
[pic]
[pic]
∴ [pic] 1
(b) Area of sector OAB
[pic] 1
[pic] 1
6. (a) [pic] 0.5
[pic]
[pic] 1
(b) [pic] 1
[pic] (from (a)) 1
[pic] 0.5
[pic] 1
Suggested solutions Marks Remarks
7. (a)
Draw a horizontal line DF such that
AE // DF // BC. 0.5
[pic] 0.5
[pic] 0.5
[pic] 1
(b) Produce ED to a point G on BC.
[pic] 0.5
[pic] 1
∵ [pic]
∴ AB is not parallel to ED. 1
8. Let $x and $y be the original amounts
Jason and Yvonne have respectively.
[pic] [pic] [pic]
From (2), we have
[pic] [pic] 1
(1) − (3) :
[pic]
By substituting x ’ 120 into (1), we have
[pic]
∴ Jason has $120 and Yvonne has $240 originally. 1
Suggested solutions Marks Remarks
9. (a) [pic] 0.5
In △ADC,
[pic] (ext. ( of △) 0.5
In △ACB,
[pic] (base (s, isos. △) 1
[pic] (( sum of △) 1
(b) [pic]
∴ (DBA ’ (BAD 1
∴ DA ’ DB (sides opp. equal (s) 1 deduct 1 mark for
incorrect / missing
reason
∴ △ABD is an isosceles triangle.
10. (a) [pic] (prop. of equil. △) 0.5
∴ [pic] (ext. ( of △) 1
In △ACD,
(CAD ’ (CDA (base (s, isos. △)
∴ [pic] (( sum of △) 0.5
∴ [pic]
i.e. △ABD is a right-angled triangle. 1
Suggested solutions Marks Remarks
(b) In △ABD,
∵ [pic] (proved in (a))
∴ [pic] (Pyth. theorem) 1
[pic] 1
Answers
S2 Second Term Examination
Mathematics (Paper 2)
1. A
2. D
3. B
4. B
5. C
6. B
7. B
8. C
9. C
10. A
11. C
12. B
13. D
14. B
15. B
16. D
17. C
18. B
19. C
20. B
21. B
22. A
23. D
24. C
25. B
26. C
27. B
28. D
29. D
30. D
31. C
32. D
33. C
34. A
35. B
36. A
37. C
38. C
39. B
40. C
S2 Second Term Examination
Mathematics (Paper 2 – Extra Questions)
1. D
2. B
3. D
4. B
5. C
6. A
7. D
8. A
9. B
10. A
-----------------------
Marks
A
B
D
E
C
x
y
z
Year
0
5
10
15
20
Sales (million)
Sales of toilet roll in 2009 and 2010
2009
2010
ABC oats
ABC oats
Small Packet
Large Packet
$60
per 750 g
$108
per 1.2 kg
B
A
F
E
D
C
y
y
26°
x
A
BA
CBA
DCBA
EDCBA
30°
20
10
5
0
59.5
69.5
79.5
89.5
99.5
109.5
119.5
15
Time (min)
Frequency
Time that students spent on completing their art model
129.5
S2A
NF
A
B
F
C
D
E
.
.
.
.
.
.
x + 8
A
B
C
D
P
Q
R
S
x
9
3
0 cm
1
2
3
4
Name: Peter
Test Report
Subject
Marks
English
68
Chinese
75
Mathematics
Total
A
B
C
D
E
a
b
48(
28(
A
B
C
D
5 cm
A
B
C
D
P
Q
R
S
r
21
4
7
15
s
NF
40(
20(
d
50(
66°
D
B
C
A
B
C
A
D
37°
#Œ$Œ&Œ'Œ(Œ9Œ:Œ;Œ*[pic]aJh+AÑh$zû5?aJ
h$zû5?aJjÏh+AÑh$zûEHâÿU[pic]aJ&j ÓP[pic]h+AÑh$zûKHU[pic]V[pic]aJo([pic]jßÌh+AÑh$zûEHèÿU[pic]aJ&j’ÓP[pic]h+AÑh$zûKHU[pic]V[pic]aJo([pic]jh+AÑh$zûU[pic]aJh+AÑh$zûaJo([pic]h+A
B
D
C
E
200(
100(
a
2a + 10(
120(
x
2x
3x
4x
5x
A
B
C
D
E
20
10
5
0
35
45
55
65
75
85
95
15
Marks
Frequency
Result of S2A and S2B students in a Mathematics test
S2A
S2B
40
20
10
0
0.5
5.5
10.5
15.5
20.5
25.5
30
Score
Cumulative frequency
Scores of a group of contestants in a singing contest
100
60
40
0
84.5
94.5
104.5
114.5
124.5
134.5
80
IQ score
Cumulative frequency
IQ scores of 100 students
20
4 cm
3 cm
A
O
B
C
50(
x
A
C
D
B
36(
72(
36(
15
10
0
3499.5
4499.5
5499.5
6499.5
7499.5
8499.5
Price ($)
Frequency
Sales of iPhones at different prices last month
5
1
1
20
10
5
0
59.5
69.5
79.5
89.5
99.5
109.5
119.5
15
Time (min)
Frequency
Time that students spent on completing their art model
129.5
S2A
S2B
1 Deduct 1 mark for not showing steps
1
2
1
40
20
10
0
34.95
35.95
36.95
37.95
38.95
39.95
30
Body temperature (°C)
Cumulative frequency
Body temperature of 40 students
(b) (ii)
(b) (i)
(c)
(c)
8
4
2
0
3
8
13
18
23
28
6
Monthly overtime record (h)
Frequency
Monthly overtime record of 20 employees
33
Marks
Marks
8 cm
[pic]
1 Method marks
[pic]
1 Method marks
[pic]
1 Method marks
F
G
[pic]
1 Method marks
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