Name : ______Class : 5 ___ Marks : _____ / 100
MID TERM EXAMINATION I 2008
MATHEMATICS
Form Five
Two hours and thirty minutes
INSTRUCTION FOR CANDIDATES
1. Answer all questions in Section A and Section B, one questions from Section C.
2. Give only one answer/solution for each question.
3. Show your working. It may help you to get marks.
4. The diagrams in the questions provided are not drawn to scale unless stated.
5. You may use a non-programmable scientific calculator.
Section A
[40 marks]
Answer all questions.
1. Round off 0.080365 correct to three
significant figures.
A. 0.08 B. 0.080 C. 0.0804 D. 0.08037
2. The number of residents in two districts is
3 700 000 and 290 000 respectively. Find the difference in the number of residents in two districts.
A. B. C. D.
3. Given that , where x is an integer,
find the value of x.
A. 30 B. 125 C. 220 D. 420
4.
A.
B.
C.
D.
5. In Diagram 1, LM is the tangent to the circle EFGH at H. LGF is a straight line.
Find the value of x.
A. 75 B. 90 C. 105 D. 135
6. Given that , find the value of .
A. B. C. D.
7. Diagram 2 shows the graph of .
The value of is
A. B.
C. D.
8.
Diagram 3 shows a cuboid. Name the angle between the planes HRK and HKLM.
A.
B.
C.
D.
9. In Diagram 4, PQ and MN are two blocks of buildings adjacent to each other on a horizontal ground.
Given that the angle of elevation of vertex M from vertex P is . Calculate the height, in m, of block MN.
A. 43.2 B. 48.5 C. 75.0 D. 83.5
10. Simplify
A. B. C. D.
11. Diagram 5 is a Venn diagram that shows the number of elements of set H, set K and set L.
Given that the universal set and , find the value of y.
A. 1 B. 2 C. 3 D. 4
12. Table 1 shows the mass of samples letters.
Calculate the mean mass, in g, of the letters.
A. 38.3 B. 38.5 C. 39.3 D. 39.5
13. Which of the following graphs represent ?
A. B.
C. D.
14.
Diagram 6 shows two straight lines PQ and QR on the cartesian plane. Gradient and the distance PQ is 15 units. Find the y-intercept for PQ.
A. B. C. D.
14. Table 2 shows the number of stamps in an envelope. A stamp is taken out from the envelope randomly.
Stamp / 10 cents / 20 cents / 30 cents / 50 centsNumber of Stamp / 10 / 30 / 50 / 10
Find the probability that the selected stamp is less than 30 cents.
A. B.
C. D.
15. Given that set M =, list all the subsets of M.
A.
B.
C.
D.
16. In Diagram 7, PQR is a tangent to the circle QSTW at Q.
The value of x is
A. 68 B. 62 C. 60 D. 58
17. Table 3 shows a cumulative frequency table.
Class / Cumulative frequency10 – 14 / 4
15 – 19 / 11
20 – 24 / 21
25 - 29 / 26
What is the frequency of the class 15 – 19?
A. 4 B. 10 C. 7 D. 11
18. Given that , then y =
A. 5 B. 10
C. 15 D. 20
19. Diagram 8 shows a right prism with a horizontal rectangular base, EFGH.
Name the angle between the plane FHJ and the plane GHJK.
A. B.
C. D.
20.
A. B.
C. D.
Section B
[60 marks]
Answer all questions.
21. Solve the quadratic equation .
[4 marks]
Answer :
22. Calculate the value of x and y that satisfies the following simultaneous linear equations :
[4 marks]
Answer :
23. On the graph provided, shade the region which satisfies the three inequalities , and .
[3 marks]
Answer :
24. a) Complete the box in the answer space with “and” / “or”.
i) This statement is TRUE.
ii) This statement is FALSE.
b) i) Complete the conclusion in the following argument.
Premise 1 : All parallel lines have equal gradient.
Premise 2 : PQ and RS are parallel lines.
Conclusion : …………………………………………………………………………………………
ii) Make a general conclusion by induction for the sequence 5, 17, 37, 65,… which follows the pattern below :
[5 marks]
Answer :
a) i)
ii)
b) i) Conclusion : ……………………………………………………………………………….………
ii) ………………………………………………………………………………………………..……
25. Diagram 9 shows a straight line AB and a straight line CD drawn on a Cartesian plane. AB is parallel to CD.
Find
a) the equation of the straight line AB,
b) the x-intercept of straight line AB.
[5 marks]
Answer :
a)
b)
26. a) i) The value of digit 2 in the number is . State the value of n.
ii) Express as a number in base 2.
b) If where , find the values of x and y. Hence, write as number in base five.
[6 marks]
Answer :
a) i)
ii)
b) i)
ii)
27. The Venn diagram in the answer space shows set P, Q and R.
On the diagram provided in the answer spaces, shade
a)
b)
c)
[6 marks]
Answer :
a) c)
b)
28. One card is drawn from each box at random as shown in Diagram 10.
a) List all the possible outcomes.
b) By listing the outcomes, find the probability of the following events
i) a consonant and an even number,
ii) the letter M or an odd number.
[5 marks]
Answer:
a)
b) i)
ii)
29. Diagram 11 shows a right prism with a horizontal rectangular base JKLM. Trapezium JKQP is the uniform cross-section of the prism. The rectangular surface QRLK is inclined.
Calculate the angle between the plane RSJ and the vertical plane RSML.
[5 marks]
Answer :
30. a) Sketch the graph of for the range on the axes provided.
b) Diagram 11 shows the graph of the function where k is an integer. Find the values of k
and p.
[5 marks]
Answer :
a)
b) k = ……………….
p = ……………….
31. a) Complete Table 4 in the answer space for the equation by writing down the values of y when and .
b) For this part of the question, use the graph paper.
You may use a flexible curve.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of for .
c) From your graph, find
i) the value of y when ,
ii) the value of x when
d) Draw a suitable line on your graph to find all the values of x which satisfy the equation for .
State the values of x.
[12 marks]
Answer :
a)
x / -3.5 / -3 / -2 / -1 / 0 / 1 / 2 / 3 / 3.5y / -17.4 / 10 / 12 / 8 / 4 / 20 / 33.4
b) Graph
c) i)
ii)
d) x = ……………….., ……………….., ………………..