Mathematic Spm 2006
SPM(U) 2006 : http://mathsmozac.blogspot.com Section A [52 marks] Answer all questions in this section. 1 The Venn diagram in the answer space shows sets P, Q and R such that the universal set, ξ = P ∪ Q ∪ R . On the diagram in the answer space, shade (a) the set P ∪ R , (b) the set (P ∩ R ) ∪ Q ' . [3 marks] Answer: (a) P Q R
(b)
P R
Q
2
Diagram 1 shows a solid cuboid. A cone is removed from this solid.
12 cm 10 cm 15 cm
DIAGRAM 1
The diameter of the base of the cone is 7 cm and the height of the cone is 9 cm. Calculate 22 ⎞ ⎛ the volume, in cm 3 , of the remaining solid. ⎜ Use π = [3 marks] ⎟ 7 ⎠ ⎝ Answer:
SAH@MOAZC2008
1
SPM(U) 2006 : http://mathsmozac.blogspot.com 3 (a) State whether each of the following statements is true or false. 3 64 = 4 (i) (ii) − 5 > −8 and 0 ⋅ 03 = 3 × 10 −1 . Write down two implications based on the following sentence. ∆ ABC is an equilateral triangle if and only if each of the interior angle of ∆ ABC is 60 o . Complete the premise in the following argument: Premise 1 : ………………………………………………… Premise 2 : 90 o ≤ x ≤ 180 o . Conclusion : sin x o is positive. [5 marks] Answer: (a) (i) ……………………………………………………………….. (ii) ……………………………………………………………….. Implication I : ……………………………………………………………………….. ……………………………………………………………………….. Implication II: ……………………………………………………………………….. ……………………………………………………………………….. Premise 1 : …………………………………………………………………………...
(b)
(c)
(b)
(c) 4
Diagram 2 shows a right prism. The base HJKL is a horizontal rectangle. The right angled triangle NHJ is the uniform cross section of the prism. M
N 8 cm L 6 cm H 12 cm
DIAGRAM 2
K
J
Identify and calculate the angle between the line KN and the plane HLMN. Answer :
[4 marks]
SAH@MOAZC2008
2
SPM(U) 2006 : http://mathsmozac.blogspot.com 5 Calculate the value of d and of e that satisfy the following simultaneous linear equations: [4 marks] 3d − 2e = 9
6d + e = −2
Answer :
6
In diagram 3, O is the origin and PQRS is
(b)
P R
Q
2
Diagram 1 shows a solid cuboid. A cone is removed from this solid.
12 cm 10 cm 15 cm
DIAGRAM 1
The diameter of the base of the cone is 7 cm and the height of the cone is 9 cm. Calculate 22 ⎞ ⎛ the volume, in cm 3 , of the remaining solid. ⎜ Use π = [3 marks] ⎟ 7 ⎠ ⎝ Answer:
SAH@MOAZC2008
1
SPM(U) 2006 : http://mathsmozac.blogspot.com 3 (a) State whether each of the following statements is true or false. 3 64 = 4 (i) (ii) − 5 > −8 and 0 ⋅ 03 = 3 × 10 −1 . Write down two implications based on the following sentence. ∆ ABC is an equilateral triangle if and only if each of the interior angle of ∆ ABC is 60 o . Complete the premise in the following argument: Premise 1 : ………………………………………………… Premise 2 : 90 o ≤ x ≤ 180 o . Conclusion : sin x o is positive. [5 marks] Answer: (a) (i) ……………………………………………………………….. (ii) ……………………………………………………………….. Implication I : ……………………………………………………………………….. ……………………………………………………………………….. Implication II: ……………………………………………………………………….. ……………………………………………………………………….. Premise 1 : …………………………………………………………………………...
(b)
(c)
(b)
(c) 4
Diagram 2 shows a right prism. The base HJKL is a horizontal rectangle. The right angled triangle NHJ is the uniform cross section of the prism. M
N 8 cm L 6 cm H 12 cm
DIAGRAM 2
K
J
Identify and calculate the angle between the line KN and the plane HLMN. Answer :
[4 marks]
SAH@MOAZC2008
2
SPM(U) 2006 : http://mathsmozac.blogspot.com 5 Calculate the value of d and of e that satisfy the following simultaneous linear equations: [4 marks] 3d − 2e = 9
6d + e = −2
Answer :
6
In diagram 3, O is the origin and PQRS is