Tkss Prelim 2009 Em P1
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- Words: 1,544
- Pages: 13
3
For Examiner’s Use
1.
2.
For Examiner’s Use
Given that 440 23 5 11 and 275 52 11. (a) Find the highest common factor of 440 and 275. (b) Find the smallest positive integer k such that 440k is a perfect square.
Answer: (a)
[1]
(b)
[1]
If p decreases by 10% and then increases by 20% to become q, find the value of p in simplest form. q
Answer: 3.
[2]
y is inversely proportional to x 2 . The difference in values of y when x = 1 and x = 10 is 9
9 . 10
Find the formula connecting y and x.
Answer:
Tanjong Katong Secondary School
[2]
Prelim Mathematics P1
4
For Examiner’s Use
4.
(a) Given that y 81 (b) Simplify
5.
6 2
x 2
3 4
For Examiner’s Use
1, evaluate y.
2 x3
31 x
.
Answer: (a)
[1]
(b)
[2]
Answer: (a)
[1]
(b)
[2]
Solve the following. 4 3 (a) 5 x 2x (b) ( x 2)( x 2) 3(2 x)
Tanjong Katong Secondary School
Prelim Mathematics P1
5
For Examiner’s Use
6.
For Examiner’s Use
(a) Find the ratio 1 exterior angle of a regular octagon : 1 exterior angle of a regular pentagon. Leave your answer in the simplest form. (b) The sum of interior angles of an n-sided polygon is 3060, find the value of n.
Answer: (a)
:
(b) n = 7.
Write down all the integers which satisfy x 4x 5
[2]
6x 13 . 2
Answer:
8.
[1]
[3]
The distance between 2 planets is 4340 megakilometres. (a) Write down the distance in standard form. (b) Given that the speed of light is 3 10 8 m/s, find the time taken to the nearest minute for light to travel this distance.
Tanjong Katong Secondary School
Answer: (a)
km[ 1 ]
(b)
mins[ 2 ] Prelim Mathematics P1
6
For Examiner’s Use
9.
For Examiner’s Use
The following stem-and-leaf diagram shows the distribution of time taken (in seconds) by 20 cars to reach a speed of 100 km/h. 3
5 6
7 7
4
0 1
2 2
2 4
5
1 3
5 6
6 8
6
0 1
5 9
Key 3 | 5 means 3.5 (a) Find the mode. (b) Find the median. (c) 30% of the cars clocked less than or equal to t seconds. Find the value of t.
Answer:
(a)
s[1]
(b)
s[1]
(c)
[1]
10. A map is drawn to a scale of 1 : 125000. (a) Find the distance on the map if the actual distance is 22.5 kilometres. (b) An area on the map is 100 cm2. Find the actual area, giving your answer in km 2.
Tanjong Katong Secondary School
Answer: (a)
cm [ 1 ]
(b)
km2 [ 2 ] Prelim Mathematics P1
7
For Examiner’s Use
For Examiner’s Use
11. P is the point (5, 12) and Q is the point (q, 12) where q is positive. OPQ is an isosceles triangle with OP = PQ where O is the origin.
(a) Write down PQ as a column vector in terms of q. (b) Find the value of q. (c) A point R (5, r) is such that OR = OP, find the possible values of r.
Answer: (a)
[1]
(b) q =
[1]
(c)
[1]
12. (a) There are 26 letters in the English Alphabet. Two letters are chosen at random without replacement. Find the probability that at least one of them is a vowel. (b) A two digit number is written down at random. Find the probability that (i) the number is less than 45, (ii) the number contains at least one digit 8.
Answer: (a)
Tanjong Katong Secondary School
[2]
(b)(i)
[1]
(ii)
[1]
Prelim Mathematics P1
8
For Examiner’s Use
For Examiner’s Use
n 13. Given that P [2a (n 1)d ]. 2 (a) Express d as the subject of the formula. (b) Find the value of P for a = 1, n = 20 and d = 2. Hence explain how this value is related to the number sequence 1, 3, 5, 7,………39.
Answer:
(a)
[2]
(b) P =
[1]
(b) [1]
14. Factorise (a) 10 x 2 15x 3 y 2 xy (b) 4 p 2 4 pq q 2 9
Tanjong Katong Secondary School
Answer: (a)
[2]
(b)
[2] Prelim Mathematics P1
9
For Examiner’s Use
For Examiner’s Use
15. In the diagram, PQ is parallel to RS and QPS SQR. (a) Explain why triangles PQS and QSR are similar. (b) Given that PQ = 9 cm and RS = 25 cm, calculate QS. R Q 25 cm
9 cm S
P
Answer: (a) [2] (b)
cm [ 2 ]
16. (a) On the Venn Diagram in the answer space, shade the set A B. (b) A universal set and its subsets A, B and C are given by = {x : x is an integer and 1 x < 10} A = {x : x is a factor of 18} B = {x : x is a prime number} C = {3, 6, 9} (i) List the elements of A. (ii) Find n(A B). (iii) Describe clearly the set C in words.
Answer: (a)
B A
[1]
(iii) Tanjong Katong Secondary School
(b) (i)
[1]
(ii)
[1] [1] Prelim Mathematics P1
10
For Examiner’s Use
For Examiner’s Use
17. (a) Sketch the graph y 8 2 x x 2 on the axes provided. (b) Write down the equation of the line of symmetry. (c) If the graph is reflected in the y – axis, write down the equation of the new graph.
Answer: (a) y
2
2
x
0
[2]
Tanjong Katong Secondary School
(b)
[1]
(c)
[1]
Prelim Mathematics P1
11
For Examiner’s Use
18.
B
For Examiner’s Use
C
D
A p
O
q
E
The diagram shows a regular hexagon, OABCDE where OA = p and OE = q. M is a point on AE such that 3MA = 2EA. (a) Express, as simply as possible, in terms of p and/or q,
(i)
EA ,
(ii) OD ,
(iii) OM . (b) Hence, what can you deduce about O, M and D?
Answer: (a)(i)
[1]
(ii)
[1]
(iii)
[2]
(b) [1] Tanjong Katong Secondary School
Prelim Mathematics P1
12
For Examiner’s Use
19.
For Examiner’s Use
In the diagram, ABCD and XY are straight lines parallel to each other. YB = 6 cm, BC = 8 cm, BCX = 20 and XAB = YBC = 90.
X
Y
A
B
20 8 cm
C
D
(a) Calculate AB. (b) Find the area of XYC. (c) Write down the value of cos YCD.
Answer:
Tanjong Katong Secondary School
(a)
cm [ 2 ]
(b)
cm2 [ 2 ]
(c)
[1]
Prelim Mathematics P1
13
For Examiner’s Use
For Examiner’s Use
20. The two solids shown are geometrically similar and made of the same material. The ratio of the areas of the bases is 16 : 25. (a) The curved surface area of solid A is 360 cm2. Calculate the curved surface area of solid B. (b) Find the ratio of the circumferences of the top of A to B.
A
B
(c) The cost of material used to make solid B is $18.75. Find the cost of material used to make solid A. (d) Both solids A and B are melted to form a number of geometrically similar solids. Each of these solids, C is such that the ratio of the areas of the bases of A : B : C is 16 : 25 : 9, find the number of such solids that can be formed.
Answer:
Tanjong Katong Secondary School
(a)
cm2[ 1 ]
(b)
[1]
(c) $
[2]
(d)
[2] Prelim Mathematics P1
14
For Examiner’s Use
For Examiner’s Use
21. The diagram shows the speed-time graph of a particle during a 25 second journey. Speed (m/s) 20
0
5
9
25
Time (s)
(a) Find the total distance travelled before it starts to decelerate. (b) Find the times when the speed is 15 m/s. (c) On the grid in the answer space, sketch the distance-time graph for the same journey.
Answer:
(a)
m[1]
(b)
s [2]
(c) Distance (m)
0
Tanjong Katong Secondary School
5
9
25
Time (s)
[2]
Prelim Mathematics P1
15
For Examiner’s Use
For Examiner’s Use
22. The diagram is a scale drawing of a map. The scale is 1 cm to 100 m. A is due North of B. (a) Find the bearing of C from A. (b) M is due East of A and on a bearing of 050 from C. Find and label M. (c) A point P inside the quadrilateral ABCM is such that it is equidistant from B and C and equidistant from AB and BC. Find and label P.
[1]
[3]
N
A
B C
Answer:
(a)
[1]
End of paper Tanjong Katong Secondary School
Prelim Mathematics P1
For Examiner’s Use
1.
2.
For Examiner’s Use
Given that 440 23 5 11 and 275 52 11. (a) Find the highest common factor of 440 and 275. (b) Find the smallest positive integer k such that 440k is a perfect square.
Answer: (a)
[1]
(b)
[1]
If p decreases by 10% and then increases by 20% to become q, find the value of p in simplest form. q
Answer: 3.
[2]
y is inversely proportional to x 2 . The difference in values of y when x = 1 and x = 10 is 9
9 . 10
Find the formula connecting y and x.
Answer:
Tanjong Katong Secondary School
[2]
Prelim Mathematics P1
4
For Examiner’s Use
4.
(a) Given that y 81 (b) Simplify
5.
6 2
x 2
3 4
For Examiner’s Use
1, evaluate y.
2 x3
31 x
.
Answer: (a)
[1]
(b)
[2]
Answer: (a)
[1]
(b)
[2]
Solve the following. 4 3 (a) 5 x 2x (b) ( x 2)( x 2) 3(2 x)
Tanjong Katong Secondary School
Prelim Mathematics P1
5
For Examiner’s Use
6.
For Examiner’s Use
(a) Find the ratio 1 exterior angle of a regular octagon : 1 exterior angle of a regular pentagon. Leave your answer in the simplest form. (b) The sum of interior angles of an n-sided polygon is 3060, find the value of n.
Answer: (a)
:
(b) n = 7.
Write down all the integers which satisfy x 4x 5
[2]
6x 13 . 2
Answer:
8.
[1]
[3]
The distance between 2 planets is 4340 megakilometres. (a) Write down the distance in standard form. (b) Given that the speed of light is 3 10 8 m/s, find the time taken to the nearest minute for light to travel this distance.
Tanjong Katong Secondary School
Answer: (a)
km[ 1 ]
(b)
mins[ 2 ] Prelim Mathematics P1
6
For Examiner’s Use
9.
For Examiner’s Use
The following stem-and-leaf diagram shows the distribution of time taken (in seconds) by 20 cars to reach a speed of 100 km/h. 3
5 6
7 7
4
0 1
2 2
2 4
5
1 3
5 6
6 8
6
0 1
5 9
Key 3 | 5 means 3.5 (a) Find the mode. (b) Find the median. (c) 30% of the cars clocked less than or equal to t seconds. Find the value of t.
Answer:
(a)
s[1]
(b)
s[1]
(c)
[1]
10. A map is drawn to a scale of 1 : 125000. (a) Find the distance on the map if the actual distance is 22.5 kilometres. (b) An area on the map is 100 cm2. Find the actual area, giving your answer in km 2.
Tanjong Katong Secondary School
Answer: (a)
cm [ 1 ]
(b)
km2 [ 2 ] Prelim Mathematics P1
7
For Examiner’s Use
For Examiner’s Use
11. P is the point (5, 12) and Q is the point (q, 12) where q is positive. OPQ is an isosceles triangle with OP = PQ where O is the origin.
(a) Write down PQ as a column vector in terms of q. (b) Find the value of q. (c) A point R (5, r) is such that OR = OP, find the possible values of r.
Answer: (a)
[1]
(b) q =
[1]
(c)
[1]
12. (a) There are 26 letters in the English Alphabet. Two letters are chosen at random without replacement. Find the probability that at least one of them is a vowel. (b) A two digit number is written down at random. Find the probability that (i) the number is less than 45, (ii) the number contains at least one digit 8.
Answer: (a)
Tanjong Katong Secondary School
[2]
(b)(i)
[1]
(ii)
[1]
Prelim Mathematics P1
8
For Examiner’s Use
For Examiner’s Use
n 13. Given that P [2a (n 1)d ]. 2 (a) Express d as the subject of the formula. (b) Find the value of P for a = 1, n = 20 and d = 2. Hence explain how this value is related to the number sequence 1, 3, 5, 7,………39.
Answer:
(a)
[2]
(b) P =
[1]
(b) [1]
14. Factorise (a) 10 x 2 15x 3 y 2 xy (b) 4 p 2 4 pq q 2 9
Tanjong Katong Secondary School
Answer: (a)
[2]
(b)
[2] Prelim Mathematics P1
9
For Examiner’s Use
For Examiner’s Use
15. In the diagram, PQ is parallel to RS and QPS SQR. (a) Explain why triangles PQS and QSR are similar. (b) Given that PQ = 9 cm and RS = 25 cm, calculate QS. R Q 25 cm
9 cm S
P
Answer: (a) [2] (b)
cm [ 2 ]
16. (a) On the Venn Diagram in the answer space, shade the set A B. (b) A universal set and its subsets A, B and C are given by = {x : x is an integer and 1 x < 10} A = {x : x is a factor of 18} B = {x : x is a prime number} C = {3, 6, 9} (i) List the elements of A. (ii) Find n(A B). (iii) Describe clearly the set C in words.
Answer: (a)
B A
[1]
(iii) Tanjong Katong Secondary School
(b) (i)
[1]
(ii)
[1] [1] Prelim Mathematics P1
10
For Examiner’s Use
For Examiner’s Use
17. (a) Sketch the graph y 8 2 x x 2 on the axes provided. (b) Write down the equation of the line of symmetry. (c) If the graph is reflected in the y – axis, write down the equation of the new graph.
Answer: (a) y
2
2
x
0
[2]
Tanjong Katong Secondary School
(b)
[1]
(c)
[1]
Prelim Mathematics P1
11
For Examiner’s Use
18.
B
For Examiner’s Use
C
D
A p
O
q
E
The diagram shows a regular hexagon, OABCDE where OA = p and OE = q. M is a point on AE such that 3MA = 2EA. (a) Express, as simply as possible, in terms of p and/or q,
(i)
EA ,
(ii) OD ,
(iii) OM . (b) Hence, what can you deduce about O, M and D?
Answer: (a)(i)
[1]
(ii)
[1]
(iii)
[2]
(b) [1] Tanjong Katong Secondary School
Prelim Mathematics P1
12
For Examiner’s Use
19.
For Examiner’s Use
In the diagram, ABCD and XY are straight lines parallel to each other. YB = 6 cm, BC = 8 cm, BCX = 20 and XAB = YBC = 90.
X
Y
A
B
20 8 cm
C
D
(a) Calculate AB. (b) Find the area of XYC. (c) Write down the value of cos YCD.
Answer:
Tanjong Katong Secondary School
(a)
cm [ 2 ]
(b)
cm2 [ 2 ]
(c)
[1]
Prelim Mathematics P1
13
For Examiner’s Use
For Examiner’s Use
20. The two solids shown are geometrically similar and made of the same material. The ratio of the areas of the bases is 16 : 25. (a) The curved surface area of solid A is 360 cm2. Calculate the curved surface area of solid B. (b) Find the ratio of the circumferences of the top of A to B.
A
B
(c) The cost of material used to make solid B is $18.75. Find the cost of material used to make solid A. (d) Both solids A and B are melted to form a number of geometrically similar solids. Each of these solids, C is such that the ratio of the areas of the bases of A : B : C is 16 : 25 : 9, find the number of such solids that can be formed.
Answer:
Tanjong Katong Secondary School
(a)
cm2[ 1 ]
(b)
[1]
(c) $
[2]
(d)
[2] Prelim Mathematics P1
14
For Examiner’s Use
For Examiner’s Use
21. The diagram shows the speed-time graph of a particle during a 25 second journey. Speed (m/s) 20
0
5
9
25
Time (s)
(a) Find the total distance travelled before it starts to decelerate. (b) Find the times when the speed is 15 m/s. (c) On the grid in the answer space, sketch the distance-time graph for the same journey.
Answer:
(a)
m[1]
(b)
s [2]
(c) Distance (m)
0
Tanjong Katong Secondary School
5
9
25
Time (s)
[2]
Prelim Mathematics P1
15
For Examiner’s Use
For Examiner’s Use
22. The diagram is a scale drawing of a map. The scale is 1 cm to 100 m. A is due North of B. (a) Find the bearing of C from A. (b) M is due East of A and on a bearing of 050 from C. Find and label M. (c) A point P inside the quadrilateral ABCM is such that it is equidistant from B and C and equidistant from AB and BC. Find and label P.
[1]
[3]
N
A
B C
Answer:
(a)
[1]
End of paper Tanjong Katong Secondary School
Prelim Mathematics P1
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