Dunearn Prelim 2009 Em P1
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- Pages: 16
3 For
Answer all the questions.
For
Examiner’s
Examiner’s Use
1
John and Obama were the only candidates for the coming Presidential election in USA. Obama received 68% of the votes cast and he had exactly 900 votes more than John. Find the total number of votes cast.
Answer ________________________ votes
2
[2]
A man bought a eggs at r cents per dozen. He sold them for s cents each. Find an expression, in terms of a, r and s, for the profit, in cents, that he made.
Answer ______________________
[2]
Use
4 For
3
Examiner’s Use
Two conical flasks A and B made of the same material are geometrically similar and the ratio of their heights is 3 : 4. (a)
The diameter of the base of the larger conical vessel B is 16 cm. Calculate the diameter of the base of the smaller conical vessel A.
(b)
Find the ratio of the base area of A : base area of B.
Answer (a) ________________________ cm [1] (b) ____________ : ____________ 4
[1]
Steve has just bought a new Creative Zen with a memory space of 512 megabytes. He needs 250 kilobytes of memory space for each song he downloads. (a) Express 512 megabytes in bytes, giving your answer in standard form. (b)
What is the maximum number of songs Steve can download if he uses up all the memory space in his Creative Zen?
Answer (a) ______________________ bytes
[1]
(b) _____________________ songs
[1]
For Examiner’s Use
5 For
5
Examiner’s
(a)
b5 b2 b3 Simplify and give your answer in the form b n b
Use
(b)
6
5 Simplify 2x
For Examiner’s
2
Use
Answer (a) __________________________
[1]
(b) __________________________
[1]
David deposited $5250 in a bank that pays 1.5% compound interest per annum. Calculate the amount David has after 5 years.
Answer $ ____________________________
[2]
6 For
7
Examiner’s
Evaluate the following, giving your answers correct to 3 significant figures: (a)
Use
(b)
8
For
2 4 3 7 1 , 7 9 5 9 0.3234 3 32.54 9.329
Examiner’s Use
Answer (a) __________________________
[1]
(b) __________________________
[1]
The temperature in Dubai at 0600 was -10 ºC. At 1500, the temperature was 17 ºC. Assuming that the temperature rose at a steady rate, calculate (a) the difference between the two temperatures, (b)
the temperature at 1400.
Answer (a) ________________________ ºC
[1]
(b) ________________________ ºC
[2]
7 For
9
Examiner’s
A model is made of the National Stadium to a scale of 1 : 150. (a) If the height of the stadium in the model is 25 cm, find the actual height of the stadium in metres.
Use
Examiner’s Use
2
(b) If the floor area of the soccer field in the stadium is 28125 m , find the floor area of the corresponding soccer field in the model in cm2
Answer (a) ________________________ m (b) _______________________ cm2 10
For
[1] [2]
(a)
The nth term of a sequence is given by 3n2 – 1. Write down the first four terms.
(b)
The first four terms of another sequence are 4, 13, 28, 49, ... (i) Write down the next term. (ii) By comparing this sequence with your answer to (a), write down the nth term of this sequence.
Answer (a) __________________________
[1]
(b)(i)_________________________
[1]
(ii) __________________________
[1]
8
For
11
(a)
Jane has three rolls of ribbons measuring 288 cm, 416 cm and 640 cm
For
respectively. The ribbons are to be cut into smaller pieces of the same length leaving no ribbon wasted. Find
Examiner’s Use
(i) the greatest possible length of each ribbon, (ii) the total number of ribbons cut from the three rolls. (b)
Find the smallest number which must be multiplied by 120 to give a cube number.
Answer (a)(i)_______________________cm [2] (ii) __________________________
[1]
(b) __________________________
[1]
Examiner’s Use
9 For
12
A
For
Examiner’s
Examiner’s
Use
Use
13 cm
B
5 cm
C
6 cm
D
In the diagram above, ABC 90 , AC = 13 cm, BC = 5 cm and CD = 6 cm. Calculate
13
(a) (b)
the length of AB, cos ACD ,
(c)
area of ACD .
(a)
(b)
Answer (a) _______________________ cm
[1]
(b) __________________________
[1]
(c) _______________________ cm2
[2]
y is proportional to x n . Write down the value of n when (i) y cm 2 is the area of a circle of radius x cm. (ii) y hours is the time taken to travel a distance x km at a constant speed. The force, F, between two particles is inversely proportional to the square of the distance between them. The force is 36 units when the distance between the particles is r metres. Find the force when the distance is 3r metres.
Answer (a)(i)_________________________
[1]
(ii) __________________________
[1]
(b) __________________________
[2]
10
For
14
(a)
Draw a quadrilateral ABCD with AB as the base given that AB = 10
[2]
(b)
cm, AD = 8 cm, ADC 100, BAD 75 and ABC 80. Construct the angle bisector of BAD
[1]
(c)
Construct the perpendicular bisector of DC
[1]
Examiner’s Use
For Examiner’s Use
11 For
15
Examiner’s Use
15 men, 8 ladies, 7 girls and 10 boys took part in a lucky draw. A winner was
For
picked at random, after which another winner was picked from the remaining people.
Examiner’s
Find the probability that (a) the first winner is a female, (b) (c)
16
a boy was chosen during both picks, among the two winners, at least one of them is an adult.
Answer (a) __________________________
[1]
(b) __________________________
[1]
(c) __________________________ 3 2 k AB , BC and CD 4 5 14 (a) Express 3 AB 2 BC as a column vector, (b) Given that CD is parallel to AB , find the value of k,
[2]
(c)
Find BD , giving your answer to the nearest whole number.
Answer (a) __________________________
[1]
(b) __________________________
[2]
(c) __________________________
[2]
Use
12
For Examiner’s Use
17
In the diagram, BC = 10 cm, AC = 14 cm, AD = 7 cm, BD = 2 cm and ABC AED .
For Examiner’s
(a)
Explain why triangles ABC and AED are similar.
(b) (c)
Find the length of DE. Calculate the area of quadrilateral BDEC if the area of AED is 9 cm2.
Use
2 D
B
10
7
A
E
C
14
Answer (a) ________________________________________________________
[2]
________________________________________________________ (b) _______________________ cm
[1]
(c) _______________________ cm2
[2]
13 For For Examiner’s Use
18
The graph represents the speed of a car, in metres per second, for its journey. Initially, it is travelling at a constant speed of 20 m/s for 2 seconds, then it slows down uniformly, coming to a rest after 4 seconds. It then started to move for the second part of its journey lasting 10 seconds and the distance covered for the whole journey is 150 m.
Speed (m/s) 20 v
0
2
4
6
8
10
12
14
16
(a) (b)
Find the speed of the car after 5 seconds. Find the value of v.
(c)
Sketch the distance time graph for the whole journey.
Time (s)
[2]
Distance (m) 16 160 0
140
14
120 0
100 12
080 10 60 0 40 20 80
0
2
4
6
8
10
12
14
16
Time (s)
Answer (a) _______________________m/s
[1]
(b) _______________________m/s
[2]
Examiner’s Use
14 For Examiner’s Use
19
The diagram shows a straight line y mx c cutting the y-axis at A (0, 4) and x-axis at B (2,0). A curve y ( x 2)( x k ) meets the x-axis at B and the y-axis at C (0, -2). (a) Find the area of triangle ABC. (b) (c)
For Examiner’s Use
Find the values of m, c and k. Write down the equation of the line of symmetry of the curve y ( x 2)( x k ) .
Answer (a) _____________________ units2 (b) m = _______________________
[1] [3]
c = _______________________ k = _______________________ (c) __________________________
[1]
15 For
20
(a)
Sketch the graph of y (2 x 4)(8 2 x) .
For
Examiner’s
Examiner’s
Use
Answer (a)
y
[2]
x
(b)
(i) (ii)
Express x 2 6 x 2 in the form ( x b)2 c Sketch the graph of y x 2 6 x 2 Answer (b)(i) x 2 6 x 2 = ___________________ (ii)
y
[1] [2]
x
x
Use
16
For Examiner’s
21
The information below show the mass of 1000 packages of 1 kg rice packed by two machines X and Y.
For Examiner’s Use
Use
Machine X Mass (g)
980 - 990
990 – 1000
1000 – 1010
1010 – 1020
Frequency
125
240
540
95
Machine Y Mean = 1003.2 Standard deviation = 9.8 (a) Find the mean and standard deviation of the mass of rice packed for Machine X. (b) Compare the performance of the two machines. If you are the owner of the rice distribution business, which machine will you buy? Why?
Answer (a) Mean = ______________ g ; Standard deviation = __________________ g
[4]
Answer (b) __________________________________________________
[2]
___________________________________________________________ ___________________________________________________________ ___________________________________________________________
17 For
22
(a)
Examiner’s
2x
Use
For
Solve the simultaneous equations 6 x 2 y 3
Examiner’s Use
1 y2 3
Answer x = __________________________
[3]
y = __________________________ (b)
Solve the inequalities 4x 4 x 1 3x 3 2
Show your solution on the number line in the answer space.
Answer (b)
[3]
-4
-3
-2
-1
0
1
2
3
4
5
6
18
Answer all the questions.
For
Examiner’s
Examiner’s Use
1
John and Obama were the only candidates for the coming Presidential election in USA. Obama received 68% of the votes cast and he had exactly 900 votes more than John. Find the total number of votes cast.
Answer ________________________ votes
2
[2]
A man bought a eggs at r cents per dozen. He sold them for s cents each. Find an expression, in terms of a, r and s, for the profit, in cents, that he made.
Answer ______________________
[2]
Use
4 For
3
Examiner’s Use
Two conical flasks A and B made of the same material are geometrically similar and the ratio of their heights is 3 : 4. (a)
The diameter of the base of the larger conical vessel B is 16 cm. Calculate the diameter of the base of the smaller conical vessel A.
(b)
Find the ratio of the base area of A : base area of B.
Answer (a) ________________________ cm [1] (b) ____________ : ____________ 4
[1]
Steve has just bought a new Creative Zen with a memory space of 512 megabytes. He needs 250 kilobytes of memory space for each song he downloads. (a) Express 512 megabytes in bytes, giving your answer in standard form. (b)
What is the maximum number of songs Steve can download if he uses up all the memory space in his Creative Zen?
Answer (a) ______________________ bytes
[1]
(b) _____________________ songs
[1]
For Examiner’s Use
5 For
5
Examiner’s
(a)
b5 b2 b3 Simplify and give your answer in the form b n b
Use
(b)
6
5 Simplify 2x
For Examiner’s
2
Use
Answer (a) __________________________
[1]
(b) __________________________
[1]
David deposited $5250 in a bank that pays 1.5% compound interest per annum. Calculate the amount David has after 5 years.
Answer $ ____________________________
[2]
6 For
7
Examiner’s
Evaluate the following, giving your answers correct to 3 significant figures: (a)
Use
(b)
8
For
2 4 3 7 1 , 7 9 5 9 0.3234 3 32.54 9.329
Examiner’s Use
Answer (a) __________________________
[1]
(b) __________________________
[1]
The temperature in Dubai at 0600 was -10 ºC. At 1500, the temperature was 17 ºC. Assuming that the temperature rose at a steady rate, calculate (a) the difference between the two temperatures, (b)
the temperature at 1400.
Answer (a) ________________________ ºC
[1]
(b) ________________________ ºC
[2]
7 For
9
Examiner’s
A model is made of the National Stadium to a scale of 1 : 150. (a) If the height of the stadium in the model is 25 cm, find the actual height of the stadium in metres.
Use
Examiner’s Use
2
(b) If the floor area of the soccer field in the stadium is 28125 m , find the floor area of the corresponding soccer field in the model in cm2
Answer (a) ________________________ m (b) _______________________ cm2 10
For
[1] [2]
(a)
The nth term of a sequence is given by 3n2 – 1. Write down the first four terms.
(b)
The first four terms of another sequence are 4, 13, 28, 49, ... (i) Write down the next term. (ii) By comparing this sequence with your answer to (a), write down the nth term of this sequence.
Answer (a) __________________________
[1]
(b)(i)_________________________
[1]
(ii) __________________________
[1]
8
For
11
(a)
Jane has three rolls of ribbons measuring 288 cm, 416 cm and 640 cm
For
respectively. The ribbons are to be cut into smaller pieces of the same length leaving no ribbon wasted. Find
Examiner’s Use
(i) the greatest possible length of each ribbon, (ii) the total number of ribbons cut from the three rolls. (b)
Find the smallest number which must be multiplied by 120 to give a cube number.
Answer (a)(i)_______________________cm [2] (ii) __________________________
[1]
(b) __________________________
[1]
Examiner’s Use
9 For
12
A
For
Examiner’s
Examiner’s
Use
Use
13 cm
B
5 cm
C
6 cm
D
In the diagram above, ABC 90 , AC = 13 cm, BC = 5 cm and CD = 6 cm. Calculate
13
(a) (b)
the length of AB, cos ACD ,
(c)
area of ACD .
(a)
(b)
Answer (a) _______________________ cm
[1]
(b) __________________________
[1]
(c) _______________________ cm2
[2]
y is proportional to x n . Write down the value of n when (i) y cm 2 is the area of a circle of radius x cm. (ii) y hours is the time taken to travel a distance x km at a constant speed. The force, F, between two particles is inversely proportional to the square of the distance between them. The force is 36 units when the distance between the particles is r metres. Find the force when the distance is 3r metres.
Answer (a)(i)_________________________
[1]
(ii) __________________________
[1]
(b) __________________________
[2]
10
For
14
(a)
Draw a quadrilateral ABCD with AB as the base given that AB = 10
[2]
(b)
cm, AD = 8 cm, ADC 100, BAD 75 and ABC 80. Construct the angle bisector of BAD
[1]
(c)
Construct the perpendicular bisector of DC
[1]
Examiner’s Use
For Examiner’s Use
11 For
15
Examiner’s Use
15 men, 8 ladies, 7 girls and 10 boys took part in a lucky draw. A winner was
For
picked at random, after which another winner was picked from the remaining people.
Examiner’s
Find the probability that (a) the first winner is a female, (b) (c)
16
a boy was chosen during both picks, among the two winners, at least one of them is an adult.
Answer (a) __________________________
[1]
(b) __________________________
[1]
(c) __________________________ 3 2 k AB , BC and CD 4 5 14 (a) Express 3 AB 2 BC as a column vector, (b) Given that CD is parallel to AB , find the value of k,
[2]
(c)
Find BD , giving your answer to the nearest whole number.
Answer (a) __________________________
[1]
(b) __________________________
[2]
(c) __________________________
[2]
Use
12
For Examiner’s Use
17
In the diagram, BC = 10 cm, AC = 14 cm, AD = 7 cm, BD = 2 cm and ABC AED .
For Examiner’s
(a)
Explain why triangles ABC and AED are similar.
(b) (c)
Find the length of DE. Calculate the area of quadrilateral BDEC if the area of AED is 9 cm2.
Use
2 D
B
10
7
A
E
C
14
Answer (a) ________________________________________________________
[2]
________________________________________________________ (b) _______________________ cm
[1]
(c) _______________________ cm2
[2]
13 For For Examiner’s Use
18
The graph represents the speed of a car, in metres per second, for its journey. Initially, it is travelling at a constant speed of 20 m/s for 2 seconds, then it slows down uniformly, coming to a rest after 4 seconds. It then started to move for the second part of its journey lasting 10 seconds and the distance covered for the whole journey is 150 m.
Speed (m/s) 20 v
0
2
4
6
8
10
12
14
16
(a) (b)
Find the speed of the car after 5 seconds. Find the value of v.
(c)
Sketch the distance time graph for the whole journey.
Time (s)
[2]
Distance (m) 16 160 0
140
14
120 0
100 12
080 10 60 0 40 20 80
0
2
4
6
8
10
12
14
16
Time (s)
Answer (a) _______________________m/s
[1]
(b) _______________________m/s
[2]
Examiner’s Use
14 For Examiner’s Use
19
The diagram shows a straight line y mx c cutting the y-axis at A (0, 4) and x-axis at B (2,0). A curve y ( x 2)( x k ) meets the x-axis at B and the y-axis at C (0, -2). (a) Find the area of triangle ABC. (b) (c)
For Examiner’s Use
Find the values of m, c and k. Write down the equation of the line of symmetry of the curve y ( x 2)( x k ) .
Answer (a) _____________________ units2 (b) m = _______________________
[1] [3]
c = _______________________ k = _______________________ (c) __________________________
[1]
15 For
20
(a)
Sketch the graph of y (2 x 4)(8 2 x) .
For
Examiner’s
Examiner’s
Use
Answer (a)
y
[2]
x
(b)
(i) (ii)
Express x 2 6 x 2 in the form ( x b)2 c Sketch the graph of y x 2 6 x 2 Answer (b)(i) x 2 6 x 2 = ___________________ (ii)
y
[1] [2]
x
x
Use
16
For Examiner’s
21
The information below show the mass of 1000 packages of 1 kg rice packed by two machines X and Y.
For Examiner’s Use
Use
Machine X Mass (g)
980 - 990
990 – 1000
1000 – 1010
1010 – 1020
Frequency
125
240
540
95
Machine Y Mean = 1003.2 Standard deviation = 9.8 (a) Find the mean and standard deviation of the mass of rice packed for Machine X. (b) Compare the performance of the two machines. If you are the owner of the rice distribution business, which machine will you buy? Why?
Answer (a) Mean = ______________ g ; Standard deviation = __________________ g
[4]
Answer (b) __________________________________________________
[2]
___________________________________________________________ ___________________________________________________________ ___________________________________________________________
17 For
22
(a)
Examiner’s
2x
Use
For
Solve the simultaneous equations 6 x 2 y 3
Examiner’s Use
1 y2 3
Answer x = __________________________
[3]
y = __________________________ (b)
Solve the inequalities 4x 4 x 1 3x 3 2
Show your solution on the number line in the answer space.
Answer (b)
[3]
-4
-3
-2
-1
0
1
2
3
4
5
6
18
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