Download Paper 1 - Objective - Penang Free School

PENANG FREE SCHOOL
MATHEMATICS ELECTIVES- ADDITIONAL MATHEMATICS
DAVID CHNG YEANG SOON.
Try the following Questions. The answers are provided at the end of the questions.
Form 5 Mixure 1
Name: ………………………………………..
Class:…………………..
1.


Given that AB = 3 p and CD = 7 p , find
~
~


(a) vector 5AB + CD in terms of p ,
~


(b) |5AB + CD | if p = 7 units.
[4 marks]
~
2.
Find the total of multiples of 11 that are between 500 to 700.
[4 marks]
3.
(a) Determine the magnitude and the direction of vector a
˜
.
(b) Determine the magnitude and the direction of vector a .
˜
[2 marks]
4.
Find the sum of the first 19 terms of the arithmetic progression -36, -37, -38, -39, ...,
[2 marks]
5.
Find the equation of the curve with gradient function,
dy
= 4x - 3, and passing through (0, 0).
dx
6.
[2 marks]
A particle moves along a straight line and passes through a fixed point O. Its velocity, v
m s-1, is given by v = 17 - 4t - t2 where t is the time, in seconds, after passing through
point O. Find the acceleration of the particle at t = 5.
7.
8.
9.
Solve the equation sin x =
1
for 0 ≤ x ≤ 
2
Given S = { 1, 2, 3, 4, 5, 6 }, A = { 1, 3, 6 } and B = { 3 }.
Find P(A  B' )
[2 marks]
[2 marks]
[3 marks]
Reduce y = 20x + 8x2 to the linear form of Y = mX + c. State the quantities to be
plotted on the Y-axis and X-axis and hence, identify the quantities of m and c.
[3 marks]
10. A particle moves along a straight line and passes through a fixed point O. Its velocity, v
m s-1, t s after passing through O is given by v = 29 - 5t. Find
(a) the time at which the particle is at instantaneous rest,
(b) the velocity of the particle after 3 s.
[2 marks]
11. 2 girls and 5 boys are to be seated in a row of 5 chairs. Find the number of ways they
can be seated if no two persons of the same sex are next to each other.
[4 marks]
12. A fair dice is rolled. Find the probability of getting
(a) a perfect square,
(b) a number that is greater than 5.
[4 marks]
13. The content of breakfast cereal packets have masses which are normally distributed with
a mean of 350 g and a standard deviation of 11.708 g. Determine the percentage
that a randomly selected packet of the breakfast cereal has a mass exceeding 372 g.
[3 marks]
14. A normal distribution has a mean of 17 and standard deviation of 7. Determine the score
[2 marks]
that corresponds to the standard score of 0.4.
15.
Given that

-1
0
g(x) dx = 2, find

0
-1
4[g(x) - 4] dx.
[2 marks]
16. Reduce xy = 7 to the linear form of Y = mX + c. State the quantities to be
plotted on the Y-axis and X-axis and hence, identify the quantities of m and c.
[3 marks]
17. 4 chairs are arranged in a column. In how many different ways can a 5 students
be seated?
[3 marks]
18. Express the following expressions as a single trigonometric function.
(a) 2 cos 60sin 60
(b) 2 tan 18
1 tan2 18
[4 marks]
19. Identify and shade the region in which every point satisfies the inequality
y  -15.
[2 marks]
20.
Find the linear inequality that defines the shaded region in the diagram.
Answers:
1.
(a) 22 p
~
(b) 154 units
2. 10791
3.
(a) |a| = 60 N
~
[3 marks]
(a) The direction of vector a is towards the west.
~
(b) |-a| = 60 N
~
(b) The direction of vector -a is towards the east.
~
4. -855
5. y = 2x2 - 3x - 0
6. a = -14 m s-2
7.
5

or
6
6
8.
1
3
9. y/x = 20x + 8;
Y = y/x,
X = x;
m = 20,
10. (a) t = 5.8 s
(b) s = 14 m s-1
11. 2  5P3 = 120
12.
1
(a)
3
1
6
3.01%
14.2
-24
y = 7(1/x);
120
(a) sin 120
(b) tan 36
c=8
(b)
13.
14.
15.
16.
17.
18.
19.
Y = y,
X = 1/x;
m = 7,
c=0
20. 3x + y < 6