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QUEEN’S COLLEGE
Half-yearly Examination, 2009-2010
Mathematics Paper II
Date: 15th Jan, 2010.
Time: 8:30-9:30
Full Marks: 80
Secondary 4
1. Write down the information required in the spaces provided in the Answer Sheet.
2. When told to open this question paper, check that all the questions are there. Look for the words
“END OF PAPER” after the last question.
3. Answer all questions. All the answers should be marked on the answer sheet provided.
4. Note that you may mark only ONE answer to each question. Two or more answers will score no
marks.
5. There are 40 questions in this paper. All questions carry equal marks.
6. The diagrams in this paper are not necessarily drawn to scale.
1
1. Which of the following numbers are rational
numbers?
I.
4. Given a is a real number. If the complex
number
0.9

II.
0. 9
III.
A.
B.
C.
D.
0.9
I only
I and II only
II and III only
I, II and III
A.
6
5
B.
6
5
C.
15
2
D.
 15
2
3  ai
is purely imaginary. Find a.
2  5i
2. Which of the following numbers is not a real
number?
5. Given that f(x) = 4x + 9, then
A.
B.
C.
D.
A.
B.
C.
4(x  2)
4(x  2)
4(x + 2)
D.
4(x + 2)
f(x + 2)  f(2x) =
2 3
2 3
16
 16
6. If 2 x 2  6 x  3  0 , then x =
3. What are the real part and imaginary part of
2  3i
?
2i
A.
3 6
.
2
A.
8
1
Real part =  , imaginary part =
5
5
B.
3 3
.
2
B.
1
8
Real part =  , imaginary part =
5
5
C.
3  15
.
2
C.
Real part =
1
8
, imaginary part = 
5
5
D.
3   15
.
2
D.
Real part =
1
8
, imaginary part = 
5
5
7. The equation of the axis of symmetry of the
graph of y = a(x + h)2 – k is
A. x = h.
B. x = –h.
2
h
.
a
C.
x=
D.
x = –k.
8. The figure shows the line y  ax  b . Which
11. Which of the following straight lines
intersects the straight line 2x + 3y – 6 = 0 at
of the following is correct?
infinitely many points?
A.
C.
2x + 3y = 0
x y
 1
3 2
3x – 2y = 0
D.

B.
A.
B.
C.
D.
a > 0, b > 0
a > 0, b < 0
a < 0, b > 0
a < 0, b < 0
12. If 2x – ky + 7 = 0 and x + 3y + 4 = 0 are
equations of two parallel lines, then k =
A.
2
3
B. 
9. Find the value(s) of k if 3x2  kx + 3 = 0 has
two equal real roots.
A.
6
B.
0
or
6
C.
D.
0
6
or
or
6
6
x
y

0
2 2
2
3
C. 6
D. -6
13. Which of the following straight lines is
perpendicular to the straight line L:
3x + 4y – 6 = 0 and has the same y-intercept
as L?
A. L1: 8x - 6y + 9 = 0
B. L2: 4x - 3y + 6 = 0
C. L3: 4x + 3y – 6 = 0
D. L4: 4x + 3y = 0
10. Find the sum and product of the roots of the
equation x(x + 12) = 7x - 1.
Sum of roots
Product of roots
A.

1
5
-1
B.
-5
1
C.
1
5
-1
D.
5
1
14. If A(1 , 1) lies on the straight line joining
B(2 , k) and C(4 , 9), then k =
3
A.
29
.
5
B.
31
.
7
C.

29
.
5
D.

31
.
7
15. Find the number of x-intercepts of the graph
of y = x(5x - 1) + 3 – x2 .
17. Which of the following quadratic equations
A.
2
B. 1
C. 0
D. Cannot be determined.
A.
B.
C.
D.
16. Which of the following may represent the
18. The equation of the parabola shown in the
figure is
have roots being 3 and 
graph of y = 2x + 8x  5?
2
1
?
2
2x2 + 5x + 3 = 0
2x2 - 5x + 3 = 0
2x2 - 5x – 3 = 0
2x2 + 5x - 3 = 0
A.
B.
A.
B.
C.
D.
C.
8
1
y   ( x  2) 2 
5
2
8
1
y   ( x  2) 2 
5
2
5
1
y   ( x  2) 2 
8
2
5
1
y   ( x  2) 2 
8
2
19. Which of the following is a factor of
x 3  3x 2  6 x  8 ?
D.
A.
B.
C.
x–3
x+4
x–4
D.
x+5
20. When 2x3 + 3x2  5x + 7 is divided by
x + 3, the quotient is
A.
B.
C.
D.
4
2x2  3x + 4.
2x2 + 4x  3.
2x2 + 3x  4.
2x2  4x + 3.
23. If x 2  x  12 is a factor of P(x), which of
the following must be true?
21. Which of the following graphs does not
represent y as a function of x?
A.
A.
B.
C.
D.
P(2) = P(–6) = 0
P(–1) = P(12) = 0
P(3) = P(–4) = 0
P(–3) = P(4) = 0
24. The figure shows the graph of a quadratic
function y = f(x). Find f(x).
B.
C.
D.
A.
3
( x  5) 2  6
2
B.
2
( x  5) 2  6
3
C.
3
( x  5) 2  6
2
D.
2
( x  5) 2  6
3
25. Referring to the graphs of the functions
below, arrange the values of A to D in the
functions in ascending order.
22. y 
1
is a function of x. Which of
x  36
2
the following is the domain of the function?
A.
B.
C.
D.
All positive real numbers.
All non-negative real numbers.
All real numbers except 6 and -6.
All positive numbers greater than or equal
to 6.
5
A.
B.
C.
A<B<C<D
D<C<B<A
C<D<A<B
D.
B<A<D<C
26. In the figure, the straight lines L1 and L2
intersect at (–1 , 2). Find the equation of L2.
28. The x- and y-intercepts of the straight line
representing
x-intercept
6
6
y-intercept
-8
8
C.
3
2
-2
D.
2
3
2
A.
B.
A.
B.
C.
x + 2y + 5 = 0
x – 2y + 5 = 0
2x + y – 5 = 0
D.
2x – y – 5 = 0
29. Which of the following may be the graph of
y  2 x 2  5x  4 ?
A.
27. Three straight lines, L1, L2, and L3, intersect
at point A:
B.
Given that their equations are:
L1 : k(x + 2) + y = 0 ,
L2 : 2x – y = 0 ,
C.
L3 : 2x + y  8 = 0 .
Find the value of k.
A.
–1
B.

C.
D.
0
1
x y 1
 
are
6 8 4
1
3
D.
6
33. The graph of y = f(x) is as follows:
30. The figure shows the graph of a quadratic
function y = f(x). Find f(x).
y
1
x
9
-1
A.
B.
C.
x2  4x + 3
3x2  4x + 1
3x2  12x + 9
D.
2x2  5x + 6
Which of the following graphs represents
y = 1 - f(x) ?
A
y
1
31. If f(x) = x2  kx  3k + 2 is divisible by
x  (k + 2), find the remainder when f(x) is
divided by kx + 6.
A.
-6
B.
-7
C.
-8
D.
-9
x
-1
B.
y
2
1
x
C.
32. The sum of the squares of three consecutive
positive even numbers is 200. Which of the
following cannot be one of the three
numbers?
y
x
-1
-2
A.
6
B.
C.
D.
8
10
12
D.
y
2
1
x
7
37. If 3x + p is a common factor of 3x2 + p and
x3 – 3x + q, find possible values of p and q.
34. The length of a rectangle is 4 cm longer
than twice its width. If its area is 70 cm2,
find the length.
A.
B.
C.
D.
A.
B.
C.
D.
5 cm
7 cm
9 cm
14 cm
p = 0, q = 0 or
p = 0, q = –3
p = 0, q = 3
p = 0, q = 2 or
p = –3, q = 2
p = –3, q = 0
38. Which of the following is(are) true
statement(s)?
35. The figure below shows the graph of the
function y = ax2 + bx  3. The graph passes
through two points (1 , 4) and (1 , 6).
Find a and b.
I.
A complex number can have its
conjugate equal to itself.
A quadratic equation with real
II.
III.
coefficients can have one imaginary root
and one real root.
0 is in both the natural and complex
number systems.
A. I only.
B. I, II only.
A.
B.
C.
D.
a = 3, b = 0
a = 2, b = 9
a = 2, b = 5
a = 3, b = 4
C. II, III only.
D. I, III only.
39. For ax2 + bx + c = 0 where a, b, and c are
real numbers, which of the descriptions of
its roots must be true for the given
discriminant range?
36. Find the maximum area of the rectangle
shown in the figure.
(x – 1) cm
A.
B.
C.
D.
10 cm
8 cm2
6 cm2
4 cm2
Discriminant
Roots
A.
<0
purely imaginary
B.
<0
complex
C.
=0
rational
D.
>0
integers
2
8
40. Consider all the parabolas represented by
the general form y = ax2 + bx + c, where a, b,
and c are real numbers. Which of the
following statement(s) is(are) true?
I. There is exactly one parabola that has its
vertex at (1,2) and intersects the x-axis at
(3,0).
II. There is exactly one parabola that passes
through (1,1), (2,2), and (4,4).
III. There is exactly one parabola that intersects
the x-axis at 3 and 6.
A. I only.
B. III only.
C. I and II only.
D. I, II, and III.
---------End of Paper---------
9
QUEEN’S COLLEGE
Half-yearly Examination, 2009-2010
Form 4 Mathematics Paper II
Answer Sheet
Question
Number
A
B
C
D
√
1
√
2
√
3
4
Question
Number
√
√
5
√
6
√
7
C
√
22
√
D
23
√
24
√
25
√
26
√
√
√
28
√
9
B
21
27
√
8
A
29
√
10
√
30
11
√
31
√
32
√
√
12
13
√
33
14
√
34
√
15
√
18
√
19
20
√
√
√
36
√
17
√
35
√
16
√
37
√
38
√
√
39
√
40
10
√