中四 數學試卷 (F4 Maths Past Paper)
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內容節錄：
Secondary 4
INSTRUCTIONS
Belilios Public School
Yearly Examination, 2017-2018
MATHEMATICS Compulsory Part
1. Write your Name, Class, Group and Class Number in the spaces provided.
Read carefully the instructions on the Answer Sheet. You should insert the
information required in the spaces provided. No extra time will be given after the
'Time is up' announcement.
4. All questions carry equal marks.
3. When told to open this book, you should check that all the questions are there.
Look for the words 'END OF PAPER' after the last question.
1718-YE-S4-MATH-CP 2
Time Allowed: 1 hours
Maximum Marks: 45
Class Number:
5. ANSWER ALL QUESTIONS. You are advised to use an HB pencil to mark all
the answers on the Answer Sheet, so that wrong marks can be completely erased
with a clean rubber. You must mark the answers clearly; otherwise you will lose
marks if the answers cannot be captured.
7. No marks will be deducted for wrong answers.
6. You should mark only ONE answer for each question. If you mark more than
one answer, you will receive NO MARKS for that question.
35. The figure shows the graphs of y=a*, y=b*, y=c* and y=d*, where a,
b, c and d are positive constants. Which of the following is true?
x(x-1) (x-1)(x+1) x(x+1)
x(x-1)(x+1)
x(x − 1)(x+1)
1718-YE-S4-MATH-CP 2
37. The graph in the figure shows the linear relation between x and log, y.
If y = ab*, then b =
38. If f(x-1) =
x² + 2x - 1
x² - 2x - 1
39. If y varies directly as x and inversely as
is a constant.
D. I, II and III
When x remains unchanged and z is halved, y is halved.
I and III only
II and III only
40. Suppose z varies directly as x² and x varies inversely as y. If y is increased by 15%,
find the percentage change in z, correct to 3 significant figures.
41. Ifx+y=180°, which of the following must be true?
I. sin x = sin y
tan (180° — x) = tan (180° − y)
D. I, II and III
I and II only
I and III only
II and III only
1718-YE-S4-MATH-CP 2
III. sin² x+cos² y = 1
√z, which of the following must be true?
42. Find the minimum value of
43. For 0°
A. 0° or 120°
60° or 300°
0°, 120°, 240° or 360°
D. 0°, 120°, 300° or 360°
45. The figure shows the graph of a periodic function y = f(x). Which of the following
must be true?
(2+ cos x)(2-cos.x)
I. The period of y = f(x) is 360°.
II. The maximum value of y is 1.
III. There are 4 solutions for the
equation 2f(x)+3=0 for
0° ≤x≤360°.
I and II only
II and III only
D. I, II and III
1718-YE-S4-MATH-CP 2
END OF PAPER
for 0°
There are 30 questions in Section A and 15 questions in Section B.
The diagrams in this paper are not necessarily drawn to scale.
Choose the best answer for each question.
36—(2m-5n)²
A. (6−2m −5n)(6+2m+5n)
B. (6−2m −5n)(6+2m −5n)
C. (6−2m+5n)(6+2m+5n)
(6-2m +5n)(6+2m −5n)
If p and q are constants such that (x−1)² + px = (x+4)(x−q)+21, then p
The cost of pepper X is $1.6/g. If 5 g of pepper X is mixed with 4 g of pepper Y so
that the cost of the mixture is $2/g, find the cost of pepper Y.
1718-YE-S4-MATH-CP 2
5. If rs 3:4, find
0.01491625=
(correct to 3 significant figures)
0.014 (correct to 4 decimal places)
0.01492 (correct to 5 significant figures)
0.014916 (correct to 6 decimal places)
Which of the follow statements about a regular 20-sided polygon are true?
The size of each exterior angle is 18°.
The size of each interior angle is 162°.
The number of folds of rotational symmetry is 10.
I and II only
I and III only
II and III only
D. I, II and III
If x+y+2=x² −9x-5y = 1, then y=
Solve the equation (x + 1)x = 3(x + 1).
x = -1 or 3
D. x = 1 or 3
1718-YE-S4-MATH-CP 2
10. In the figure, the graph of y = k(x − 1)(x − 3), where k is a constant, cuts the x-axis
at P and Q, and the y-axis at R. If the area of APQR is 6 square units, find the
value of k.
11. If a and ß are the roots of the quadratic equation 3x²–5x-9=0, then
The graph does not pass through the origin.
II. The y-intercept of the graph is negative.
The graph has two x-intercepts.
I and II only
I and III only
II and III only
D. I, II and III
12. Which of the following about the graph of y=kx2² -5x-k (where k‡0) must
f(x) = 3x² - 2x + 4, then f(x + 1)-f(x - 1) =
6x² - 4x + 14.
1718-YE-S4-MATH-CP 2
y=k(x-1)(x-3)
14. The equation of the quadratic graph shown in the figure is
y=(x-3)(x+1).
y = (x+3)(x-1).
y = 2(x − 3)(x+1).
D. y = 2(x+3)(x-1).
15. If the two straight lines L₁:3x-y+9=0 and L₂:ax-9y+5=0 are
perpendicular to each other, find the value of a.
16. In the figure, the straight line L₁: 2x-y-1=0 and L₂: 2x+y+1=0 intersect
the y-axis at the same point. . Find the area of the region bounded by L1, L2 and
the x-axis.
17. If both b and c are positive but a is negative, which of the following represents the
graph of ax + by = c?
1718-YE-S4-MATH-CP 2
y L₁:2x-y-1=0
L₂: 2x+y+1=0
18. Let f(x) = x³ + ax² + 12x - 7. When f(x) is divided by x - 1, the remainder is 3.
When f(x) is divided by x + 1, the remainder is
19. If a polynomial f(x) is divisible by x+1, then f(x+1) must be divisible by
20. Which of the following has the greatest value?
If a and b are positive numbers, then
22. If 10 = 2 and 10²y = 16, then
1718-YE-S4-MATH-CP 2
√√√a³
23. The two curves in the figure represent the graphs of y=log, x and y = log₁ x.
They cut the x-axis at the same point P.
Which of the following is true?
The equation of C₁ is y=log, x
The equation of C₁ is y = log₁ x
The equation of C₁ is y=log, x
D. The equation of C₁ is y = log₁ x
24. Find the minimum value of k such that the simultaneous equations
have real solutions.
25. Solve 16* -3(4*) -4 = 0.
C. x = 0 or 1
26. Solve log₂ (x − 1) +
C. x=3 or 5
= −3 or −5
1718-YE-S4-MATH-CP 2
log₂ (x - 1)
and the coordinates of P is (1, 0).
and the coordinates of P is (1, 0).
and the coordinates of P is (10, 0).
and the coordinates of P is (10, 0).
[y −5x = k
27. If a varies directly as √ and inversely as c², then which of the following must
be a constant?
D. a√√bc²
28. It is given that z varies jointly as the square of x and the positive square root of y.
If z=7 when x=1 and y = 36, find the value ofz when x=3 and y= 144 .
29. If sin cos 0 <0, in which quadrant does lie?
Quadrant I or III
Quadrant II or IV
Quadrant II or III
Quadrant III or IV
30. sin(360° – 0) -
cos(90° + 0)
1718-YE-S4-MATH-CP 2
31. Let z=(a−4)i⁹ −(a+7)i¹⁰, where a is a real number. If z is an imaginary
number, then a =
32. The figure shows the graph of y=(ax-h)² +k, where a, h and k are constants.
Which of the following must be true?
I and II only
II and III only
33. The figure shows the straight lines L₁: ax+by-c=0 and L₂: bx-ay-d = 0.
Given that I and L₂ cut the y-axis at the same point. Which of the following
must be true?
L and L are perpendicular to each other.
D. I, II and III
I and II only
I and III only
II and III only
1718-YE-S4-MATH-CP 2
y = (ax-h)² + k
34. Find the L.C.M. of 2x²-x−3, 2x² −7x+6 and 2x²+3x-9.
(2x − 3)(x − 2)(x+1)(x+3)
D. (x-3)(x-1)(x+2)(2x+3)