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Secondary 4

INSTRUCTIONS

Belilios Public School

announcement.

Yearly Examination, 2015-2016

MATHEMATICS Compulsory Part

3. All questions carry equal marks.

Time allowed: 1 hours

1. Read carefully the instructions on the Answer Sheet. After the announcement

of the start of the examination, you should insert the information required in the

spaces provided. No extra time will be given after the Time is up'

Maximum Marks: 45

Group: C___/ M_

2. 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.

6. No marks will be deducted for wrong answers.

4. 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.

5. You should mark only ONE answer for each question. If you mark more than

one answer, you will receive NO MARKS for that question.

37. The graph in the figure shows the linear relation between x and log, y. If

y = ab*, then b

Ģ -ião -in mi

39. If x, y> 0 and x, y #1, calculate

38. If a polynomial f (x) is divisible by x + 2, which of the following must be a factor

of f(3x + 1)?

log₁ √√x³ +log, √√y

log, √x-logy

40. If 3n+2 +2×3″ -3n-1 = 96,find n.

41. If f(2x)=8x³-4x+5, then f(k)=

k³ - 2k +5.

42. It is known that x varies directly as y² and inversely as z³. If y and z are both

decreased by 20%, then x is

A. decreased by 25%.

decreased by 40%.

C. increased by 25%.

increased by 40%.

43. For 0°≤0 ≤ 360°, how many roots does the equation 5sin 0+ sin 0-4 = 0

44. If x is acute angle and y is an obtuse angle such that x+y=180°, which of the

following are true?

sin x = sin y

COS X = cos y

III. sin = COS

A. I and II only

B. I and III only

C. II and III only

D. I, II and III

45. The greatest value of

END OF PAPER

Belilios Public School

Yearly Examination, 2015-2016

S4 MATHEMATICS Compulsory Part

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.

² × (5a²)-³=

16-(2a-3b)² =

A. (4-2a-3b)(4+2a+3b).

B. (4-2a-3b)(4+2a −3b).

C. (4-2a+3b)(4+2a+3b).

D. (4-2a+3b)(4+2a − 3b).

If 7p+3q=4p + q = 5, then q =

If m and n are non-zero numbers such that (3n-4m): (2m+n) = 5:6, then

If (3x+4)(x− a) = 3x² + b(x-4), then

If a is a root of the equation 6x² - 9x+1=0, then 6a² − 9a +5 =

Find the y-intercept of the graph of y = −(x+2)(x−5)+8.

a=-1, b = -1.

a = 1, b = 1.

a = -2, b = -2.

a = 2, b = 2.

The figure shows the graph of y = a(x−b)(x-c), where a, b and c are constants.

Which of the following is true?

A. a 0 and bc < 0

a> 0 and bc < 0

a < 0 and bc > 0

D. a>0 and bc > 0

Which of the following equations has no real roots?

(x + 1)²-1=0

D. (x+1)² = 0

y = a(x −b)(x − c)

10. If the length of the line segment joining the points (-1, 2) and (k +4, k), is 13,

D. -10 or 7.

If the two straight lines 2x + y + 3 = 0 and 3x + hy + 1= 0 intersect at (k, -1), then

12. The straight line 4x - 3y = 2 is perpendicular to the straight line

3x - 4y + 2 = 0.

3x + 4y + 2 = 0.

4x-3y + 2 = 0.

D. 4x + 3y + 2 = 0.

13. In the figure, the equation of the straight line L is

C. x + y + 5 = 0.

D. x-y + 5 = 0.

14. If ab 10°, then c =

B. (loga)(logb).

loga + logb.

15. log₂16×log2 √√32 =

16. If the selling price of 4 eggs is equal to the cost price of 5 eggs, the percentage

profit in selling an egg will be

17. When a polynomial P(x) is divided by 3x - 2, the quotient is x +3 and the

remainder is 7. Find P(x).

3x³ +7x² - 6x+7

3x³ - 2x² +9x+1

3x³ - 2x² +9x-13

D. 3x³ +5x² +9x+15

18. When 4x³-5x+7 is divided by 2x + 3, the remainder is

19. If f(x)= x(3+k) and ƒ(2) = 8, find k.

20. If the simultaneous equations

solution, then k =

[y=x² +7x+4

have only one set of real

21. Solve log(3x+1)=1+ log(2x - 5).

22. Solve 32* =

23. If (log₂ x)² – 3(log₂ x) +2=0, then x =

24. How many real roots does the equation x4 +5x²-36=0 have?

25. Suppose x varies inversely as √y. The table below shows some pairs of x and y.

Find the values of a and b.

A. a = 4, b = 4√√2

B. a = 4, b = 2√√2

C. a = 16, b = 4√2

D. a = 16, b = 2√2

27. If (a-b) varies inversely as

26. Suppose y is partly constant and partly varies directly as x². If y = 9 when x = 1

and y = 15 when x = 2, find y when x = = 3.

(a−b)x ab.

C. (a²-b²) x

D. (a²-b²) ab

The second quadrant

The third quadrant

D. The fourth quadrant

28. If costan 0 >0 and cos 0 <0, which quadrant does lie in?

A. The first quadrant

29. If sin 0

A. -√√k²-1.

and 0° <0<90°, then tan(0-90°) =

B. √1-k².

C. √√k² +1.

30. The figure shows the graph of y=2 sin

B. (270,-2).

C. (270,-1).

D. (540,-2)

The coordinates of the point P are

31. If 3+2i is a root of the quadratic equation x²+bx+c= 0, where b and c are

real numbers and i = √√−1, then c =

32. If the difference between two positive integers and their product are 24 and 112

respectively, then the sum of these two integers is

33. Let a b > 1. Which of the following may be the function represented by C?

A. y = a + b

35. If pq and

34. In the figure, L₁ // L₂ and OQ = 2OP. The equation of L₁ is ax+by+c=0.

Find the equation of L₂.

A. ax+by+2c=0

B. ax+by-2c=0

C. ax+2by+c=0

D. ax+2by-c=0

then (2² (2ª)=

36. The L.C.M. of 15a, 12a¹b³ and 9a²b is

D. 180a¹2b4.