FURTHER MATHS MOCK EXAM QUESTIONS FOR SS3
SS3 FURTHER MATHEMATICS MOCK EXAM QUESTIONS – EDUDELIGHT.COM
MOCK EXAMINATION
Examination malpractices may lead to a repeat of the subject or suspensions don’t be involved.
SUBJECT: FURTHER MATHEMATICS TIME ALLOWED: 3HRS CLASS: S.S 3
OBJECTIVES
1. Which of the following sets is equivalent to (PUQ)∩(PUQ)? A. P B.P∩Q C. PUQ D.
2. Simplify: A. –Tan
B. -cos
C. tan
D. cos
.
3. Solve the inequality x2 – 2x 3. A. -1
x
3 B. x
3 or
-1 C. x
3 or x
-1 D. -1
x
3
4. Given that sin x = –√3/2 and cos x > 0, find the value of x. A. 3000 B. 2400 C. 1200 D. 600
6. Evaluate: log10 (1/3 + 1/4) + 2 log102 + log10(3/7). A. -3 B. 0 C. 5/6 D. 1
7. Simplify: x3n+1
X2n+5/2 √x2n-3 A. 0 B. ½ C. 1 D. 10
8. If (x + 1) is a factor of the polynomial x3 + px2 + x + 6 = 0, Find the value of p. A. -8 B. -4 C. 4 D. 8
9. The Equation of a circle is 3x2 + 3y2 + 24x – 12y = 15, Find it radius. A. -8 B. -2 C. 2 D. 8
10. The polynomial is defined by f(x+1) = x3 + 3x2 – 4x + 2,Find f (2). A. -8 B. -2 C. 2 D. 8
11. If the midpoint of the line joining (1-k, -4) and (2, k+1) is (-k, k), Find the value of k. A. -4 B. -3 C. -2 D. -1
12. Evaluate ∫3-2 (3x2 – 2x -12)dx A. -30 B. -18 C. -6 D. 6
13. If y =x3 – x2 –x + 6, find the values of x at the turning points. A. ½, -3 B. 1/3, -1/2 C. 1, -1/3 d. 1, 1/3
14. Given that nPr = 90 and nCr = 15, find the value of r. A. 2 B. 3 C. 5 D. 6
15. Which one of the following options is not a measure of central tendency? A. Mode B. Variance C. Mean D. Median
16. A fair die is tossed twice. Find the probability of obtaining a 3 and a 5. A. 5/12 B. 1/18
C. 2/9 D. 1/36
17. Find the values of x at the point of intersection of the curve y = X2 + 2x -3 and the line y +x=1. A. (1, -2) B. (0, 4) C. (2, -3) D. (1, -4)
18. Find the constant term in the binomial expression of (2x – 3/x)8. A. 90720 B. 1296 C. 1120 D. 672
19. Find the values of x at the turning points of the curve y =x3 – 2x2+ x + 1 A. 1 and 1/3 B. -1 and 3 C. 0 and 1/3 D. -1 and 1/3
20. If ƒ:x=1 +2x and g:x=-,where x
R,and x ≠ -1,find g (f(2)) A. -5/3 B. -1/6 C. 1/6 D. 5/3
21. If r = 2i + j, m = 2i – j and n = -12i + 3j, find r + 2m + 1/2n A. 3/2j B. 1/2j C. 1/3j D. -1/2j
22. Find the limit of the function A. -6 B. -3 C. 3 D. 6
23. Evaluate log4 0.3 – log4 0.48 + log4 0.05 A. -8 B. -5/2 C. -2/5 D. -1/8.
24. In triangle PQR.PQ =3i – 4j and PR =- 2i – 7j. Find QR. A. -5i + 11j B. -5i + 3j C. -5i – 3j D. -5i – 11j
25. If V = 4 µr3 and S = 8 µr2, find dv/ds. A. 1/4r B. 1/2r C. 2/3r D. 3/4r
26. If x = Y =
and z =
, find 2x – 3y +z A.
B.
C.
D.
27. Simplify 8n × 22n ÷ 43n. A. 2-n B. 21-n C. 2n D. 2n+1
28. Simplify ( – 1)3 A. 6
– 9 B. 2
– 10 C. 2
– 9 D. 6
– 10
29. Given that the domain of f(x) = x2 + 1 is {-2, -1, 0, 1, 2}. A. {3, 0, -1} B. {5, 2, 1} C. {3, 1, 5} D. {2, 0, -1}
30. If = 3r2 – 1 and A = 2 when r = 1, find A when r = 2. A. -10 B. -8 C. 8 D.10.
31. calculate the angle between a = -4i + 2j and b = I – 3j. A. 450 B. 600 C. 1350 D. 3150
32. The constant term in the expansion of (x-6 is A. -20 B. 15 C. 60 D 120
33. If f(x) = , x ≠ 1, find f ( –
) A. -22 B. -11 C. 11 D. 22
34. Express (14N, 2400 ) as a column vector. A. B.
C.
D.
35. If = 33, find the value of x. A. 2 B. 3 C. 4 D. 5 E. 6
36. What force will produce a velocity of 1.6ms-1 in 8s on a body of mass 0.4kg? A. 0.8N B. 0.06N C. 0.06N D. 0.8N E. 0.1N
37. Give that =
+
A. A =
, B =
B. A =
, B =
C. A =
, B =2 D. A =
, B =
38. A matrix is said to be singular if the determinant is. A. Negative B. One C. Positive D. Undefined
39. Evaluate log, 512 = 3. A. 2 B. 3 C. 8 D. 16
40. Find h-1 (-) if h (x) =
, x ≠ 5 A. -20 B.
C.
D.
SS3 FURTHER MATH MOCK EXAM QUESTIONS – EDUDELIGHT.COM
THEORY: Answer any ten question from this part.
1. Find the centre and radius of the circle. 3x2 + 3y2 + 4x – 5y +2 = 0
2. if xC3= , Find x
xP2
3. Write out the equation of the following ellipse in its canonical or standard form.
2x2 + 5y2 + 8x – 10y 3 = 0
4. A binary operation is defined on the set R of real numbers by x y = 2x + 2y – 1
2
x,y €R. find the neutral element in R under the operation.
5. If U = {1,2,3,4,5,6,7,8,9,10} and A= {2, 5, 8} while B = {even numbers}, find (i) A ∩ B (ii) A U B (iii) A ∩ B1 (iv) A1∩ B
6. Vectors p, q and r are given by p = q =
and r =
Find (i) 4p – q + 5r (ii) Position vectors of p, q and r
7. A binary operation is defined on the set R, of real numbers by
x * y = x2 where x, y €R
x + y (a)Evaluate (2 * 3) * 5 (b)if (x +1) * (x +2) = , Find the value of x
8. Using the binomial theorem, obtain the expansion of (1 + 3x)6 + (1 – 3x)6
9. Given that tan 2A= 2 tan A
1 – tan2 A. Evaluate tan 150, leaving your answers in surd form
10. (i) In a hotel, the breakfast menu is a choice between yam (Y) or plantain (P) or both. The following venn diagram shows the choices made by guests of the Hotel.
P Y
(2x + 1) x (x – 2)2
(a) Find the value of x.
(b) Number of guest who choose only one of yam and plantain.
11. (i) Prove that the equation of a parabola is given by y2
(ii) Write the equation of parabola in its canonical or standard form. Hence, y2 – 6y – 2x + 19 = 0
12. The position vectors of two points x and y are x= -2i + 5j and y = i -7j
Find:
(i) 3x + 2y (ii) y – 2x
(iii) the angle between x and y
(iv) the unit vector in the direction of x + y
13. (a) A committee of 4 people is to be chosen from 5 married couple’s. find the number of ways the committee can be chosen if:
(i) everyone is equally eligible
(ii) the committee should include at least one woman.
(b) Find the number of ways of arranging N people in a straight line, if two particular people must always be separated.
SS3 FURTHER MATHEMATICS MOCK EXAM QUESTIONS – EDUDELIGHT.COM
Answer