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Practice JUPEB MATHEMATICS: SCI-J154 Past Questions Essay and Objectives

Practice JUPEB MATHEMATICS: SCI-J154 Past Questions Essay and Objectives. JOINT UNIVERSITIES PRELIMINARY EXAMINATIONS BOARD

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2015 EXAMINATIONS MATHEMATICS: SCI-J154

MULTIPLE CHOICE QUESTIONS

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1.  Find the non-zero negative value of x which satisfies the equation

x     1     0

1      x     1  = 0

0      1      x

     A.        2

B.       -2

C.         2

D. −   2

⎡2

3      3 ⎤

2. If

Z = ⎢4

⎢⎣1

1      0 ⎥,

4      0⎥⎦

find determinant of  Z.

A.  35

B.  45

C.  -35

D.   48

‘  

3. Compute   1 +   #      .

$%&

A.   )* −  $- 𝑖

    ‘   ‘

B.    4 −  $- 𝑖

C.     $0 −  $- 𝑖

‘    ‘

D.     4

4.  Find the centre and radius of the circle  8×2+8y2-24x-40y+18=0.

A.  (3/2, 5/2) and r = 3/2

B.  (-3/2, 5/2) and r = 5/2

C.  (3/2, -5/2) and r = 3/2

D.  (3/2,  5/2) and r = 5/2

5.  Find the equation of the tangent to the circle  2x 2  + 2 y 2  = 30 at the point (−3, 6) .

A.  x + y – 15=0

B.  x – 2y + 5=0

C.  x + 2y – 5=0

D.  x – 2y+15=0

6. Given the equations of the ellipse x2/2+y2=1. Find the equation of the directrices.

     A.    𝑥 = (0, ±1)

B.    𝑥 = (0, ±2)

C.    𝑥 = (0, ±3)

D.    𝑥 = (0,±4)

7. Find the gradient of the curve  𝑦 = 𝑥 # − 6𝑥 ‘ + 11𝑥 − 6  at the point (1, 0)

A.  -1

B.   -2

C.    1

D.    2

8. Given sets 𝐴 =   𝑎, 𝑏, 1, 3    and  𝐵 =   𝑎, 2, 4 , find 𝐴 ∪ 𝐵.

      A.   ∅

B.     𝑎, 𝑏, 1,2,3,4

C.    𝑎, 𝑏, 1,3

D.   𝑏, 1,2,3,4

9.  Let P be the set of prime factors of 42 and Q be the set of prime factors of 45. Find 𝑃 ∩ 𝑄.

      A.   2

B.   3

C.   7

D.   5

10.  A polynomial 2𝑥 # + 𝑎𝑥 ‘ + 𝑏𝑥 − 1  has a factor (𝑥 − 1) and the remainder when it is divided by  (𝑥 − 2) is −4. Find 𝑎 + 𝑏.

A.  −1

B.   1

C.  −2

D.    2

$K

11. Solve the equation log# 𝑥 + logJ 3 =  #

       A.       3  ,  9

B.     27 ,    3

C.    10 ,  9

D.     27 , L  3

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