Mathematics - ENS BAMBILI | COMPETITIVE ENTRANCE EXAMINATION INTO THE FIRST YEAR OF THE FIRST CYCLE OF ENS BAMBILI

SAMPLE EXTRACT PAPER 2016

COMPETITIVE ENTRANCE EXAMINATION INTO FIRST YEAR OF THE FIRST CYCLE

ACADEMIC YEAR: 2015/2016

DEPARTMENT: MATHEMATICS

Instructions: Answer all the questions in section A and section B by selecting the most appropriate option that answers each MCQ. Write the letter (A, B, C or D) that corresponds to the most correct option in the Answer Booklet provided. Make sure you insert the question paper inside the answer Booklet before you leave the Examination Hall

Time allowed: 3 Hours.

SECTION 1: MAJOR PAPER: MATHEMATICS

Answer all questions

1.     What is the complete solution to equation |3 – 6x| =15?

A)  x = 2, x = 3   B) x = - 2, x = 3   C) x = 2, x = 13  D) x = -2, x= -3

2.     What is the possible values of x in |12 – 4x| = 2? 

A) x = , or x =   B) <, x =    C) > x >     D) , or x = 

3.     What is the solution to the system of equations shown below?

A)  (0, 4, 4,)   B) (1, 4, 10/3)    C) no solution D) infinitely many solutions

4.     What is the solution to the following system of equation?

A)  (5, - 2)         B) (- 2, 5)          C) ( -1, -2)      D) (-2, -1)

5.     The expression  equals to: A)     B)          C)      D) - 

6.     If 2x³+ x² – 5x – 1  leaves a remainder 3 when divided by (2x + 1), then  is:  

A) -7                B) -5           C) 5               D) -1

7.     The cubic equation 2x³ + x² – 22X + 24 = 0 has roots a, β, and . The value of  +  is:  A) 11/12         B) -11/12            C) 1/12        D) -1/2

8.     If cosA = 3/5 and A is acute, then sin2A is equal to:

A)  6/25              B) 8/25      C) 12/25       D) 24/25

9.     The tangent to the circle, C, with equation x² + y² + 4x – 10y – 5 = 0 at the point (3, 2) has equation:  

A) 3x + 5y – 9 = 0    B) 5x – 3y – 9 = 0    C) 5x – 3y – 19 = 0    D) 3x + 5y + 19 = 0

10.                        

11.                        (-2x² + 6x + 1) - 2(4x² – 3x + 1) = 

A) 6x² – 1     B) -10x² – 1      C) 6x² + 12x – 1    D) -10x² + 12x – 1

12.                        Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?   A) 33     B) 35   C) 37     D) 39

13.                        Lucas wants to create several different 7-character screen names. He wants to use arrangements of the first three letters of his first name (Luc, followed by arrangements of 4 digits in 1984, the year of his birth). How many different screen names can he create in this way?      A) 72             B) 144          C) 288          D) 576 

14.                        Ndong and Ngong are among 10 students who have applied for a trip to Yaounde. Two students from the group will be selected at random for the trip. What is the probability that Ndong and Ngong will be the 2 studentsselscted?  

A) 5/12         B) 7/20         C) 5/8          D) 1/5

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NUMBER OF PAGES: 80

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