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PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: TUEDAY 2, JUNE 2015

COURSE CODE: MST124/B

Question 1

Which of the following is equivalent to x - 42x+ 2+3x(1-x) ?

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Answer: A

Question 2

Which of the following is equivalent to ?

Question 3

Which of the following is equivalent to ?

Question 4

If   , which of the following is equal to x ?

Question 5

What is the gradient of the straight line passing through the points ?

Question 6

Choose the option that is equivalent to the expression .

Question 7

What is the x-coordinate of the vertex of the parabola with equation ?

Question 8

What is the y-intercept of the line with the equation ?

Question 9

What is the rule of the inverse function of  ?

Question 10

Which one of the following expressions is equivalent to  ?

Question 11  

Which of the following is the solution set of the inequality  

Question 12

What is the image set of the function

  ?

Question 13

If f(x) = and g(x) =1+x2   , what is the rule of the function f 0 g ?

Question 14

The right-angled triangle below has an angle of 40 ⁰ and the hypotenuse  has length 12.

What is the length, to one decimal place, of the side opposite the 40⁰ angle?

Question 15

The triangle below has an angle of between two sides of lengths 5.7 and 9.1.

What is the length of the third side, to one decimal place?

Question 16

The triangle below has sides of lengths 4 and 7. The angle opposite the side of length 7 is 50?.

Question 17

How many values of θ in radians between −π and 2π satisfy sin θ = 0.5 ?

Question 18

What is the distance between the two points (-2, 4) and (3, -1) ?

Question 19

What angle does the vector −3i − 2j make with the positive x-direction, to the nearest degree?

Question 20

 Which of the following is the derivative of  ?

Question 21

Which of the following is the derivative of   ?

Question 22

Which of the following is the derivative of  ?

Question 23

Which of the following is the  derivative of  ?

Question 24

Which of the following is equal to  , where c is an arbitrary constant

Question 25

Which of the following is equal to  

Question 26

What is the area between the graph of  and the x-axis, from x = 0 to x = ?

Question 27

Which of the following is equal to  , ?

Question 28

If A =  and B =  , which option represents  2A – 3B

Question 29

If P =  and Q =  , Which option represent PQ?

Question 30

What  is the inverse of the matrix Q = ?

Question 31

Which of the following is true for the sequence (an) given by

 

Question 32

What is the sum of the geometric series

 ?

Question 33

Which of the following is equal to the complex number (7 − 4i)(3+2i) ?

Question 34

Which of the following is a solution of the equation ?

Question 35

Which of the following is the x-coordinate of a point where the line  intersects the parabola

Question 36

The displacement s (in metres) of an object in terms of time t (in seconds) is given by the expression

           

What is the acceleration of the object (in m ) at time t =5?

Question 37

The velocity v (in metres per second) of an object in terms of time t (in seconds) is given by the equation . The displacement of the object at time t = 0 is 20 m. What is its displacement in metres at time t = 2?

Question 38

Which of the following is equal to   where c is an arbitrary constant?

Question 39

What is  

Question 40

What is the linear Taylor polynomial about  for the function  ?

Question 41

What is the coefficient of  in the Taylor series about 0 for  ??

Question 42

Which of the following complex numbers is a solution of  ?

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Last updated: Sep 02, 2021 12:40 PM

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