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PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: TUESDAY 12, SEPTEMBER 2017

COURSE CODE: MST124/D

Question 1

Which of the following is equivalent to  ?

ANSWERS(Purchase full paper to get all the solutions):

 

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Answer: D

Question 2

Which of the following is equivalent to    where a> 0 and b > 0 ?

Question 3

If    , where    , which of the following is equal to x ?

Question 4

Which of the following is equivalent to ?

Question 5

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

Question 6

Consider the following simultaneous equations:

               

Which of the following values of x, together with an appropriate value of y, is a solution of these equations?

Question 7

Which of the following could be the graph of the equation y =  ?

Question 8

Which of the following is a factor of ?

Question 9

The graph of a function  is shown below.         

Which of the following statements is true?

Question 10

Which of the following transformations will change the graph of the function   to the graph of the function ?

Question 11  

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

Question 12

If , where a > 0 and b > 0, which of the following is equal to x ?

Question 13

Which of the following is equivalent to the inequality  

Question 14

The two shorter sides of the right-angled triangle shown below (which is not drawn to scale) have lengths 9 and 5, respectively

What is the size, in radians to one decimal place, of the angle marked θ, opposite the side of length 5 ?

Question 15

The triangle below (which is not drawn to scale) has two sides of lengths 4 and 7, and the angle between them is  

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

Question 16

The triangle below (which is not drawn to scale) has two sides of lengths 9 and 6. The angle opposite the side of length 9 is

What is the size, to the nearest degree, of the angle θ opposite the side of length 6?

Question 17

How many values of θ in radians between satisfy cos θ = ?

Question 18

What is the radius of the circle with equation ?

Question 19

What is the magnitude of the vector 2i − j ?

Question 20

What is the derivative of f ?

Question 21

Which of the following is the x-coordinate of a stationary point of ?

Question 22

What is the derivative of    ?

Question 23

What is the second derivative of   ?

Question 24

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

 

Question 25

What is the area between the graph of y =  and the x-axis, from x = 1 to x =5?

Question 26

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

Question 27

What, to one decimal place, is

Question 28

If P =  and Q =  what is 3P - 2Q?

Question 29

If W =   what is

Question 30

What is the inverse of the matrix   ?

Question 31

Which of the following is an alternative specification of the sequence (an ) given by the recurrence system

             ?

Question 32

What is the sum of the arithmetic series 58 + 55 + 52 + ... – 1145?

Question 33

Which of the following is equal to the complex number ?

Question 34

Which of the following is the Cartesian form of the complex number ?

Question 35

If  and  are the x-coordinates of the points where the line  intersects the parabola , what is |  −  | ?

Question 36

The velocity v (in metres per second) of an object in terms of the time t (in seconds) is given by the equation

 .

The displacement of the object at time t = 0 is 15 m. What is the displacement of the object (in metres) at time t =4?

Question 37

Which of the following is equal to ?

Question 38

The graph of the derivative of a function f is shown below

Which of the following could be the graph of f?

Question 39

What is the coefficient of x4  in the expansion of ?

Question 40

What is the coefficient of   in the Taylor series about x = 

Question 41

What is the linear Taylor polynomial about 2 for the function  ?

Question 42

What is the Cartesian form of the complex number

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