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PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: WEDNESDAY 17, SEPTEMBER 2014

COURSE CODE: MST124/D

Question 1

Which of the following is equivalent to

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Answer: D

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

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

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 is a factor of ?

Question 8

What is the x-coordinate of the vertex of the parabola with equation y=x² -7x+10?

Question 9

What is the rule of the inverse function of  ?

Question 10

If   , which of the following is equal to x ?

Question 11  

The graph of a function f, and a second graph, are shown below.

Which of the following could be the equation of the second graph?

Question 12

What is the image set of the function

  ?

Question 13

The graph of a function f(x) is shown below.

Which one of the following statements is true?

Question 14

In the right-angled triangle below (which is not drawn to scale), the two shorter sides have lengths 10 and 7.

What is the size, to the nearest degree, of the angle θ opposite the side of length 7?

Question 15

The triangle below(which is not drawn to scale) has an angle of between two sides of lengths 5.7 and 9.1.

What is the area of the triangle, to one decimal place?

Question 16

The triangle below (which is not drawn to scale) has two angles of sizes  and . The side opposite the angle of size  has length 9.2.

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

Question 17

Suppose that Which of the following is equivalent to ?

Question 18

What is the radius of the circle with equation ?

Question 19

What angle does the vector −2i +3j 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 h(x) =2x2sinx ?

Question 23

Which of the following is the  derivative of p(t) =(t2-6)8?

Question 24

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

Question 25

What is the area between the graph of  and the x-axis, from x = 3 to x = ?

Question 26

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

Question 27

Given that the areas of some regions on the graph of a function f are as marked below, what is the value of  

Question 28

If P =  and Q =  ,What is PQ?

Question 29

What  is the inverse of the matrix  ?

Question 30

If T =  what is

Question 31

Which of the following is a closed form for arithmetic sequence () with first four terms

?

Question 32

What is the sum of the arithmetic series

46 + 49 + 52 + ... + 775 ?

Question 33

Which of the following is equal to the complex number (2+i)(3 − 5i) ?

Question 34

If z =  and w =  which of the following is equal to z/w?

Question 35

What is the angle, to the nearest degree, between the vectors a = 3i − j and b = i + 5j ?

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 velocity of the object  at time t =15?

Question 37

Which of the following is the derivative of f(u) =

Question 38

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

Question 39

What is the coefficient of x6 in the binomial expansion of  ?

Question 41

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

Question 42

What is the Cartesian form of the complex number  ?

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