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PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: TUESDAY 5, JUNE 2018

COURSE CODE: MST124/B

Question 1

Which of the following is equivalent to  ?

ANSWERS(Purchase full paper to get the solutios):

 

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Answer: E

Question 2

Which of the following is equivalent to

Question 3

If  , which of the following is equal to x ?

Question 4

Which of the following is equivalent to  ?

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

What is the image set of the function whose graph is shown below?

Question 10

Which of the following transformations will change the graph of the function f(x) = sin x to the graph of the function  ?

Question 11  

What is the rule of the inverse function of   ?

Question 12

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

Question 13

Which of the solution set of the inequality  

Question 14

The two shorter sides of the right-angled triangle shown below (which is not drawn to scale) have lengths 3 and 6, respectively.

What is the size, in radians to two decimal places, of the angle marked θ, opposite the side of length 6 ?

Question 15

The triangle below (which is not drawn to scale) has two sides of lengths 3 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 3 and 5. The angle opposite the side of length 5 is

What is the size, to the nearest degree, of the angle θ opposite the side of length 3?

Question 17

How many values of θ in radians between - satisfy tan θ =   ?

Question 18

Which of the following equations represents the circle with centre (5, 1) and radius 4?

Question 19

Which of the following, where i and j are the Cartesian unit vectors, is the component form of the vector v with magnitude 2 that makes an angle of π/3 with the negative direction of the x-axis, as shown below?

Question 20

 What is the derivative of ?

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

The graph of a function f is shown below, with the areas of the shaded regions marked.

What is the value of 

Question 26

Which of the following is equal to   

Question 27

The velocity v (in m/s) of an object at time t (in seconds) is given by

.  

What is the change in the displacement of the object (in metres) from t = 1 to t =5?

Question 28

If P =  and Q =  what is 2P + 4Q?

Question 29

If T =  what is

Question 30

What is the determinant of the matrix   ?

Question 31

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

Question 32

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

                 ?

Question 33

Which of the following is equal to the complex number ?

Question 34

What is the principal argument of the complex number  ?

Question 35

What is the angle, to the nearest degree, between the vectors 5i − j and 3i + 2j ?

Question 36

A function f has derivative given by  What are the x-coordinates of the stationary points of f, and their natures ?

Question 37

What is the derivative of ?

Question 38

What is ?

Question 39

What is

Question 40

What is the linear Taylor polynomial about  for cos x

Question 41

The Taylor series about 0 for tan x is

 

and the Taylor series about 0 for  is

 

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

Question 42

Which of the following complex numbers is Equal to   ?

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Last updated: Sep 02, 2021 01:09 PM

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