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PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: FRIDAY 21, SEPTEMBER 2018

COURSE CODE: MST124/D

Question 1

Which of the following is equivalent to  ?

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

 

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Answer: E

Question 2

Which of the following is equivalent to

Question 3

Which of the following is equivalent to  where s > 0 and t > 0 ?

Question 4

If   , where t > , which of the following is equal to t?

Question 5

What is the gradient of the straight line passing through the points (-6, 7) and (1, 4) ?

Question 6

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

Question 7

When the quadratic expression is written in the completed-square form , what is the value of s ?

Question 8

What is the x-coordinate of the vertex of the parabola with equation y = -3x²- 15x - 12  ?

Question 9

Which of the following is the graph of a one-to-one function?

Question 10

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

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

Question 11  

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

Question 12

Which of the following is equivalent to   ?

Question 13

Which of the solution set of the inequality x²≤3x-2 ?  

Question 14

The right-angled triangle below (which is not drawn to scale) has hypotenuse of length 4 and another side of length 1. What is the size, in radians to three decimal places, of the angle θ between these two sides?

Question 15

The triangle below (which is not drawn to scale) has sides of lengths 3, 5 and 7

What is the size, to the nearest degree, of the angle θ opposite the side of length 5 ?

Question 16

The triangle below (which is not drawn to scale) has two sides of lengths 2 and 5. The angle opposite the side of length 5 is 37⁰ .

What is the size, to the nearest degree, of the angle θ opposite the side of length 2?

Question 17

Which of the following is equivalent to sin(2θ)cosec θ ?

Question 18

Which of the following equations represents the circle with centre (4, −1) and radius 2 ?

Question 19

What is the scalar product of −5i + 3j − 2k and i − 3j + 2k, where i, j and k are the Cartesian unit vectors?

Question 20

 What is the derivative of   ?

Question 21

What is the derivative of ?

Question 22

What is the derivative of  ?

Question 23

What is the second derivative of x²e^x  

Question 24

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

 

Question 25

What is the area between the x-axis and the graph of y = cos x, between x = 0 and x = ?.

Question 26

Which of the following, where c is an arbitrary constant, 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 =2?

Question 28

If P =  Q =   and R = 

which of the following expressions is defined?

Question 29

If A =   and B =   , what is AB ?

Question 30

What is the determinant of the matrix   ?

Question 31

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

-2 , 2 , 6 , 10?

Question 32

What is the sum of the geometric series

 ?

Question 33

Which of the following is equal to the complex number (6 + 5i)(1 − 4i) ?

Question 34

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

Question 35

What is the equation of the perpendicular bisector of the line segment joining the points (2, 6) and (10, 0) ?

Question 36

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

Question 37

What is the derivative of ?

Question 38

What is the derivative of    ?

Question 39

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

 

Question 40

What is  

Question 41

What is the coefficient of  in the Taylor series about x = 1 for the function   ?

Question 42

Which of the following complex numbers is a solution of   ?

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