Premium Resources

PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: TUESDAY 13, SEPTEMBER 2016

COURSE CODE: MST124/C

Question 1

Which of the following is equivalent to  ?

SOLUTION

 

Expand

 

  

Answer: D

Question 2

Which of the following is equivalent to  ?

Question 3

Which of the following is equivalent to  ?

Question 4

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

Question 5

Which of the following could be the graph of the equation y = 2x-4 ?

Question 6

What is the gradient of the line with equation 5x − 3y − 3 = 0 ?

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 ?

Question 9

What is the domain of the function shown in the graph below?

Question 10

Which of the following transformations will change the graph of the function f(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 following is equivalent to the inequality  

Question 14

The right-angled triangle below (which is not drawn to scale) has an angle of size . The side opposite this angle has length 9.

What is the length, to one decimal place, of the side is labelled a in the diagram?

Question 15

The triangle below (which is not drawn to scale) has two sides of lengths 3 and 6, 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 7 and 8. The angle opposite the side of length 8 is  .

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

Question 17

How many values of θ in radians between satisfy sin θ = -25?

Question 18

Which of the following equations represents the circle with centre (-2, 5) and radius 3?

Question 19

What is the scalar product of −2i + 3j +4k and 5i − 3j + 3k, where i, j and k are the Cartesian unit vectors?

Question 20

 Which of the following is the derivative of ?

Question 21

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

?

Question 22

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

  

Question 27

Which of the following is equal to

Question 28

If P =  and Q =  what is 3P - 2Q?

Question 29

If T =  what is

Question 30

What is the determinant of the matrix  ?

Question 31

What is the sum of the arithmetic series

54 + 50 + 46 + . . . − 1574 ?

Question 32

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

 

Question 33

Which of the following is equal to the complex number ?

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, 8) and (6, 0) ?

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 (in metres per second) of the object at time t = 3 seconds?

Question 37

What is the derivative of  ?

Question 38

Which of the following is equal to ?

Question 39

What is  

Question 40

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

Question 41

The Taylor series about 0 for tan x is

  

and the Taylor series about 0 for ex is

 

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

Question 42

Which of the following complex numbers is Equal to  ?

(Purchase full paper by adding to cart)

Last updated: Sep 02, 2021 12:38 PM

add to cart ← Back