Premium Resources

PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: FRIDAY 7, SEPTEMBER 2015

COURSE CODE: MST124/F

Question 1

Which of the following is equivalent to ?

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

 

Expand

 

  

Answer: E

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 y ?

Question 5

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

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 y-coordinate of the vertex of the parabola with equation ?

Question 9

What is the rule of the inverse function of   ?

Question 10

Which one of the following expressions is equivalent to 2z + 4 ln z ?

Question 11  

Which of the following is the solution set of the inequality    

Question 12

What is the image set of the function

   ?

Question 13

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

Answer: C

Question 14

A right-angled triangle has a hypotenuse of length 10 and another side of length 7. What is the size, to the nearest degree, of the angle between these two sides?

Question 15

A triangle has sides of lengths 3.5, 5.7 and 8.2. What is the size, to the nearest degree, of the angle opposite the side of length 8.2?

Question 16

A triangle has an angle of and another angle of  . The side opposite the angle is of length 6.4. What is the length, to 1 decimal place, of the side opposite the  angle?

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 anti-clockwise 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  ?

Question 23

Which of the following is the  derivative of   ?

Question 24

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

Question 25

Which of the following is the area between the graph of  and the x-axis, from x = 0 to x = ?

Question 26

Which of the following is equal to  

Question 27

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

Question 28

If P =    and Q =   , which option represents  3P – 2Q

Question 29

If A =  and B =  , Which of the following represent AB?

Question 30

What of the following is the inverse of the matrix ?

Question 31

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

?

Question 32

What is the sum of the geometric series

 ?

Question 33

Which of the following is equal to the complex number (11+3i)(6 − 4i) ?

Question 34

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

Question 35

Which of the following is the x-coordinate of a point where the line   intersects the circle 

Question 36

The displacement s (in metres) of an object in terms of time t (in seconds) is given by the expression

           

At which one of the following times t is the acceleration of the object (in m s⁻² ) equal to zero?

Question 37

Which of the following is the  derivative of  ?

Question 38

Which of the following is the value of

Question 39

What is the coefficient of  in the expansion of ?

Question 40

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

Question 41

The Taylor series about 0 for sin 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 a solution of  ?

(Purchase full paper by adding to cart)

Last updated: Sep 02, 2021 12:40 PM

add to cart ← Back