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PAPER TITLE: ESSENTIAL MATHEMATICS 1

EXAM DATE: TUESDAY 7, JUNE 2016

COUSRE CODE: MST124/D

Question 1

Which of the following is equivalent to ?

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

 

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Answer: D

Question 2

Which of the following is equivalent to  ?

Question 3

Which of the following is equivalent to  where a> 0 and b > 0 ?

Question 4

If   , which of the following is equal to x ?

Question 5

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

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

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

Question 8

Which of the following is a factor of  ?

Question 9

What is the image set of the 

 ?

Question 10

The graph of a function is shown below.

Which of the following statements is true?

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  radians. The side opposite this angle has length 6.

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

Question 15

The triangle below (which is not drawn to scale) has angles of sizes  and . The side opposite the angle of size  has length 10.

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

Question 16

The triangle below (which is not drawn to scale) has sides of lengths 5, 3 and 6.

What is the size, to the nearest degree, of the angle θ opposite the side of length 6 ?

Question 17

If Which of the following is equivalent to  ?

Question 18

What is the radius of the circle with equation  ?

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 3 that is  shown below?

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

What is the second derivative of   ?

Question 24

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

 

Question 25

What is the area between the graph of  and the x-axis, from x = 1 to x = 2?

Question 26

Which of the following is equal to   where x >  ? In the options below, c is an arbitrary constant.

Question 27

The velocity v (in m s−1) of an object at time t (in seconds) is given by

 v =  .

What is the change in the displacement (in metres) of the object from time t = 0 to t =2?

Question 28

If P =   Q =  and R =

which of the following matrices is defined?

Question 29

If S =   and T =  , what is 4S - 2T

Question 30

If R =  and S =   , what is RS

Question 2

Which of the following is equivalent to ?

Question 3

Which of the following is equivalent to   where a> 0 and b > 0 ?

Question 4

If    , which of the following is equal to x ?

Question 5

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

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

When the quadratic expression 3x²+18x-1 is written in the completed-square form , what is the value of s ?

Question 8

Which of the following is a factor of ?

Question 9

What is the image set of the

 ?

Question 10

The graph of a function is shown below.

Which of the following statements is true?

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  radians. The side opposite this angle has length 6.

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

Question 15

The triangle below (which is not drawn to scale) has angles of sizes  and . The side opposite the angle of size  has length 10.

What is the length, to one decimal place, of the side opposite the angle of size 760 ?

Question 16

The triangle below (which is not drawn to scale) has sides of lengths 5, 3 and 6.

What is the size, to the nearest degree, of the angle θ opposite the side of length 6 ?

Question 17

If Which of the following is equivalent to cotθcosecθ ?

Question 18

What is the radius of the circle with equation ?

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 3 that is  shown below?

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

What is the second derivative of  ?

Question 24

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

 

Question 25

What is the area between the graph of and the x-axis, from x = 1 to x = 2?

Question 26

Which of the following is equal to   where x >  ? In the options below, c is an arbitrary constant.

Question 27

The velocity v (in m s−1) of an object at time t (in seconds) is given by

 v =  .

What is the change in the displacement (in metres) of the object from time t = 0 to t =2?

Question 28

If P =  Q =  and R =

which of the following matrices is defined?

Question 29

If S =  and T =  , what is 4S - 2T

Question 30

If R =  and S =  , what is RS

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

 21 + 23 + 25 + ... + 641 ?

Question 33

Which of the following is equal to the complex number (6 − 8i)(2 + 3i) ?

Question 34

What is the principal argument of the complex number  ?

Question 35

What, to the nearest degree, is the angle between the vectors i − 5 j and 2 i + 4 j ?

Question 36

What is the derivative of  ?

Question 37

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

Question 38

The graph of a function f is shown below.

Which of the following graphs is the graph of the derivative of f?

Question 39

What is  

Question 40

What is the linear Taylor polynomial about  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 equivalent to   ?

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Last updated: Sep 02, 2021 12:41 PM

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