BASIC MATHEMATICS

MJ

QUESTION ONE

  1. (i) Compute |x-2| for x= -3, x= 0 and x= 4. (3mks)

(ii)            The area of a square with sides of length x is x2. What is the area if the sides are doubled?                                                          (2mks)

(iii)           If ab2= 2, compute a3b6 + a-1b-2.                                  (2mks)

 

  1. (i) How much money should you have deposited in the bank 5 years ago in order to have $1000 today, given that the interest rate has been 8% per year over this period?                                     (4mks)

(ii)            Which of the following sets are empty?

  1. A = {x : x + 8 = 8, xƐɌ}
  2. B = {x : x = √6, xƐZ}
  3. C = {x : x + 9 = -14, xƐN}
  4. D = {x : 6x = -5, xƐQ}                         (4mks)
  5. Rationalize the denominator and simplify:
  • 2 / √3√8
  • (√54 – √24) / √6
  • [x(√x + 1)] / √x                         (3mks)

 

  1. Solve the equations:
  • 6P – ½(2P – 3) = 3(1 – P) – 7/6(P + 2)             (3mks)
  • X + 2 –  __8__    =   _2_                                                                        (3mks)

X – 2      x2 – 2x           x

 

  1. Given the arithmetic sequence:

4, 11, 18…….

Find:

  1. The common difference.
  2. The 6th term                                     (4mks)

QUESTION TWO

  1. List the members of the following sets.
    1. {x/x is a real number such that x2 = 1}
    2. {x/x is the square of an integer and x < 100}

 

  1. Expand and simplify;

(2pq – 3p2) (p + 2q) – (q2 – 2pq) (2p – q)                                      (6mks)

 

  1. If ab2 = 2 compute the following:
  2. a2b4                                                                                     (2mks)
  3. a-4b-8                                                                                     (2mks)
  • a3b6 + a-1b-2                                                                         (2mks)

           

QUESTION THREE

  1. Differentiate the following functions with respect to x. (6mks)
  • Y = x4
  • f(x) = 5x3 + 2x2 + x + 7
  1. A fridge manufacturer produces and sells all the fridges he produces. The total cost of producing x fridges is 300x + 200. The price demand function is estimated as 500 – 2x.

Determine:

  1. The revenue function of the manufacturer. (3mks)
  2. The profit function.                                                 (3mks)
  • The marginal profit function.                                     (3mks)

QUESTION FOUR

  1. Solve and graph the following
  • 7 – 2x > -11 xCR                                                             (3mks)
  • -5x + 4 < 2x – 10 xCZ                                                     (3mks)

 

  1. Solve the equations:
  2. 8x – 6 = 5x + 9                                                 (3mks)
  3. 3x + 34 – 8x = 11 – 9x – 13                                                 (3mks)

 

  1. Solve the equations
  • 2x = 4y = -2
  • 5x + 4y = 33                                     (3mks)

 

QUESTION FIVE

  1. A two digit number is such that its value equals four times the sum of its digits. If 27 is added to the number, the result is equal to the value of the number obtained when the digits are interchanged. What is the number?                                                                         (6mks)
  2. In a survey of 260 college students, the following data is obtained.

64 students – Maths

94 students – Computer Science

58 students – Business Studies

28 students – both Maths and Business English

26 students – both Maths and Computer

22 students – both Computer Science and Business English

 

  1. How many students in the survey did not take any of the three courses?                                                                         (5mks)
  2. How many students took computer science only?(4mks)
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