MATHS EXAMINATION

CHILDREN & YOUTH DEVELOPMENT INITIATIVE CENTRE (CYDIC)

PRE-NATIONAL EXAMINATION

BASIC MATHEMATICS

Time: 2:30 HRS                                                                  Tues. 13^th Aug 2017

Instructions:

(i)          This paper consists of  section:  A and B.

(ii)        Attempt ALL question in sections A and any FOUR (4) questions from section B

(iii)      All necessary working and answers for question done must be shown clearly.

(iv)      Four figure mathematical tables may be used unless otherwise stated

(v)        Cellular phones are not allowed in the examination room.

SECTION A (60 Marks)

1.      a). Evaluate without using table and express the answer as a fraction in its simplest form

b). Write 0.00607049 correct to

i.                    4 significant figures

ii.                  3 decimal places.

c). Write in to fraction

     2.  a) Rationalize the denominator

          b). Solve the equation log₄5x – log₄ (x + 2) – log₄3 = 0.

     3. a) Find the value of p and q if 9x² – 12x + p = (3x – q)²

         b) A shopkeeper sold 500 books. Some cost Shs.5000 and some costs Shs. 8000. The cash received for the more expensive books was Sh. 100,000 more than for the  cheaper books. Find the number of each kind of books which were sold

    4. Write the y – intercept and the equation of a linear function f(x) in which f(1) = 3         with the slope the same as the slope of the line whose equation is 3x – 4y = 12

    5. The interior angle of a regular polygon is twice as much as the exterior angle.Find

             a). The number of sides of the polygon.

             b). The sum of all interior angles.

            c). Write the name of regular polygon

    6. a) make r the subject of the formula

         b) IfA and B are any two disjoint sets, show the region represented byon a       venndiagram.

    7. a). The ratio of men:women:children living in Madalle village is 6:7:3 if there are 42,000          women, find how many

            i. Children live in Madalle village

            ii. People altogether live in Madalle village.

        b) 84 people can complete a certain work for 24 days. How many more people are       needed in order to complete that work for 21 days.

   8. a) If  , evaluate  A is an acute angle.

        b). A ladder reaches the top of a wall 18m high when the other end on the ground is 8m           from the wall. Find the length of the ladder.

  9. a). A function is defined as by f(x) = x² – 2. Find

            i. The inverse f ^{– 1} (x) of this function.

            ii. The value of f ^{– 1} (-2)

            iii. The domain of f ^{– 1} (x)

        b). Find the value of  (64) ^{– 2/3}+

10. a). Matrix A=   B=. Compute A² + 2AB.

       b). in the figure below find the value of angle x⁰, y⁰, and z⁰

SECTION B (40 Marks)

11. The function f is defined by

            a). Sketch the graph of f.

            b) Determine the domain and range.

            c) Find the value of f(-5), f(0) and f(2).

            d) Is f(x) one to one function

12. the table below shows the body masses of 50 adults(body masses nearest to kg)

            56        58        58        60        60        61        62        63        64        64       

            65        65        65        66        66        66        66        67        67        68

            68        68        68        69        69        69        70        70        70        70

            74        74        74        73        73        72        72        72        72        70

            80        80        83        81        76        78        75        79        75        75

i. Construct a frequency distribution table taking five equal interval, 55 – 59, 60 – 64, ...      80 – 84.

      ii. From the frequency distribution table, what is the modal class?

      iii. Calculate mean

      iv. Draw a cumulative frequency curve and estimate the median.

13. a) The sum of the first two terms of geometric progression is 10 and the sum of the first four is 40. Given that all terms of the progression are positive, show that the common  ratio is

       b). The second, fourth, and eighth term of an arithmeticprogression form three   consecutive term of geometric progression. Ifthe sum of the third and fifth term of   geometric progression is 20. Find the sum of the first ten terms of the geometric   progression.

14. a). If such that  and  note A and B are     subset. Find     i).                                     ii). .

       b). In a class of 20 pupils, there are 12 pupils who study English but not History, 4 who            study History but not English and 1 who studies neither English nor History. Find by    using Venn diagram how many pupils in the class study History?

15. The company GD makes products A and B, A requires 2 hours of processing at work     center 1 and 1 hour of processing at work center 2. B requires 1 hour of processing at          work centre 1 and 2 hours at work centre 2. Work centre 1 and work centre 2 are in         operation 280 and 330 hours respectively. If the company makes the profit of Shs       1000 per unit of product A and Shs 1500 per unit of product B. how much of each  product should be produced each month?

16. The following trial balance was extracted from Ernest’s book account at the end of March          2017. The opening stoke worth 50,000/= and the closing stock worth 40,000/=    prepare profit and loss account.

S/NO	Name of Account	Dr	Cr
1	Cash	95,000
2	Capital		100,000
3	Sales		160,000
4	Purchases	90,000
5	Rent	25,000
6	Wages	35,000
7	Transport	15,000
		260,000	260,000