The marks scored by 40 students in a mathematics class were shown in the table below:

(a) State the upper class limit of the modal class     (1mks)

(b) Estimate the mean mark    (3mks)

(c) If the pass mark is 55%, how many students passed?    (3mks)

(d) Find the range of marks scored by the middle 50% of the students.    (3mks)

(a) Using a ruler and a pair of compasses only, construct a parallelogram ABCD such that AB = 7cm, BC = 5cm and <ABC = 120°.     (3mks)

(b) Construct the following loci on the same diagram above

i. P is such that AP = BP.           (1mk)

ii. R is such that it is equidistant from DA and BA.          (1mk)

iii. Q is such that AQ = 3.5 cm.              (1mk)

(c) A region T is such that ATBT, <DAT  <BAT and AT  3.5 cm. By shading, show the region T.          (1mks)

(d) Locate point S such that <ASB = 60° and the area of triangle ASB is 11.2 cm² . Hence measure the shortest distance from S to C         (3mks)

The table below shows monthly income tax rates for a certain year

Mr Tundu earned a salary of Ksh 58 000, a house allowance of Ksh. 8 200 and a commuter allowance of Ksh. 6 000. He gets a monthly personal relief of Ksh. 1280.

a. Calculate

i. Mr Tundu’s monthly taxable income in Ksh.               (2mks)

ii. The tax payable by Mr Tundu in that month.            (5mks)

b. The following month that year, Tundu’s basic salary was raised by 5%. Determine his net salary for that month. (3mks)

Using the diagram below, find the angle;

(a) Plane BFC makes with ABCD                        (2mks)

(b) Plane ABFE makes with ABCD                     (2mks)

Write r in terms of u, y, p and t                                        (3mks)

Three quantities A, B and C are such that A varies directly as B and inversely as the square root of C. Find the percentage decrease in A if B decreases by 5.2% and C increases by 44%.     (3mks)

Find the percentage error in evaluating (a + b) - c, if a = 3.2 cm, b = 5cm and c = 2.0cm, leaving your answer to the nearest 4 s.f     (3mks)

A two digit number is made by combining any two of the digits 1, 3, 5, 7, 9 at random.

a) Write down all the possible outcomes.              (1mk)

b) Find the probability that the number is prime.       (1mk)

(a) Expand (1 – ¹/₂x) ⁵ in ascending powers of x leaving the coefficients as fractions in their simplest form.       (2mks)

(b) Using the first three terms in the expansion in (a) above, estimate the value of ( ¹⁹/₂₀) ⁵     (2mks)

The n^th term of G.P is given by 5 x 2^n-2

(i) Write down the first 4 terms of the G.P            (1mark)

(ii) Calculate the sum of the first 6 terms.             (2marks)