SECTION I (50 MARKS)
Answer ALL Questions in this section in the spaces provided.
- Use the table of logarithms to evaluate. (4 marks)
- Form the three inequalities that satisfy the unshaded region in the diagram below. (3 marks)
- Form the quadratic equation whose roots are x = -5/3 and x = 2.Give your answer in the form ax2 +bx +c =0 (2 marks)
- Given that Where a and b are rational numbers, find the values of a and b. (3marks)
- Mwangi truncated 7/9 to 3 decimal places. Calculate the percentage error resulting from the truncating. (3 marks)
- Expand (1+2x)8 in ascending powers of up to and including the term in x8. Hence evaluate (1.02)8 (3 marks)
- Log27(x + 5) – log27 (x – 3) = 2/3 (3 marks)
- Find the inverse of the matrix. (1 mark)
- Hence determine the point of intersection of the lines. (2 marks)
y + x = 7
3x + y = 15
- The first term of an arithmetic sequence is (2x+1) and the common difference is (x+1) if the product of the first and the second terms is zero, find the first three terms of the two possible sequences. (4 marks)
- Machine A can complete a piece of work in 6 hours while machine B can complete the same work in 10 hours. If both machines start working together and machine B breaks down after two hours, how long will it take machine A to complete the rest of the work. (3 marks)
- An item that costs sh 24000 cash can be bought on hire purchase. A customer pays sh 6000 as deposit and then makes 6 monthly instalments of sh 3500 each. Calculate the monthly rate of compound interest, giving your answer to 1 d.p. (3 marks)
- In the figure below CB is a tangent to the circle, DEB is a straight line DE:EB=1:3
Find BD and EB given that CB=8√3cm (4 marks)
- Make N the subject of the formula. (3 marks)
- An arc subtends an angle of 0.9 radians. If radius of circle is 13cm, find the length of the arc. (3 marks)
- The masses of 40 children being interviewed to join Std 1 by a certain school were as recorded in the table below.
9 - 11
12 - 14
15 - 17
18 - 20
21 - 23
24 - 26
No of children
Calculate the mean mass of the students giving your answer to 4 S.F. (3 marks)
- The equation of a circle is given by 2x2 + 8x + 2y2 – 10 = 0. Determine the centre and the radius of the circle. (3 marks)
SECTION II (50 MARKS)
Answer ONLY 5 Questions in this section in the spaces provided.
- The figure below shows a triangle inscribed in a circle. AB = 6cm, BC = 9cm and AC = 10cm.
- The interior angles of DABC. (5 marks)
- The radius of the circle. (2 marks)
- The area of the shaded part. (3 marks)
- The table alongside shows the rates of taxation in a certain year.
In that year Mr. Kariuki a civil servant was earning a basic salary of Ksh. 27 000 per month. In addition he was entitled to other taxable allowances totalling to Ksh 11 000 per month and a personal relief of Ksh 1056 per month. He lives in a government house where he is paying a nominal rent of Ksh. 3 500 per month.
- Calculate how much income tax Mr. Kariuki pays per month (in sh) (7 marks)
- Kariuki’s other deductions per month were co-operative society contribution of sh 2500 and loan repayment of sh. 3000, calculate his net salary per month. (3 marks)
- A group of young men decided to raise Ksh.480000 to start a business. Before actual payment was made four members pulled out and each of the remaining had to pay an additional Ksh.20000. Write an expression in terms of P for.
- Original contribution of each member. (1 mark)
- Contribution after withdrawal of four members. (1 mark)
- Form an equation in P and hence determine the number of initial members. (5 marks)
- Three men Kamau, James and Hassan shared Shs.480000 such that Kamau: James is 3: 2 and James: Hassan is 4: 2. Find how much each got. (3 marks)
- Draw a cumulative frequency curve for the following data which shows the marks obtained by 80 form four students in a school. (5 marks)
Use your graph to find:
- The lower quartileQ1), median(Q2) and upper quartile(Q3) (3 marks)
- The pass mark if 85% of these student are to pass (2 marks)
- In chemistry form 4 classes, 1/3 of the class are girls and the rest boys, 4/5 of the boys and 9/10 of the girls are right handed while the rest are left handed. The probability that a right-handed student breaks a conical flask in any practical session is 3/10 and the corresponding probability of a left-handed student 4/10 . The probabilities are independent of the students gender.
- Represent the above information on a tree diagram with independent probabilities. (2 marks)
- Determine the probability that student chosen at random form the class is left handed and does not break a conical flask in simplest form. (3 marks)
- Determine the probability that a conical flask is broken in any chemistry practical session in simplest form. (3 marks)
- Determine the probability that a conical flask is not broken by a right-handed student in the simplest form. (2 marks)
- Two straight lines and intersect at a point P.Q and R are on the lines and respectively such that PQ=5cm, PR=7cm and ÐRPQ=500
- Draw the two lines. (2 marks)
- Using a ruler and pair of compasses only, draw a circle which is a tangent to line PR at R and passes through Q. (3 marks)
- The line cuts the circle again at point S. Mark the point S and measure QS. (2 marks)
- Locate a point T on the minor arc such that QT<TS (3 marks)
- In the figure below, circle ABDF has centre O. CE is a tangent to the circle at D and AF = 12cm is the diameter, AB = BD and angle DAF = 27º.
- Find the size of
- Angle ADE. (2 marks)
- Angle ADB. (2 marks)
- Find the length of
- AD. (2 marks)
- BD. (4 marks)
- Find the size of
- ABCD is a quadrilateral with vertices A (3, 1), B (2, 4), C (4, 3), D (5, 1).
- On the grid provided draw the image A¹B¹C¹D¹ image of ABCD under transformation matrix and write down the co-ordinates. (4 marks)
- A transformation represented by maps A¹B¹C¹D¹ onto A¹¹B¹¹C¹¹D¹¹ determine the co-ordinates of the image and draw A¹¹B¹¹C¹¹D¹¹. (3 marks)
- Determine the single matrix of transformation which maps ABCD onto A¹¹B¹¹C¹¹D¹¹ and describe the transformation fully. (3 marks)
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