Click the link below to download as a full set with all the subjects. (PDF)
ALLIANCE HIGH SCHOOL
2018 PRE-TRIAL EXAM
INSTRUCTIONS TO CANDIDATES
- The paper contains TWO sections: Section I and Section II
- Answer ALL the questions in section I and ONLY FIVE questions from section II.
- All answers and working must be written on the question paper in the spaces provided below each question.
- Non-programmable silent electronic calculators and KNEC Mathematical tables may be used, except where stated otherwise.
SECTION I: ANSWER ALL QUESTIONS IN THIS SECTION (50 MARKS)
- Use logarithm table to evaluate. (4 mks)
- Gombe and Miheso working together can dig a piece of land in 44/5 days. Gombe working alone takes 4 days less than Miheso. How many days does Miheso take to dig the piece of land alone? (3 mks)
- Given the co-ordinates of a point P is (-1,3,5) and Q is (2,-2,4) find:
- PG in terms of i,j,k (1 mk)
- The distance between P and Q (2 mks)
- Without using a mathematical table or a calculator, evaluate leaving your answer in the form a + b√c
- Expand and simplify (x - y)5 (2 mks)
- Use the first four terms of the expansion to evaluate (-0.8)5 (2 mks)
- A student expands (x - y)2 as x2 - y2. If the student uses this expansion to evaluate (12-9)2, find the percentage error in his calculation. (2 mks)
- A sum of Ksh 10,000 is invested at 12% p.a compounded quarterly. After how many years will this sum amount to Ksh. 24,760? (3 mks)
- Using a ruler and a pair of compasses, construct triangle WXY such that WX = 6.4cm, XY = 6cm and <WXY = 60o . (1 mk)
- Construct the locus of M such that <WMY + <WXY = 180o (2 mks)
- Find P-1 if P = (2312) hence use P-1 to find the point of intersection of the lines 6x + 3y = 63 and 6x + 4y = 68 (3 mks)
- A candidate in a certain school has 60% chance of passing an exam at the first attempt. Each time a candidate fails and repeats the exam; his chances of passing are increased by 15%. Calculate the probabilty that the candidate in the school passes an exam at the second or third attempt. (3 mks)
- Determine the equation of the normal to the curve at x = 2 (3 mks)
- Make t the subject of the formula (3 mks)
- A value R is partly constant and partly varies as T. when T = 27, R =55 and when T = 57, R = 58. Find the relationship between R and T. (3 mks)
- The points co-ordinates (6,1) and (-4,9) are the end points of a diameter of a circle centre A.
- Find the co-ordinates of A. (1 mk)
- Find the equation of the circle in the form x2 + y2 + ax + by + c = 0, where a, b and c are constants. (2 mks)
- An industrialist has 450 liters of a chemical which is 70% pure. He mixes it with a chemical of the same type but 90% pure so as to obtain a mixture which is 75% pure. Find the amount of the 90% pure chemical used. (3 mks)
- In the figure below, XY and YZ are chords of a circle centre O, XY = 5cm, YZ = 6cm and XZ = 9cm.
- Calculate <XYZ (2 mks)
- Calculate the length OX. (2 mks)
SECTION II: ANSWER ONLY FIVE QUESTIONS FROM THIS SECTION (50 MARKS)
- PQRS is a quadrilateral with vertices P(1,4) Q(2,1),R(2,3) and S(6,4). On the grid provided, draw the quadrilateral. (1 mark)
- Draw P'Q'R'S' the image of PQRS under a positive quarter turn about the origin and write down its coordinates. (3 marks)
- Draw P''Q''R''S'' the image of P'Q'R'S' under the transformation whose matrix is (1-201) and write down its co-ordinates. (3 marks)
- Determine the matrix T of a single transformation that maps PQRS onto P''Q''R''S'' (3 mks)
- The fourth, seventh, and sixteenth term of an arithmetic progression are in geometric progression. The sum of the first six terms of the arithmetic progression is 12.
- First term and the common difference of the arithmetic progression. (6 mks)
- Common ration of the geometric progression. (2 mks)
- Sum of the first six terms of the geometric progression. (2 mks)
- On the same axes, draw the graph of y = 2 sin x and y = 3 sin (x + 30o) for the domain 0o ≤ x ≤ 360o (5 mks)
From your graph determine:
- The period of each of the functions. (1 mk)
- The amplitude of each of the functions. (1 mk)
- The solution of 3 sin (x + 30o) - 2 sin x = 0 (1 mk)
- The transformation that maps the graph of y = 2 sin x onto the graph of y = 3 sin (x + 30o) (2 mks)
- A plane leaves P(75oN,30oE) and follows a longitude via the north pole flying at 300 knots to Q it takes 10hrs to reach point Q.
- The distance covered by the plane in nautical miles. (1 mk)
- The position of Q (4 mks)
- After spending 2 hours at Q, it then flies westwards to T which is 1360km west of Q, find:
- The longitude of T (using R = 6370km) to the nearest degree. (3 mks)
- The local time at T when the local time at Q is 5:30pm (2 mks)
- Kipchumba makes two types of wedding cakes. Types A and B. Type A requires 200g of flour and 80g of cooking oil. Type B requires 400g of flour and 50g of cooking oil. On a particular day, they had 1600g of flour and 400g of cooking.
- If they make x cakes of type A and y cakes of type B, write down inequalities in x and y to represent the above conditions. (4 mks)
- Graph the inequalities in (a) above. (4 mks)
- The profit on type A cake is sh. 30 and the profit on type B cake is sh. 40. Determine the number of cakes of each type he should make to maximize profits. (2 mks)
- The figure below represents a solid cuboid ABCDEFGH with a rectangular base. AC = 13 cm, BC = 5 cm and CH = 15cm. M is the midpoint of GH.
- Calculate the surface are of the cuboid. (3 mks)
- Calculate the angle between line AH and the base ABCD (2 mks)
- Calculate the angle between the base ABCD and the plane ADM. (2 mks)
- Calculate the angle betwen line AV and MF. (3 mks)
- The table below shows the analysis of examiniation marks scored by 160 candidates.
Marks % 1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 No. of candidates 2 6 15 22 36 34 20 15 6 4
- using an assumed mean of 45.5, calculate.
- The mean. (3 mks)
- The variance (2 mks)
- The standard deviation (2 mks)
- Calculate the semi interquartile range. (3 mks)
- using an assumed mean of 45.5, calculate.
- Using the mid-ordinates rule, estimate the area under the curve y = 1/2 x 2 - 2, using six strips between x = 2 and x = 8 and x axis. (5 mks)
- Use integration to determine the exact area under the curve. (3 mks)
- Find the percentage error in calculating the area using the mid-ordinate rules. (2 mks)