INSTRUCTIONS TO CANDIDATES
- This paper consists of two sections: Section I and Section II.
- Answer ALL questions in section 1 and ONLY FIVE questions from section II
- All answers and workings must be written on the question paper
- Show all the steps in your calculation, giving your answer at each stage in the spaces below each question.
- Non – Programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.
FOR EXAMINERS USE ONLY
SECTION I
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SECTION II
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QUESTIONS
SECTION I: Answer all questions in this section.
- Find the quadratic equation whose roots are -3/4 and 2/3 and write it in the form
ax2 + bx + c = 0 where a, b and c are integers. (3mks) - Given that . Express m in terms of n, q and G. (3mks)
- The heights, in centimeters of 7 students were; 143, 139, 145, 154, 159, 147,156. Find the mean absolute deviation of the data. (3mks)
- Triangle ABC has vertices A (4, 1), B (6, 1) and C (8, 3). The image of ABC under a transformation N is A’ (2, 1), B’ (4, 1) and C’ (2, 3). Find the matrix N. (3mks)
- State the amplitude, period and phase angle of; (3mks)
- The points P (-6, 5) and Q (2, -1) are the ends of a diameter of a circle centre M. Determine:
- The coordinates of M (1mk)
- The equation of the circle in the form x2 + y2 + ax + by + c = 0 (2mks)
- Without using mathematical table or a calculator, express sin 45o in surd form. Hence simplify; leaving your answer in surd form. (3mks)
- Simplify completely; (3mks)
9x2 – 16x +7
162x2 - 98 - A sum of Ksh 8000 was partly lent at 10% p.a simple interest and 12.5% p.a simple interest. The total interest after 2 years was Ksh. 1775. How much was lent at 10% simple interest? (3mks)
- The position vectors of points X and Z are 8i + 3j – 4k and 4i + 6j -2k respectively. If Y divides line XZ in the ratio 9: -5, find the coordinates of Y. (3mks)
- In the figure below AB is a tangent to the circle centre O and radius 12cm. The area of the triangle AOB is 120cm2. OXB is a straight line.
Calculate XB (3 mks) - A die and a coin are cast simultaneously.
- Draw a table to show all possible outcomes. (2mks)
- What is the probability of a tail and a number less than 4 showing up. (1mk)
- Calculate the percentage error in the area of the triangle below given the included angle is exactly 50º. (3mks)
- Use binomial expansion to simplify;
(√2 + √5)4 - (√2 - √5)4 (4mks) - Solve the simultaneous equation. (4mks)
2x – y = 3
x2 – xy = - 4 - Without using logarithms table or calculator, solve for x in Log 5 – 2 + log (2x +10) = log (x-4) (3mks)
SECTION II
Answer ANY FIVE questions in this section.
- In the figure below OP = p, OQ = q. QX meets OY at R, OX: OP = 2:3 and QY: YP = 1:3.
- Express the following in terms of p and q.
- QP (1mk)
- OY (2mks)
- QX (1mk)
- Given that OR = hOY and QR = kQx
- Express OR in terms of h, q and p. (1mk)
- Express OR in terms of k, q and p. (1mk)
- Solve for h and k (4mks)
- Express the following in terms of p and q.
- The sum of quantities A and B is y. A varies inversely as x and B varies directly as x. When x=4, Y =17 and when x =6, y = 13.
- Express y in terms of x. (7mks)
- Find y when x = 10 and x when y = 11.5. (3mks)
- The figure below is a right pyramid on a rectangle base. TC = TB =TA = 17cm and TO = 15cm. AB is twice BC
Calculate;- The length AB (4mks)
- The angle between TC and plane ABCD. (2mks)
- The angle between TO and plane TAB. (2mks)
- The angle between TAD and ABCD. (2mks)
-
- In mathematics, the scores obtained by 30 students were recorded as shown in the table below.
Score x 59 61 65 k 71 72 73 75 No. of Students 2 3 5 6 7 4 2 1
Ʃf- Score k (4mks)
- Standard deviation (4mks)
- The data below represents the ages in months at which 9 babies started walking 9, 11, 12, 11, 10, 8, 10, 13, 9. Find quartile. range (2mks)
- In mathematics, the scores obtained by 30 students were recorded as shown in the table below.
- Under a transformation represented by the matrix , the image of A(-1, 2), B (-1, -1) and c (1, -1) are A’ (-3, 2), B’ (0,-1) and C’ (x, y)
- Find the matrix m. (3mks)
- Find the coordinates of C’ (1mk
- Plot triangles ABC and A’B’C’ on the grid provided below. (2mks)
- Describe fully the transformation M. (2mks)
- Draw the triangle A’’ B’’C’’, the image of A’B’C’ under a stretch of scale factor -2 with the y-axis invariant. (2mks)
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- The first term of an arithmetic progression (AP) is 6. The sum of the first 7 terms of the AP is 126.
- Find the common difference of the AP (2mks)
- Find the 19th term of the AP. (1mk)
- The 2nd, 3rd and 11th terms of an increasing arithmetic progression (AP) form the first 3 terms of a geometric progression (GP). The first term of the AP is -2.
- Find the common difference of the AP and the common ratio (r) of the GP. (4mks)
- Find the sum of the first 5 terms of the geometric progression (GP) (3mks)
- The first term of an arithmetic progression (AP) is 6. The sum of the first 7 terms of the AP is 126.
-
- Complete the table below.
x
0
30
60
90
120
150
180
210
240
270
300
330
360
y = Sin (x+300)
0.50
0.00
-0.50
y = 2Cos (x+300)
1.73
0.00
-1.73
2.00
1.73
- On the same axes, draw the graphs of y = sin (x+30)º and y = 2Cos (x + 30º) (5mks)
- Use your graphs to solve the equation. (2mks)
2 Cos (x + 30º) = 1
Sin (x + 30º) - State the amplitude of Sin (x + 30º) (1mk)
- Complete the table below.
- Using a ruler and a pair of compasses only for all constructions in this question.
- Construct triangle ABC in which AB = 6cm, BC =7cm and angle ABC = 75º. (3mks)
- Find the locus x such that Ax = 3cm. (1mk)
- On the same side of BC as ∆ , Construct the locus of P such that angle BPC = 120º. (3mks)
- Show by stating the locus of Q inside triangle ABC such that ∟BPC ≥ BQC. (1mk)
- On the side of AB opposite C, construct the locus of T such that the area of triangle ATB is 60cm2. (2mks)
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