Section 1 ( compulsory section – 50 marks)
- Solve the equation (2mks)
- If point A (1,3), B(5, -2) and C(-11, y) are collinear, calculate the value of y. (3mks)
- Simplify (3mks)
- Vector a passes through the point (5,10) and (3,5) and vector b passes through (x, 6) and (-5, -4). If a and b are parellel, find the value of x. (3mks)
- Make t the subject of the formula
P =(1/n) - Find the equation of a line that passes through (3,7) and which is perpendicular to another line whose equation is 3y = 9x-5. (3mks)
- Two similar containers have masses of 256kg and 108kg respectively. If the surface area of the smaller container is 810cm2, calculate the surface area of the larger container.(3mks)
- In the figure below, O is the center of the circle <BCA =80º and <CBO =10º. Determine the size of < CAB (3mks)
- Expand (1 –a)8 Hence use the expansion to evaluate 0.988 to 4 Significant figures. (4mks)
- Simplify the expression giving your answer in the form ,where a, b and c are real numbers (3mks)
- The dimensions of a rectangle are given as 12.5cm and 6.75cm respectively. Calculate the percentage error in its area correct to 2 decimal places (4mks)
- Factorise the expression 2x2 + x – 15, and hence value the equation 2x2 + x – 15 = 0 (3mks)
- Find the integral value of x for which. (3mks)
5 ≤ 3x + 2
3x – 7 ≤ 2
- Wanjiru Ayuma and Atieno shared the profits from their joint business in the ratio 3:7:9 respectively. If Ayuma received sh. 60,000. Find how much profit they realized. (2mks)
- Basket A contain 5 oranges and 3 lemons while basket B contain 4 oranges and 3 lemons. A basket is selected at random and two fruits picked from it, one at a time without replacement. Find the probability that the fruits picked are of the same type. (3mks)
- The fiqure below shows atringle PQR, PR = 15CM, TR= 5cm and ST is parallel to QR. If the area of triangle PQR is 315cm2 find the area of the quadrilateral QRTS.(4mks)
SECTION II (Attempt only five questions 50) - Using a ruler and a pair of compasses only construct a triangle ABC in which BC = AC= 6cm and <ACB = 135º measure AB. (3mks)
- Measure AB (3mks)
- From A drop aperpendicular to meet BC, extended at D.(3mks)
- Measure the length of AD (1mk)
- Calculate the area of the triangle ABC. (3mks)
- The table below shows marks scored by 38 students in a test.
35
47
69
57
75
58
48
56
46
49
81
67
63
56
80
72
62
70
46
26
41
58
68
73
64
49
64
54
74
35
51
25
41
61
56
57
28
40
- Starting with the mark of 25 and using a class internal of 10, make a frequency distribution table. (3mks
- State the modal class. (1mk)
- Calculate the mean mark. (3mks)
- Calculate the median mark. (3mks)
-
- Complete the table below for the equation y = x3 + 4x2 – 5x – 5 for the range -5 ≤ × ≤ 2 (2mks)
X
-5
-4
-3
-2
-1
0
1
2
3
Y
19
-5
- On the grid provided,draw the graph of y=x3 + 5x2 5x5 for -5 ≤ ×≤ 2. Using a scale of 1cm to represent 1 unit in the horizontal axis and 1cm to represent 5 units vertically. (3mks)
- Use the graph to solve the equation x3 + 4x2 – 5x – 5 =0 (2mks)
- By drawing a suitable line graph, solve the equation x3 + 4x2 – 5x – 5 = -4x.- 1 (3mks)
- Complete the table below for the equation y = x3 + 4x2 – 5x – 5 for the range -5 ≤ × ≤ 2 (2mks)
- In the figure below, PQR is a tangent to the circle at Q. TS is a diameter and TSR and QUV are straight lines. QS is parallel to TV. <SQR = 40º And < TQV =55º
- Find the angles below giving reasons for each answer.
- QTS (2mks)
- QRS(2mks)
- QVT(2mks)
- UTV(2mks)
- USQ(2mks)
- Find the angles below giving reasons for each answer.
- In the diagram below OPQ in such that QN : NP = 1:2, OT:TN =3:2, and M is the mid point of OQ
- Given that OP = p and OQ = q. Express the following vectors in terms of p and q
- PQ
- ON
- PT
- PM
-
- Show that point P,T and M are collinear (3mks
- Determine the ratio MT:TP (1km)
- Given that OP = p and OQ = q. Express the following vectors in terms of p and q
-
- The first term of an AP is 2. The sum of the first 8 terms is 156
- Find the common difference of the AP (2mks)
- Given that the sum of the first n in terms of the AP. is 416. Find n. (2mks)
- The 3rd , 5th and 8th terms of another AP correspond to the first three consecutive terms of a GP . If the common difference of the AP in 3, find
- The first term of the AP (3mks)
- The sum of the first 8 term of the GP to 4 significant figures (3mks)
- The first term of an AP is 2. The sum of the first 8 terms is 156
- Three variables P, Q and R are such that P various directly as Q and inverserly as the square of R
- When P = 9, Q=12 and R=2 Find P when Q = 15 and R=5 (4mks)
- Express Q in terms of P and R (1mk)
- If P is increased by 20% and R reduced by 10%, find
- a simplified expression for the change in Q in terms of P and R (3mks)
- The percentage charge in Q (2mks)
- OABC is a parallelogram with verities 0(0,0), A(2,0) B(3,2) and C(1,2). O,A,B,C is the image of OABC under transformation matrix.
- Find the coordinates of O1A1B1C1 (2mks)
- On the grid provided, draw OABC and O1A1B1C1 (2mks)
- Find O11A11B11C11, the image of O1A1B1C1 under transformation matrix (2mks)
- On the same grid draw O11A11B11C 11 (1mk)
- Find a single matrix that maps O11A11B11C11 onto OABC (3mks)
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