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EVALUATION EXAMINATION 2025
MATHEMATICS
- Use logarithm table to evaluate (4marks)
5
2
00521
4 x 4. 83
2Make b the subject of the formula given that a = Nb d
bd (^2) (3 marks)
- Line PQ is the diameter of a circle such that the coordinates of P and Q are (-2, 2) and (-2,-6)
respectively. Find the equation of the circle in the form ax^2 ay^2 bx cy d 0.
(4marks)
- Use completing the square method to solve the equation 4 - 3x - 2x^2 = 0 (3marks)
- Simplify the expression
2 2
2 2 6 19 15
9 25 t at a
t a
(3marks)
- The table below shows the temperature readings of four different solutions recorded by students
to nearest 0. 10 C during a laboratory lesson. Calculate the percentage error in S R
P Q
to 3 d.p.
(3marks) Quantity (^) Temperature in^0 C P 22. Q 19. R 17. S 26.
- Use matrix method to solve the simultaneous equations 2x + y = 2x +2y =14 (3marks)
- (a) Expand (1+2x)^5 to the fourth term. (1 mark)
(b) Hence evaluate (1.02)^5 correct to 3 decimal places. (3 marks)
- It is known that the value of land appreciate at 7% p.a in a town. John bought a plot in the town at Ksh 500,000. Given that he plans to sell the plot after 6 years, find out how much profit he expects to get. (Give your answer correct to the nearest thousand). (3marks)
- The mass of a wire varies jointly with its length and with the square of its diameter. A section of the wire 500m long, with diameter 3mm has a mass of 31.5kg. what is the mass of 1000m of wire of diameter 2mm? (3marks)
- Mr. Gatua has a salary of sh.80000 per annum. He lives rent free in company house and is entitled to a monthly personal relief of sh.1056. Based on the tax rates given below, calculate his PAYE. (3 marks) Taxable income Rate (KE p.a.) 1 - 1500 10% 1501 - 3000 15% 3000 - 4500 25% Above 4500 35%
- The third term and sixth term of a geometric series are 3^1 / 3 and 11^1 / 4 respectively. Calculate the common ratio and hence find its first term. (3marks)
- Use the figure below to answer the question that follows
R Q
Given that angle RSQ = 50^0 , SQ= 11.83 cm and QR=12cm.A circumcirle is drawn on the triangle.Find the radius of the circle (2marks)
- A Business man bought commodity A and commodity B at shs.60 and sh.72 respectively. In what ratio must he mix so that when he sells at shs.78, he makes a profit of 200%. (3 marks)
- Form three inequalities that satisfy the unshaded region R. (3marks)
S
11.83cm M
12cm
Given that the distance between O and Q is 12cm and that the line AB meets OQ at X, find:
(a) the length of the chord AB. (3marks)
(b) the reflex angle AOB. (3marks)
(c) the area of the shaded region. 3. 142 (4marks)
- In the figure below, EG is the diameter of the circle centre O. Points B, G, D, E and F are on the
circumference of the circle. (^) BFD 500 , (^) BEO 250 and line ABC is a tangent to the circle at B
Giving reasons, calculate the size of
CBD^ (2marks)
BED (2marks)
The reflex angle BOD (2marks
A
B
C
O
F D
E
G
EBA (2marks)
BGD (2marks)
- OAB is a triangle in which OA= a, OB= b , M is a point on OA such that OM:MA=2:3 and N is another
point on AB such that AN:NB = 1:2. Lines ON and MB intersect at X.
a) Express the following vectors in terms of a and b
i) AB (1mark)
ii) ON (1mark)
iii) BM (1mark)
If OX =k ON and BX =h BM , express ON in two different ways. Hence or otherwise find the value of h and k
(6marksc)
Determine the ratio OX: XN (1mark)
22. The data below shows the sample of age distribution of some of the people who reside in a Yoruba village in years.
Age group Number of persons in age group
1 - 5 4
6 - 10 12
11 - 20 9
21 - 30 6
(b) Using the grid provided draw the graph for y = -6 + x + 4 x^2 + x^3 for -4 x 2 (c) (i) Use the graph to solve the equations:- (i) x^3 + 4 x^2 + x – 4 = 0 (ii) -6 + x + 4 x^2 + x^3 = 0 (iii) -2 + 4 x^2 + x^3 = 0
The figure below represents a model of a solid structure in the shape of frustrum of a cone with a hemisphere top. The diameter of the hemispherical part is 70cm and is equal to the diameter of the top of the frustrum. The frustrum has a base diameter of 28cm and slant height of 60cm.
Calculate : (a) the area of the hemispherical surface (b) the slant height of cone from which the frustrum was cut (c) the surface area of frustrum (d) the area of the base (e) the total surface area of the model
