SECTION A (50 MARKS)
Answer all questions in this section in the spaces provided
- Use logarithms to evaluate. (4 marks)
- Given that Find the values of a, b and c. (3 marks)
- Use completing square method to solve. (3 marks)
2x2+5x=-3
- In the figure below O is the centre of the circle. DC is diameter chord BA and DC intersect at R and TP is a tangent. AT = 8cm, PT = 12cm and OD = 8cm.
Find the length of: BA (2 marks)
- The equation of curve;Find the equation of the tangent to the curve at point x = 1. (3 marks)
- A quantity M is partly constant and partly varies as the cube root of N. If M = 24.5 when N = 64 and M = 18.5 when N = 27; Find the constants and determine equation connecting M and N. (4 marks)
- Draw a line PQ = 4 cm. Indicate by shading the region within which a variable point must lie if PA≤3cm and PA>AQ.(3 marks)
- Solve using matrix method.(4 marks)
2x+3y=23
x+5y =29
- Given that , make p subject of the formula. (3 marks)
- Find the area under curve y=x2+2 , between x = 2 and x = 6 by trapezium rule sing 4 strips. (3 marks)
- Solve for ϑ in the equation. (4 marks)
Sin(2θ-10)=-0.5 for 00≤θ≤3600
- Solve the equation: (3 marks)
- State the amplitude, period and phase angle of
- Amplitude (1 mark)
- Period (1 mark)
- Phase angle (1 mark)
- Obtain the centre and radius of the circle represented by the equation. (3 marks)
x2+y2-10y+16=0
-
- Use binomial expansion to expand (2+3/x)5up to the fourth term. (2 marks)
- Use the expansion above to evaluate: (9.5)5 (2 marks)
SECTION B (50 MARKS)
Answer any five questions in this section
- Two towns P and Q lie on the same parallel latitude such that P is due east of Q. When local time at Q is 9.50 am, the local time at P is 3.12 pm.
- Find the latitude difference between P and Q. (2 marks)
- Give that the longitude of P is 520E, find the longitude of Q. (2 marks)
- A pilot took off from town Q and flew to town P along the parallel of latitude. The pilot took 3 ¼ hours travelling at an average speed of 860km/h to reach P. Calculate to 1 d.p the latitude of town P and Q if they both lie in the northern hemisphere. (3 marks)
- Two towns R and S are both on the equator and 3820nm apart. Town R is due west of town S. Find the local time at R when the local time at S is 2.20 pm. (Take R = 6370km and π= 22/7 ) (3 marks)
- In the figure below OA = a and OB=b, M is the mid-point of OA and AN:NB= 2 : 1.
- Express in terms of a and b.
- BA (1 mark)
- BN (1 mark)
- ON (2 marks)
- Given that BX = hBM and OX = kON, determine the values of h and k. (6 marks)
- Express in terms of a and b.
- The table below shows Kenya Tax Rates in a certain year.
The table below shows the payable tax.
Income in (K£ per annum)
Tax rates(Ksh. Per £)
1 – 4512
2
4513 – 9,024
3
9,025 – 13,536
4
13,537 – 18,048
5
18,049 – 22,560
6
Over 22,560
6.5
In that year Muhando earned a salary of Ksh. 16,510 per month. He was entitled to a monthly tax relief of Ksh. 960.
Calculate:- Muhando’s annual salary in K£. (2 marks)
- The monthly tax paid by Muhando in Ksh. (6 marks)
- Find her net pay in Ksh. (2 marks)
- A box contains 3 brown, 9 pink and 15 white cloth pegs. The pegs are identical except for the colour.
- Find the probability of picking.
- A brown peg. (1 mark)
- A pink or a white peg. (2 marks)
- Two pegs are picked at random, one at a time without replacement. Find the probability that:
- both are brown pegs. (3 marks)
- both pegs are of the same colour. (4 marks)
- Find the probability of picking.
- The first, fifth and seventh terms of an arithmetic progression (AP) correspond to the first three consecutive terms of a decreasing Geometric Progression (GP). The first term of each progression is 64, common difference of the AP is d and the common ratio of the G.P is r.
- Write term equations involving d and r. (2 marks)
- Find the values of d and r. (4 marks)
- Find the sum of the first 10 terms of:
- the Arithmetic Progression (AP) (2 marks)
- the Geometric Progression (GP) (2 marks)
- The quantities P and Q are connected by the equation P=kRn. The table below shows values of P and R.
P
1.2
1.5
2.0
2.5
3.5
4.5
R
1.6
2.3
3.4
4.7
7.9
11.5
- State the linear equation connecting P and R. (1 mark)
- Using a scale of 2cm rep. 0.1 units on the y-axis and 1cm rep. 0.1 units on the x-axis; Draw a suitable line graph on the grid provided. (5 marks)
- From the graph you have drawn, estimate the values of;
- n (2 marks)
- k (1 mark)
- Find the linear law connecting P and R. (1 mark)
-
- Determine the stationary points of the curve; y=x3-3x2-9x+2
- Sketch the given curve above. (4 marks)
- The dimensions of a rectangular floor are such that:
- the length is greater than the width but utmost twice the width.
- the sum of width and length is more than 8m but less than 20m. If x represents the width and y the length.
- Write the inequalities to represent the above information. (4 marks)
-
- Represent the inequalities on the grid below. (4 marks)
- Using the integral values of x and y, find the maximum possible area of the floor. (2 marks)
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