Questions
SECTION A ( 50 MARKS )
Answer all the questions in this section
- Use logarithm table to evaluate. 4 mks
- 200 cm3 of acid is mixed with 300 cm3 of alcohol. If the densities of acid and alcohol are 1.08g/cm3 and 0.8 g/cm3 respectively, calculate the density of the mixture. 3 mks
- The coordinates of P and Q are P(5, 1) and Q(11, 4) point M divides line PQ in the ratio 2 : 1. Find the magnitude of vector OM. (3 marks)
- The table below shows income tax rates in a certain year.
Monthly income in Ksh Tax rate in each Ksh 1-9680 10% 9681-18800 15% 18801-27920 20% 27921-37040 25% Over 37040 30%
In that year, a monthly personal tax relief of Ksh. 1056 was allowed. Calculate the monthly income tax paid by an employee who earned a monthly salary of Ksh 32500. (4 mks) - Make w the subject of the formulae. 3mks
- A line passes through points (2, 5) and has a gradient of 2.
- Determine its equation in the form y=mx+c. 2mks
- Find the angle it makes with x-axis. 1mk
- A quantity P is partly constant and partly varies as the cube of Q. When Q=1, P=23 and when Q =2, P= 44. Find the value of P when Q = 5. 3 mks
- The vertices of a triangle are A(1, 2) , B(3, 5) and C(4, 1). The co-ordinates of C’ the image of C under a translation vector T are (6, -2).
- Determine the translation vector T. 1mk
- Find the co-ordinates of A’ and B’ under the translation vector T. 2mks
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- Expand (1 -x)4 using the binomial expansion. 1mk
Use the first three terms of the expansion in (a) above to find the value of (0.98)4 correct to nearest hundredth. 2mks
- Expand (1 -x)4 using the binomial expansion. 1mk
- Find the centre and radius of a circle with equation:
x² + y² - 6x + 8y – 11 = 0 (3mks) - Two grades of coffee one costing sh.42 per kilogram and the other costing sh.47 per kilogram are to be mixed in order to produce a blend worth sh.46 per kilogram in what proportion should they be mixed. (3mks)
- Pipe A can fill an empty water tank in 3 hours while pipe B can fill the same tank in 5 hours. While the tank can be emptied by pipe C in 15 hours. Pipe A and B are opened at the same time when the tank is empty. If one hour later pipe C is also opened. Find the total time taken to fill the tank. 4 mks.
- Simplify the expression: 3mks.
- A business bought 300 kg of tomatoes at Ksh. 30 per kg. He lost 20% due to waste. If he has to make a profit 20%, at how much per kilogram should he sell the tomatoes. 3mks.
- Evaluate without using a Mathematical table or a calculator. (2mks)
Log6 216 + (Log 42 - Log 6) ÷ Log 49 - Given that the ratio x: y = 2:3, find the ratio (5x-2y)∶ (x+y) (3 mk)
SECTION II (50mks)
Answer only five questions in this section in the spaces provide
- Draw the graph of y= x3+2x2-5x-8 for values of x in the range -4≤x≤3. 5mks
x -4 -3 -2 -1 0 1 2 3 x3 -64 27 2x2 -5x -8 y -20 - By drawing suitable straight line on the same axis, solve the equations.
- x3+2x2-5x-8=0 1mks
- x3+2x2-5x-7=0 2mks
- 3+3x-2x2-x3=0 2mks
- By drawing suitable straight line on the same axis, solve the equations.
- A transformation represented by the matrix (21 1-2)maps the points A(0, 0), B(2, 0), C(2, 3) and D(0, 3) of the quad ABCD onto A¹B¹C¹D¹ respectively.
- Draw the quadrilateral ABCD and its image A¹B¹C¹D¹. (3mks)
- Hence or otherwise determine the area of A¹B¹C¹D¹. (2mks)
- Another transformation (0-1-10) maps A¹B¹C¹D¹ onto A¹¹B¹¹C¹¹D¹¹. Draw the image A¹¹B¹¹C¹¹D¹¹. (2mks)
- Determine the single matrix which maps A¹¹B¹¹C¹¹D¹¹ back to ABCD. (3mks)
- In the figure below (not drawn to scale) AB = 8cm, AC = 6cm, AD = 7cm, CD = 2.82cm and angle CAB = 50°.
Calculate (to 2d.p.)- the length BC. (3 marks)
- the size of angle ABC. (3 marks)
- size of angle CAD. (3 marks)
- Calculate the area of triangle ACD. (2 marks)
- Three variables P, Q and R are such that P varies directly as Q and inversely as the square of R.
- When P = 18, Q = 24 and R = 4.
Find P when Q = 30 and R = 10. (3mks) - Express P in terms of Q and R. (1mk)
- If Q is increased by 20% and R is decreased by 10% find:
- A simplified expression for the change in P in terms of Q and R. (3mks)
- The percentage change in P. (3mks)
- When P = 18, Q = 24 and R = 4.
- A surveyor recorded the following information in his field book after taking measurement in metres of a plot.
- Sketch the layout of the plot. 4 mks.
- Calculate the area of the plot in hectares. 6mks
- A line L passes through points (-2, 3) and (-1,6) and is perpendicular to a line P at (-1,6).
- Find the equation of L. (2 mks)
- Find the equation of P in the form ax + by = c, where a, b and c are constant. (2 mks)
- Given that another line Q is parallel to L and passes through point (1,2) find the x and y intercepts of Q. (3 mks)
- Find the point of intersection of lines P and Q. (3 mks)
- The figure below shows a square ABCD point V is vertically above middle of the base ABCD. AB = 10cm and VC = 13cm.
Find;- the length of diagonal AC (2mks)
- the height of the pyramid (2mks)
- the acute angle between VB and base ABCD. (2mks)
- the acute angle between BVA and ABCD. (2mks)
- the angle between AVB and DVC. (2mks)
- The diagram below represents a conical vessel which stands vertically.
The vessels contains water to a depth of 30cm. The radius of the surface in the vessel is 21cm. (Take Π=22/7).- Calculate the volume of the water in the vessels in cm3 3mks
- When a metal sphere is completely submerged in the water, the level of the water in the vessels rises by 6cm.
Calculate:- The radius of the new water surface in the vessel; (2mks)
- The volume of the metal sphere in cm3 (3mks)
- The radius of the sphere. (3mks)
Answers
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