121/1
MATHEMATICS
PAPER 1
TIME: 2 ½ HOURS
INSTRUCTION
- This paper consists of TWO sections: section I and Section II.
- Answer ALL the questions in Section I and only five questions from section II.
- Show all the steps in your calculations, giving your answers at each stage in the stage in the spaces below each question.
- Marks may be given for correct working even if the answer is wrong.
- Non-programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.
ANSWER ALL THE QUESTIONS
- Simplify completely (4 mks)
- Given that x: y=1:2 and y: z=3:2 find the value of (3mks)
- Solve the simultaneous inequalities given below and list all the integral values of x. (3mks)
- The sum of K terms of sequence 3,9,15,21............is 7500. Determine the value of K. (3mks)
- The length of a rectangle is (3x + 1) cm, its width is 3 cm shorter than its length. Given that the area of the rectangle is 28cm2, find its length. (3 mks)
- The curved surface area of a cylindrical container is 1980cm2. If the radius of the container is 21cm, calculate to one decimal place the capacity of the container in litres. (4 mks)
- The figure below is a triangular prism ABCDEF with sides AB = BF =AF = 3cm and BC = AD = EF = 5cm.
- Draw the net of the solid. (2mks)
- Calculate the surface area of the solid. (2mks)
- Two similar containers hold 2000cm3 and 6.75litres respectively. If the smaller container has a diameter of 15.50cm, what is the radius of the larger container correct to one decimal place. (3mks)
- A tourist on holiday in Kenya had Us£7500. She changed all the amount into Kenya Shillings at the rate of Us$ 1 = kshs. 80.04, While in Kenya she spent two thirds of the money and changed the remainder back to Us $ at Us $1 = kshs. 80.50. How much to the nearest Us dollars did she get? (3mks)
- Determine the quartile deviation of the following data. (2mks)
4,9,5,4,7,6,2,1,6,7,8,3 - A farmer has a piece of land measuring 840m by 396m. He divides it into square plots of equal size. Find the maximum area of one plot. (3 mks)
- A seven sided polygon has two of its interior angles as 140o and 160o and the remaining angles are equal. Find the size of one of the equal angles. (3mks)
- If and |P|=|Q|. Find the value of y . (3 mks)
- Find the value of x if. (3 mks)
- Use reciprocal and square tables to evaluate, to 4 significant figures, the expression. (3 mks)
1 – 4.1512
0.03654 - The following were recorded on a field note book by a surveyor. Taking the base line as 550M find the area in M². (3 mks)
SECTION II (50 MARKS)
Answer ONLY FIVE questions in this section
- A tank has two water taps P and Q and another tap R. When empty the tank be filled by tap P alone in 5 hours or by tap Q in 3 hours .When full the tank can be emptied in 8 hours by tap R
- The tank is initially empty . Find how long it would take to fill up the tank
- If tap R is closed and taps P and Q are opened at the same time (2mks)
- If all the three taps are opened at the same time .Giving your answer to the nearest minute (2mks)
- Assume the tank initially empty and the three taps are opened as follows
P at 8:00 am
Q at 9:00 am
R at 9:00 am
Find the fraction of the time that would be filled by 10:00 am. (3mks) - Find the time the tank would be fully filled up. Give your answer to the nearest minute. (3mks)
- The tank is initially empty . Find how long it would take to fill up the tank
- A straight line L1 has a gradient -½ and passes through point P (-1, 3). Another line L2 passes through the points Q (1, -3) and R (3, 5). Find.
- The equation of L1. (2mks)
- The equation of L2 in the from ax+by+c =0. (2mks)
- The equation of a line passing through a point S (0, 1.5) and is perpendicular to L2. (3mks)
- The point of intersection of a line passing through S and L2. (3mks)
- The figure below shows a velocity – time graph of a car journey.
The car starts from rest and accelerates at 2.75m/s2 for t seconds until its speed is 22m/s. It then travels at this velocity until 40 seconds after starting. Its breaks bring it uniformly to rest. The total journey is 847m long and takes T seconds.
Calculate the- Value of t (3mks)
- Distance travelled during the first t seconds. (2mks)
- Value of T (3mks)
- Final deceleration (2mks)
- Four towns P, R, T and S are such that R is 80km directly to the north of P and T is on a bearing of 290° from P at a distance of 65km. S is on a bearing of 330° from T and a distance of 30 km. Using a scale of 1cm to represent 10km, make an accurate scale drawing to show the relative position of the towns. (4mks)
Find:- The distance and the bearing of R from T. (3mks)
- The distance and the bearing of S from R. (2mks)
- The bearing of P from S (1 mk)
- On the Cartesian plane given below, draw the quadrilateral ABCD with vertices A(6,6)B(2,2)C(4,-6) and D(8,0). (1mk)
- Draw the image A1B1C1D1 of ABCD under enlargement scale factor 1/2 ,centre origin. State the coordinate of A1B1C1D1 (3mks)
- Describe the transformation that maps A1B1C1D1 onto the given image A11B11C11D11 (2mks)
- Rotate A11B11C11D11 with center (-2,-1) through a positive quarter turn to get A111B111C111D111 .state the coordinate of A111B111C111D111. (3mks)
- State a pair of quadrilateral that are oppositely congruent. (1mk)
- The figure below shows a triangle ABC inscribed in a circle.AC = 10cm, BC = 7cm and AB = 10cm.
- Find the size of angle BAC. (3 mks)
- Find the radius of the circle. (2 mks)
- Hence calculate the area of the shaded region. (5 mks)
- The diagram below shows a triangle OPQ in which QN:NP = 1:2, OT:TN = 3:2 and M is the midpoint of OQ.
- Given that OP = p and OP = q, Express the following vectors in terms of p and q
- PQ (1 mk)
- ON (2 mks)
- PT (2 mks)
- PM (1 mk)
-
- Show that point P, T and M are collinear. (3 mks)
- Determine the ratio MT: TP. (1 mk)
- Given that OP = p and OP = q, Express the following vectors in terms of p and q
- A school in Murang’a East decided to buy x calculators for its students for a total cost of ksh.16,200. The supplier agreed to offer a discount of ksh.60 per calculator. The school was then able to get three extra calculators for the same amount of money.
- Write an expression in terms of x, for the
- Original price of each calculator. (1mk)
- Price of each calculator after the discount. (1mk)
- Form an equation in x and hence determine the number of
Calculators the school bought. (5mks) - Calculate the discount offered to the school as a percentage. (3mks)
- Write an expression in terms of x, for the
Marking Scheme
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