Category: Kcse-2003

K.C.S.E Mathematics Q & A - MODEL 2003PP2QN024

8/9/2020

Form 2 Mathematics

The figure below represents a right pyramid with vertex V and a rectangular base PQRS. VP = VQ = VR S = 18cm and QR =16cm and QR = 12cm. M and O are the midpoints of QR and PR respectively.

Find:

a) The length of the projection of line VP on the plane PQES (2mks)
b) The size of the angle between line VP and the plane PQRS. (2mks)
c) The size of the angle between the planes VQR and PQRS. (2mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN023

8/9/2020

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Form 4 Mathematics

a) Complete the table below, giving your values correct to 2 decimal places.

b) Using the grid provided draw, on the same axes, the graph of y = cos 2x and y = sin (x+ 30⁰) for 0⁰< x< 180⁰ Take the scale: 1cm for 150 on the x axis 4cm for 1 unit on the y- axis. (4mks)
c) Find the periods of the curve Y = axis (1mks)
d) Using the graphs in part (b) above, estimate the solutions to the equation Sin (x + 30⁰) = Cos 2x (4mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN022

8/9/2020

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Form 4 Mathematics

The line PQ below is 8cm long and L is its midpoint

a)
- i) Draw the locus of point R above line PQ such that the area of triangle PQR is 12cm².
- ii) Given that point R is equidistant from P and Q,show the position of point R..
b) Draw all the possible loci of a point T such that ∠RQL = ∠RTL. (4mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN021

8/9/2020

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Form 4 Mathematics

a)
- i) Find the coordinated of the stationary points on the curve y = x² – 3x + 2 (2mks)
- ii) For each stationary point determine whether it is minimum or maximum.
b) In the space provided below, sketch the graph of the Function y = x² – 3x + 2 (2mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN020

8/9/2020

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Form 4 Mathematics

Omondi makes two types of shoes: A and B. He takes 3 hours to make one pair of type A and 4 hours to make one pair of type B. He works for a maximum of 120 hours to x pairs of type A and Y pairs of type B.It costs him sh 400 to make a pair of type A and sh 150 to make a pair of type B.
His total cost does not exceed sh 9000. He must make 8 pairs of type A and more than 12 pairs of type B.

aNSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN019

8/9/2020

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Form 4 Mathematics

A ship leaves port p for port R though port Q.Q is 200 km on a bearing of 220⁰ from P.R is 420 km on the bearing of 140⁰ from from Q.

a) Using the scale 1:4,000,000, draw a diagram, showing the relative positions of the three ports P,Q, and R.
b) By further drawing on the same diagram, determine how far R is to the east of p Distance = 3.5 x40
c) If the ship has sailed directly from P to R at an average speed of 40 knots, find how long it would have taken to arrive at R.(Take 1 nautical mile = 1.853 km)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN017

7/9/2020

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Form 2 Mathematics

Given the simultaneous equations
5x + y = 19
-x + 3y = 9

a) Write the equations in matrix form. Hence solve the simultaneous equations. (5mks)
b) Fins the distance of the point of intersection for the line
5x +y = 19 and –x +3y = 9 from the point (11,-2) (3mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN018

7/9/2020

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Form 1 Mathematics

A dealer has three grades of coffee X,Y and Z. Grade X costs sh 140 per kg, grade y costs sh 160 per kg grade Z costs sh.256 per kg.

a) The dealer mixes grades X and Y in the ration 5:3 to make a brand of coffee which sells at sh 180 per kg.
b) The dealer makes a new brand by mixing the three grades of coffee. In the ratios X:Y =5:3 and Y:Z =2:5

Determine:

i) The ratio X: Y: Z in its simplest form (2mks)
ii) The selling price of the new brand of he has to make a 30% profit. (3mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN016

7/9/2020

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Form 3 Mathematics

A distance s metres of an object varies with time t seconds and partly with the square root of the time.
Given that s = 14 when t = 9, write an equation connecting s and t.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN015

7/9/2020

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Form 3 Mathematics

A colony of insects was found to have 250 insects at the beginning. Thereafter the number of insects doubled every 2 days. Find how many insects there were after 16 days. (3 mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN014

7/9/2020

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Form 2 Mathematics

Three business partners Atieno, wambui and Mueni contributed sh 50,000, Sh.40,000 as sh 25,000 respectively to start a business. After some time, they realized a profit, which they decided to share in the ration of their contributions. If Mueni’s share was sh 10.000, by how much was Atieno’s share more than wambui’s? (3mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN013

7/9/2020

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Form 1 Mathematics

Machine A can do a piece of work in 6 hours while machine B can do the same work in 9 hours. Machine A was set to do the piece of work but after 3¹ ⁄ ₂ hours, it broke down and machine B did the rest of the work. Find how long machine B took to do the rest of the work (3mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN012

6/9/2020

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Form 4 Mathematics

A mixed school can accommodate a maximum of 440 students. The number of girls must be at least 120 while the number of boys must exceed 150. Taking x to represent the number of boys and y the number of girls, write down all he inequalities representing the information above.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN011

6/9/2020

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Form 3 Mathematics

a) Expand and simplify the binomial expression (2 – x)⁶ (2mks)
b) Use the expansion up to the term in x² to estimate 1.99⁶ (2mks)

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN010

6/9/2020

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Form 1 Mathematics

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN008

6/9/2020

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Form 3 Mathematics

Find the coordinates of the turning point of the curve whose equation is y =6 +2x – 4x²

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN007

6/9/2020

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Form 2 Mathematics

In the figure below, triangle A’B’C’ is the image of triangle ABC under a rotation, centre O.

By construction, find the label the centre O of the rotation. Hence, determine the angle of the rotation.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN006

5/9/2020

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Form 1 Mathematics

A train moving at an average speed of 72km/h takes 15 seconds to completely cross a bridge that is 80 metres long.

a) Express 72km/h in metres per second (1mk)
b) Find the length of the train in metres (2mks)

aNSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN005

5/9/2020

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Form 3 Mathematics

Solve the equation

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN004

5/9/2020

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Form 2 Mathematics

A straight line passes through points A(-3,8) and B(3, -4). Find the equation of the straight line through(3,4) and parallel to AB. Give the answer in the form y – mx +c, and c are constants. (3mks)

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN003

5/9/2020

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Form 3 Mathematics

The table below shows the number of goals scored by a football team in 20 matches

Find:

a) The mode (1 mk)
b) The mean number of goals (2 mks)

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN002

5/9/2020

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Form 1 Mathematics

A shirt whose marked price in shs. 800 is sold to a customer after allowing him a discount of 13%. If the trader makes a profit of 20%, find how much the trader paid for the shirt.

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN001

5/9/2020

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Form 2 Mathematics

Use logarithm tables to evaluate

ANSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN024

4/9/2020

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Form 4 Mathematics

Two towns A and B lie on the same latitude in the northern hemisphere. When its 8am at A, the time at B is 11.00am.

a) Given that the longitude of A is 150 E find the longitude of B. (2mks)
b) A plane leaves A for B and takes 3 1/2 hours to arrive at B traveling along a parallel of latitude at 850km/h. Find:
- (i) The radius of the circle of latitude on which towns A and B lie. (3mks)
- (ii) The latitude of the two towns (take radius of the earth to be 6371km) (3mks)

aNSWER

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN023

4/9/2020

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Form 1 Mathematics

A businessman obtained a loan of sh.450,000 from a bank to buy a matatu valued at the same amount. The bank charges interest at 24% per annum compounded equation. 2x² + x – 5 = 0 to 1 decimal place.

a) Calculate the total amount of money the businessman paid to clear the loan in 1 – ½ years.
b) The average income realized from the matatu per day was sh.1500. The matatu worked for 3 years at an average of 280 days year. Calculate the total income from the matatu.
c) During the three years, the value of the matatu depreciated at the rate of 16% per annum. If the businessman sold the matatu at its new value, calculate the total profit he realized by the end of three years. (3mks)

ANSWER

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