Category: Section B

QUESTION AND ANSWER ON VECTORS II MODEL06012023003

5/1/2023

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QUESTION AND ANSWER ON STATISTICS II MODEL06012023007

5/1/2023

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QUESTION ON LONGITUDES AND LATITUDES MODEL06012023001

5/1/2023

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QUESTION AND ANSWER ON GRAPHICAL METHODS MODEL06012023004

5/1/2023

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QUESTION AND ANSWER ON COMMERCIAL ARITHMETIC II MODEL06012023005

5/1/2023

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QUESTION ON SEQUENCE AND SERIES MODEL06012023002

5/1/2023

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QUESTION AND ANSWER ON LOCI MODEL06012023006

5/1/2023

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question and answer on graphical methods MODEL06012023012

5/1/2023

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MAKE P THE SUBJECT OF THE FORMULA IN THE EQUATION:

2/1/2023

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EXPAND BINOMIAL EXPRESSION:

2/1/2023

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Two inlet taps P and Q opened at the same time can fill a tank in 2 1/2 h. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find:

2/1/2023

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QUESTIONS

Two inlet taps P and Q opened at the same time can fill a tank in 2 1/2 h. The two taps were opened together at the same time and after 1 hour 10 minutes tap Q was closed and P continued alone and filled the tank after a further 4 hours. Find:

a) The fraction of the tank filled by both taps for 1 hour.     (1 marks)
b) The fraction of the tank filled by tap P after Q was closed. (2 marks)
c) The time which each tap working alone would have taken to fill the tank.   (7 marks)

ANSWERS

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The coordinates of two points A and B are (2, -3) and (-4, 5) and R is the mid-point of AB.

2/1/2023

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questions

The coordinates of two points A and B are (2, -3) and (-4, 5) and R is the mid-point of AB.

a) Determine the coordinates of R. (2 marks)
b) Find the equation of a straight line joining A and B, expressing it in the form y=mx+c where m and c are constants. (3 marks)
c) The straight line L_(1 ) which is a perpendicular bisector of AB meets the X-axis at T. Find the coordinates of T. (3 marks)
d) If the straight line L_(1 )is parallel to a line that passes through the point (-1, 6) and (a, 8), find a. (2 marks)

answers

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A Business man is paid a commission of 5% on sales ofgoods worth over ksh 100,000. He is paid a monthly salary of ksh 15,000but 2% of his total earning is remitted as tax. In a certain month hesold goods worthy khs 500,000.

2/1/2023

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QUESTIONS

A Business man is paid a commission of 5% on sales of goods worth over ksh 100,000. He is paid a monthly salary of ksh 15,000 but 2% of his total earning is remitted as tax. In a certain month he sold goods worthy khs 500,000.

a) Calculate his monthly net earnings that month. (5marks)
b) The following month, his monthly salary increased by 20%. His commission was increased to 10% but on goods worth over ksh 200,000. If his total earnings that month was ksh 64,800, Calculate the money received from the sale of goods. (5marks)

aNSWERS

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Complete the table of values for the equation y=x^(2 )+3x-6, given that -6≤x≤4.

2/1/2023

Comments

a) Complete the table of values for the equation y=x²+3x-6, given that -6≤x≤4.

b) Using a scale of 1cm to represent 2 units in both axes, draw the graph of y=x²+3x-6 . (3 marks)

c) Using the graph drawn above Solve the equation
i) x²+3x-6=0 (2 marks)
(ii) x²+3x-2=0 (3 marks)

Answers

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The distance between two towns P and Q is 300 km. A bus started at P at10.30 am and travelled towards town Q at 80 km/h. After 45 minutes acar started at Q and travelled to town P at x km/h. The car met the busafter 1hour 20 minutes.

2/1/2023

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The distance between two towns P and Q is 300 km. A bus started at P at 10.30 am and travelled towards town Q at 80 km/h. After 45 minutes a car started at Q and travelled to town P at x km/h. The car met the bus after 1hour 20 minutes.

a) Determine the value of x.     (3 marks)
b) Find the distance from P where the car met the bus.   (2 marks)
c) At what time did the car meet the bus?     (2 marks)
d) If t a shuttle started at P, 1hour after the car left Q for P. Calculate the speed to the nearest km/h at which the shuttle should be driven in order to arrive at Q at the same time with the bus.      (3 marks)

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A piece of wire, 18 cm long is cut into two parts. The first part is bent to form the four sides of a rectangle having length x cm and breath 1 cm.

27/12/2022

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A piece of wire, 18 cm long is cut into two parts. The first part is bent to form the four sides of a rectangle having length x cm and breath 1 cm.
a). State two expressions in terms of x only for the perimeter of the square and the rectangle. (2 marks)

If the sum of the areas of the square and the rectangle is A cm², show that

If A =8 cm², Solve the equation in (b) above for x, hence find the possible dimensions of the two pieces of wire. (6 marks)

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If the bucket above has a hole and 1.1 cm3 of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can. (4 marks)

27/12/2022

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The diagram below shows a bucket in the shape of a frustum of a cone with diameters 36 cm and 24 cm and a vertical height of 28 cm. The bucket contains water such that the diameter of the water surface is 30cm. Calculate the volume of the bucket. (6 marks)

If the bucket above has a hole and 1.1 cm³ of water leaks out every 5 seconds and collects in a cylindrical can of base radius and height 10 cm and 25 cm respectively. Calculate how long it takes to fill the cylindrical can. (4 marks)

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A tower is on a bearing of 030o from a point P and a distance of 100m.From P, the angle of elevation of the top of the tower is 15o and the angle of depression of the foot of the tower is 1o.

27/12/2022

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A tower is on a bearing of 030^o from a point P and a distance of 100m.From P, the angle of elevation of the top of the tower is 15^o and the angle of depression of the foot of the tower is 1^o.

a). Calculate the height of the tower. (4 marks)

b). A point Q is on the same horizontal plane as point P. The tower is on a bearing of 330^ofrom Q and a distance of 70 m. Calculate:

i) The distance from P to Q. (3 marks)

ii) The bearing of P from Q. (3 marks)

Comments

A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

2/12/2021

Comments

(a) A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

On the grid provided, show the figure ABCD and its final image under the successive transformations ERS. (6mks)

(a) ERS =

(b) Find the matrix representing the single transformation mapping the image found in (a) above
back to the object figure ABCD. (2mks)

(c) A(2,2), B(2,0) and C(3,2) are co-ordinates of the vertices of triangle ABC. Triangle ABC undergoes a shear factor 3 parallel to the x-axis. Determine the coordinates of A’B’C’ (2mks)

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Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

2/12/2021

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Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

(a) Draw a probability tree diagram to show all the possible outcomes. (2mks)

(b) Calculate the probability that
(i) No one hit the target. (2mks)

(ii) Only one of them hit the target. (2mks)

(iii) At least one of them hit the target. (2mks)

(iv) At least one of them missed the target. (2mks)

Comments

Mr. Kimutai a teacher from Tuiyotich Secondary School earns K₤ 12000 per annum and lives in a house provided by the employer at a minimum rent of Ksh.2000 per month. He gets a family relief of K₤ 1320p.a. and is entitled to a relief of 10% of his i

30/11/2021

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COMMERCIAL ARITHMETICS II | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

Mr. Kimutai a teacher from Tuiyotich Secondary School earns K₤ 12000 per annum and lives in a house provided by the employer at a minimum rent of Ksh.2000 per month. He gets a family relief of K₤ 1320p.a. and is entitled to a relief of 10% of his insurance of K₤ 800p.a.

(a) Calculate his annual tax bill based on the table below. (6mks)

(b) Kimutai other deductions include.
- W.C.P.S = sh 600.00pm
- NHIF = sh 500.00pm
Calculate Kimutai’s net salary monthly. (4mks)

Comments

A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t]2 - 5t – 12

30/11/2021

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INTEGRATION | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t² - 5t – 12

Find;
(a) The value of t when P is instantaneously at rest. (2mks)

(b) An expression for the distance, S metres, moved by P after t seconds given that when t = 0, s = 0 (2mks)

(c) The total distance traveled by P in the first 3 seconds after passing point Q. (3mks)

(d) The distance of P from Q when the acceleration is zero. (3mks)

Comments

The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = 1/4 PQ. Lines PM and ON meets at X.

30/11/2021

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VECTORS (2) | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ. Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q the vectors.
(i) PQ

PQ=q-p

(ii) PM. (2mks)

(iii) ON. (2mks)

(b) You are further given that OX = KON and PX = hPM.
(i) Express OX in terms of P and q in two different ways. (2mks)

(ii) Find the value of h and K. (2mks)

(iii) Find the ratio PX : XM. (1mk)

Comments

Complete the table for y = Sin x + 2cos x

29/11/2021

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TRIGONOMETRY III | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

(a) Complete the table for y = Sin x + 2cos x. (2mks)

(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

(d) Find the range of values of x for which y≤-0.5. (3mks)

Comments

The diagram below shows a square based pyramid V vertically above the middle of the base. PQ = 10cm and VR = 13cm. M is the midpoint of VR.

29/11/2021

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VECTORS II | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

The diagram below shows a square based pyramid V vertically above the middle of the base. PQ = 10cm and VR = 13cm. M is the midpoint of VR.

Find
(a) (i) the length of vector PR. (2mks)

(ii) The height of the pyramid. (2mks)

(b) (i) the angle between VR and the base PQRS. (2mks)

(ii) The angle between MR and the base PQRS. (2mks)

(iii) The angle between the planes QVR and PQRS. (2mks)

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Atika School HAS A VARIETY OF MATHEMATICS QUESTIONS AND ANSWERS SORTED ACCORDING TO LEVELS, PAPERS AND TOPICS

KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

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QUESTIONS

ANSWERS

questions

answers

QUESTIONS

aNSWERS

Answers

​(a) A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

On the grid provided, show the figure ABCD and its final image under the successive transformations ERS. (6mks)

(b) Find the matrix representing the single transformation mapping the image found in (a) above back to the object figure ABCD. (2mks)

​(c) A(2,2), B(2,0) and C(3,2) are co-ordinates of the vertices of triangle ABC. Triangle ABC undergoes a shear factor 3 parallel to the x-axis. Determine the coordinates of A’B’C’ (2mks)

​Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

(a) Draw a probability tree diagram to show all the possible outcomes. (2mks)

​(b) Calculate the probability that (i) No one hit the target. (2mks)

​(ii) Only one of them hit the target. (2mks)

​(iii) At least one of them hit the target. (2mks)

​(iv) At least one of them missed the target. (2mks)

COMMERCIAL ARITHMETICS II | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

​Mr. Kimutai a teacher from Tuiyotich Secondary School earns K₤ 12000 per annum and lives in a house provided by the employer at a minimum rent of Ksh.2000 per month. He gets a family relief of K₤ 1320p.a. and is entitled to a relief of 10% of his insurance of K₤ 800p.a.

​(a) Calculate his annual tax bill based on the table below. (6mks)

​(b) Kimutai other deductions include. - W.C.P.S = sh 600.00pm - NHIF = sh 500.00pm Calculate Kimutai’s net salary monthly. (4mks)

INTEGRATION | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

​A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t² - 5t – 12

​Find; (a) The value of t when P is instantaneously at rest. (2mks)

(b) An expression for the distance, S metres, moved by P after t seconds given that when t = 0, s = 0 (2mks)

​(c) The total distance traveled by P in the first 3 seconds after passing point Q. (3mks)

(d) The distance of P from Q when the acceleration is zero. (3mks)

VECTORS (2) | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

​The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ. Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q the vectors. (i) PQ

​(ii) PM. (2mks)

​(iii) ON. (2mks)

​(b) You are further given that OX = KON and PX = hPM. (i) Express OX in terms of P and q in two different ways. (2mks) (ii) Find the value of h and K. (2mks) (iii) Find the ratio PX : XM. (1mk)

TRIGONOMETRY III | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

(a) Complete the table for y = Sin x + 2cos x. (2mks)

​(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

​(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

(d) Find the range of values of x for which y≤-0.5. (3mks)

VECTORS II | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION B

The diagram below shows a square based pyramid V vertically above the middle of the base. PQ = 10cm and VR = 13cm. M is the midpoint of VR.

​Find (a) (i) the length of vector PR. (2mks)

​(ii) The height of the pyramid. (2mks)

(b) (i) the angle between VR and the base PQRS. (2mks)

(ii) The angle between MR and the base PQRS. (2mks)

(iii) The angle between the planes QVR and PQRS. (2mks)

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(a) A figure whose co-ordinates are A(-2, -2), B(-4, -1), C(-4, -3) and D(-2, -3) undergoes successive transformation ERS; where E, R and S are transformations represented by the matrices,

(b) Find the matrix representing the single transformation mapping the image found in (a) above
back to the object figure ABCD. (2mks)

(c) A(2,2), B(2,0) and C(3,2) are co-ordinates of the vertices of triangle ABC. Triangle ABC undergoes a shear factor 3 parallel to the x-axis. Determine the coordinates of A’B’C’ (2mks)

Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

(b) Calculate the probability that
(i) No one hit the target. (2mks)

(ii) Only one of them hit the target. (2mks)

(iii) At least one of them hit the target. (2mks)

(iv) At least one of them missed the target. (2mks)

Mr. Kimutai a teacher from Tuiyotich Secondary School earns K₤ 12000 per annum and lives in a house provided by the employer at a minimum rent of Ksh.2000 per month. He gets a family relief of K₤ 1320p.a. and is entitled to a relief of 10% of his insurance of K₤ 800p.a.

(a) Calculate his annual tax bill based on the table below. (6mks)

(b) Kimutai other deductions include.
- W.C.P.S = sh 600.00pm
- NHIF = sh 500.00pm
Calculate Kimutai’s net salary monthly. (4mks)

A particle P moves in a straight line such that t seconds after passing a fixed point Q, its velocity V m/s, is given by the equation V = t² - 5t – 12

Find;
(a) The value of t when P is instantaneously at rest. (2mks)

(c) The total distance traveled by P in the first 3 seconds after passing point Q. (3mks)

The diagram below shows a triangle OPQ in which M and N are points on OQ and PQ respectively such that OM = ⅔ OQ and PN = ¼ PQ. Lines PM and ON meets at X.

(a) Given that OP = P and OQ = q express in term of P and q the vectors.
(i) PQ

(ii) PM. (2mks)

(iii) ON. (2mks)

(b) You are further given that OX = KON and PX = hPM.
(i) Express OX in terms of P and q in two different ways. (2mks)

(ii) Find the value of h and K. (2mks)

(iii) Find the ratio PX : XM. (1mk)

(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

Find
(a) (i) the length of vector PR. (2mks)

(ii) The height of the pyramid. (2mks)