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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~Topically Analyzed

QUESTION AND ANSWER ON FORMULA AND VARIATIONS MODEL06012023015

5/1/2023

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QUESTION AND ANSWER ON VECTORS II MODEL06012023017

5/1/2023

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QUESTION AND ANSWER ON SURDS MODEL06012023014

5/1/2023

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QUESTION AND ANSWER ON LOGARITHMS `AND INDICES MODEL06012023010

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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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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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)

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If the sum of the areas of the square and the rectangle is A cm2, show that
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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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Solve for θ in the equation

27/12/2022

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​Solve for θ in the equation 

SOLVE FOR Θ IN THE EQUATION
SOLVE FOR Θ IN THE EQUATION
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The average rate of depreciation in value of a laptop is 10% per annum. After three complete years its valuewas ksh 35,000. Determine its value at the start of the three-year period.(3marks)

16/12/2022

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The average rate of depreciation in value of a laptop is 10% per annum. After three complete years its valuewas ksh 35,000. Determine its value at the start of the three-year period.(3marks)

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Given that, the coordinates of two points P and Q are  (■(2,&3,&5))   and  (■(6,&k-1,&15)) respectively and that their position vectors are parallel, Calculate the value of  |PQ|.  (4marks)

11/12/2022

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The mass of maize flour to the nearest 10 grams is 8. 67kg.Determine the percentage error in this measurement.

9/12/2022

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​The mass of maize flour to the nearest 10 grams is 8. 67kg. Determine the percentage error in this measurement. (3marks)
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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)

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

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

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

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

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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)

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

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​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.

​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
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​(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)

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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.

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

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

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

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

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

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Expand a Binomial expression (5+x/2)]6 to the term x]3 and use it to answer (11/2)]6

28/11/2021

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BIONOMIAL EXPANSION | FORM 3 | PAPER 2 QUESTIONS | SECTION A

​(i) Expand

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​to the term in x cubed. 

​(ii) Use your expansion to estimate the value of

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​Correct to one decimal place.         (2mks)

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​Chords AB and CD of a circle meet at X.

28/11/2021

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ANGLE PROPERTIES OF A CIRCLE | CIRCLES: CHORDS AND TANGENTS | | PROPERTIES OF CHORDS INTERSECTING EXTERNALLY | FORM 3 | PAPER 2 QUESTIONS | SECTION A

​Chords AB and CD of a circle meet at X.

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​If AB = 8cm, BX = 5cm and DX = 6.  Calculate the length of chord CD. (3mks)



WORKED ANSWER:

Let CD be x
CX * DX = AX * BX (PROPERTIES OF CHORDS INTERSECTING EXTERNALLY)
  • CX = x+6
  • DX = 6
  • AX = AB + BX = 8 + 5 = 13
  • BX = 5
THEREFORE:
(X + 6)6 = 13 * 5
6X + 36 = 65
6X = 29
X = 29/6 = 4.83CM

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2X]2 + 2y]2 - 6X + 10y + 9 = 0 is the equation of a circle.  Find the radius and the centre of the circle.

28/11/2021

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GRAPHICAL METHODS | Determining of the centre and radius of a circle | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION A

2X² + 2y² - 6X + 10y + 9 = 0 is the equation of a circle.  Find the radius and the centre of the circle. (4mks)

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Given that P = QX]n make n the subject of the formula and simplify your answer.

28/11/2021

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FORMULAE AND VARIATIONS | Change of the subject | FORM 3 LEVEL | PAPER 2 QUESTIONS | SECTION A

​Given that P = QXⁿ make n the subject of the formula and simplify your answer.                     (3mks)

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Solve for θ in the equation sin (3θ+120) degrees

27/11/2021

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​Solve for θ in the equation sin (3 θ + 120)degrees

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Worked Answer:

Solve for θ in the equation sin (3 θ + 120)degrees



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​The initial salary of Mr. Lutta is sh. 42, 000 per annum. His salary increases by 13% each year. Determine his total earnings after 15 years. Give your answer to the nearest thousands

26/11/2021

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​The initial salary of Mr. Lutta is sh. 42, 000 per annum. His salary increases by 13% each year. Determine his total earnings after 15 years. Give your answer to the nearest thousands.  (3mks)

​​Worked Answer:

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Find the value of a and b where a and b are ​rational numbers

26/11/2021

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Find the value of a and b where a and b are ​rational numbers.   (3mks)

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​Worked Answer:

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Solve the equation below.

26/11/2021

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Solve the equation below.  (3 marks)

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Worked Answer:

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Use logarithms correct to 4 decimal places to evaluate.

26/11/2021

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Use logarithms correct to 4 decimal places to evaluate. (3mks)

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Worked Answer:

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