KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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 SIMULTANEOUS EQUATIONS  FORM 3 LEVEL  SECTION I  PAPER 1  ALT B  KCSE 2011  QUESTION 15 Solve the simulataneous equations:
p  q = 3 p²  q² = 21
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ALT B  quadratic equations   FORM 3 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 3Solve by factorisation, the quadratic equation:
2x²3x50 = 0 (3 marks) ALT B  QUADRATIC EQUATIONS  SECTION 1  QUESTION 19  KCSE 2010  FORM 3 LEVELThe length and width of a rectangular plot of land are given as (7x + 5) m and (x + 10) m respectively.
QUESTION 12  KCSE 2023  QUADRATIC EQUATIONS  PAPER 2  FORM 4 LEVELThe length and width of a rectangular floor of a room are 10 m and 7 m respectively. A rectangular carpet of area 28 m² is placed on the floor. The carpet leaves a uniform space of x m with each of the walls of the room.
Form a quadratic equation in x and hence solve for x. (3 marks) QUESTION 7  KCSE 2023  Quadratic Expressions  PAPER 1  FORM 3 LEVELSimplify and hence factorise the expression (5x  4y) (4x + 5y)  9xy. (3 marks)
QUESTION 18  KCSE 2021  AREA  PAPER 2  FORM 3 LEVELA rectangular plot measures 50 m by 24 m. A lawn, rectangular in shape, is situated inside the plot with a path surrounding it as shown in the figure below. The width of the path in x m between the lengths of the lawn and those of the plot and 2x m between the widths of the lawn and those of the plot.
QUESTION 3  KCSE 2021  Quadratic Equations  PAPER 2  FORM 3 LEVELThe expression ax²  30x + 9 is a perfect square, where a is a constant. Find the value of a.
(2 marks) QUESTION 21  KCSE 2021  Quadratic Equations  PAPER 1  FORM 3 LEVEL(a) Solve for x (x  4)^2 = (x  8)(2x + 7). (4 marks) (b) John cycled 6 km from his home to school at an average speed of (2x  3) km/h.
Peter walked 2.4 km from his home to the school at an average speed of x km/h. Peter took 16 minutes less than John. Determine the time, in minutes, that John took to reach the school. (6 marks) QUESTION 7  KCSE 2021  Quadratic Expressions  PAPER 1  FORM 3 LEVELSimplify (4 + 2y)²  (2y  4)². (2 marks)
K.C.S.E MATHEMATICS Q & AMODEL 1997PP1QN20(A) Draw The Graph Of Y = 6 + X  X2, Taking Integral Value Of X In 4 ≤ X ≤ 5. (The Grid Is Provided. Using The Same Axes Draw The Graph Of Y = 2 – 2x
(B) From Your Graphs, Find The Values Of X Which Satisfy The Simultaneous Equations Y = 6 + X  X2; Y = 2 – 2x (C) Write Down And Simplify A Quadratic Equation Which Is Satisfied By The Values Of X Where The Two Graphs Intersect. QUESTION 5  KCSE 2022  QUADRATIC EQUATIONS  PAPER 2  FORM 3 LEVELThe perimeter of a rectangle is 48 cm while it area is 108 cm². Form a quadratic equation to represent the situation and hence determine the dimensions of the rectangle. (3 marks)
QUESTION 5  KCSE 2022  QUADRATIC EQUATIONS  PAPER 1  FORM 3 LEVELSimplify: [18ax  (3a4x)(3a + 4x)] / (3a8x) (3 marks)QUESTION 1  KCSE 2022  QUADRATIC EQUATIONS  PAPER 1  FORM 3 LEVELSolve for n: 6n/na = 25/n
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 A =8 cm^{2}, Solve the equation in (b) above for x, hence find the possible dimensions of the two pieces of wire. (6 marks)
Form 3 Mathematics
(a)Complete the table below for the equation y = x^{2}4x+2
(b) On the grid provided draw the graph y = x^{2}  4x + 2 for 0 ≤ x ≤ 5. Use 2 cm to represent 1 unit on the xaxis and 1 cm to represent 1 unit on the yaxis.
(c) Use the graph to solve the equation, x^{2} 4x + 2 = 0 (d) By drawing a suitable line, use the graph in (b) to solve the equation x^{2} 5x + 3 = 0. 
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