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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)
Form 3 Mathematics
(a)Complete the table below for the equation y = x2-4x+2
(b) On the grid provided draw the graph y = x2 - 4x + 2 for 0 ≤ x ≤ 5. Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis.
(c) Use the graph to solve the equation, x2 -4x + 2 = 0 (d) By drawing a suitable line, use the graph in (b) to solve the equation x2 -5x + 3 = 0.
ANSWERS
Form 3 Mathematics
Use completing the square method to solve 3x2 + 8x — 6 = 0, correct to 3 significant figures.
answer
Form 3 Mathematics
The table below shows values of x and some values of for the curve y = x3 -2x2 -9x + 8 for -3 ≤ x ≤ 5. Complete the table.
(b) On the grid provided, draw the graph of y = x3- 2x2- 9x + 8 for -3 ≤ x ≤ 5 for Use the scale; 1 cm represents 1 unit on the x-axis 2 cm represents 10 units on the y-axis
(c) (i) Use the graph to solve the equation x2 - 2x3 -9x + 8 = 0. (ii) By drawing a suitable straight line on the graph, solve the equation x2 - 2x2- 11x + 6 = 0.
answers
Form 3 Mathematics
The roots of a quadratic equation are x = -3/5 and x = 1. Form the quadratic equation in the form ax2 + bx + c = 0 where a, b and c are integers.
answers
Form 3 Mathematics
An institution intended to buy a certain number of chairs for Ksh 16 200. The supplier agreed to offer a discount of Ksh 60 per chair which enabled the institution to get 3 more chairs.
Taking x as the originally intended number of chairs, (a) Write an expressions in terms of x for: (i) original price per chair; (ii) price per chair after discount. (b) Determine: (i) the number of chairs the institution originally intended to buy; (ii) price per chair after discount; (iii) the amount of money the institution would have saved per chair if it bought the intended number of chairs at a discount of 15%.
answers
Form 3 Mathematics
Murimi and Naliaka had each 840 tree seedlings. Murimi planted equal number of seedlings per row in x rows while Naliaka planted equal number of seedlings in (x + 1) rows.
The number of tree seedlings planted by Murimi in each row were 4 more than those planted by Naliaka in each row. Calculate the number of seedlings Murimi planted in each row.
answer
Form 3 Mathematics
a)Solve the equation
b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m2
.i)Calculate the perimeter of the floor ii)A rectangular carpet is placed on the floor of the wall leaving an area of 64m2. If the length of a carpet is twice its width, determine the width of the carpet.
answers
Form 3 Mathematics
The simultaneous equations below, are satisfied when x = 1 and y = p
-3x + 4y = 5 qx2 – 5xy + y2 = 0
a) Find the values of P and Q.
b) Using the value of Q obtained in (a) above, find the other values of x and y which also satisfy the given simultaneous equations.
Answer
Form 3 Mathematics
(a) Complete the table below for y = x3+4x2-5x-5
(b) On the grid provided, draw the graphs of y = x3 +4x2-5x-5 for -5 ≤ x ≤ 2
(c) (i) Use the graph to solve the equation x3 +4x2 – 5x – 5 = 0 (ii) By drawing a suitable straight line on the graph, solve the equation x3 + 4x2 – 5x -5 = - 4x – 1
answers
Form 3 Mathematics
A quadratic curve passes through the points (-2, 0) and (1, 0). Find the equation of the curve in the form y = ax2 +bx +c, where a, b and c are constants
answer
Form 3 Mathematics
(a) solve the equation;
(b) The length of a floor of a rectangular hall is 9m more than its width. The area of the floor is 136m2.
i. Calculate the perimeter of the floor. ii. A rectangular carpet is placed on the floor of the hall leaving an area of 64m2. If the length of the carpet is twice its width, determine the width of the carpet.
answers
Form 3 Mathematics
(b) Neema did y tests and scored a total of 120 mks. She did two more tests which she scored 14 and 13 mks. The mean score of the first y tests was 3 mks more than
the mean score for all the tests she did. Find the total number of tests that she did.
answers
Form 3 Mathematics
The cost C, of producing n items varies partly as n and partly as the inverse of n. To produce two items it costs Ksh 135 and to produce three items it costs Ksh 140. Find:
(a) the constants of proportionality and hence write the equation connecting C and n; (b) the cost of producing 10 items; (c) the number of items produced at a cost of Ksh 756.
answers
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