FORM 3&4 Maths Assignment 1

1. Find the L.C.M of X2 + X, X2 – 1, X2 – X.   (3 marks)

2. Evaluate     -8÷2+12×9-4×6            (3 marks)

                             56÷7×2

 3. What must be added to the number below to make it divisible by 11,    (3 marks)

                           826049

4. If x = -2,   y= -6 and z= 4,   find the value of   4xy          (3 marks)

5.Find the greatest number which divides 181 and 236 and leaves a remainder of 5 in each case            (2mk)

6.A rectangle measures 20cm by 15cm.If each dimension is increased by 2.5cm, by what percentage is

a) the perimeter of the rectangle increased                                                                         (2mk)

b)the area of the rectangle is increased                                                                               (2mk)

7.The angle of elevation of the top of a tree from a point P on horizontal ground is 30º. From another point Q 8 metres from the base of the tree, the angle of elevation of the top of the tree is 48º.

a) Calculate to one decimal place the height of the tree.                                                    (1mk)

b) Calculate the distance between P and Q                                                                        (2mk)

8.Given that cos θ= –0.8070 , find θ  for  0≤θ≤720                                                           (3mk)

9.A piece of wire 40cm is bent to form a right-angled triangle whose hypotenuse is 17cm long. Find the lengths of the other two sides of the triangle                                              (4mk)

10.Solve for x in log 5–2+log(2x+10)=log(x–4)                                                                  (3mk)

 SECTION B

11. A bookseller bought a number of cartons of books at a cost of ksh 57600 from Kagumo bookstore. Had he bought the same books from Kerugoya bookstore, it would have cost him ksh 480 less per carton. This would have enabled him to buy 4 extra cartons of books for the same amount of money. By taking x to be the number of cartons of books he actually bought;

a) write an expression in x

i) for the cost of each carton he bought at Kagumo bookstore                                     (1mk)

ii)for the cost of each carton had he bought from Kerugoya bookstore                             (1mk)

b)find the value of x                                                                                                           (6mk)

c)the bookseller later sold all the books he had bought each carton at ksh 720 more than he had paid for it. Determine the percentage profit he made                                                               (2mk)

12. A cylindrical metal bar of diameter 14cm and length 2m is melted and moulded into spherical balls. In the process, 5% by volume of metal is lost and what remains makes balls of radius 3.5cm.

a)calculate the volume of metal used to make the balls.                                                    (3mk)

b)find to the nearest whole number the number of balls made                                          (3mk)

c)find the total surface area of the metal bar                                                                      (2mk)

d)find the total surface  area of the balls made                                                                   (2mk)

Optional Questions

13. Kinyua spent 1/4 of his net January salary on school fees. He spent 1/4 of the remainder on electricity and water bills. He spent 1/9 of what remained on transport. If he finally had sh.3,400, calculate

a)  His net January salary.   (5 marks)

b)  Money spent on school fees. (1 mark)

c)  Money spent on transport. (2 marks)

d)  Money spent on electricity and water bills.

14. A minibus had 23 passengers at the beginning of a journey. Twelve passengers alighted at the first stop while 9 boarded six of those who boarded at the first stop alighted at the second stop and 12 got in. The minibus should not stop again up to the final destination. The charges from the starting point were sh. 50 up to the first stop, sh. 70 up to the second stop and sh. 85 up to the final destination.

a) How many passengers alighted at the final destination?    (3 marks)

   b) How many passengers were ferried by the minibus through the journey? (3 marks)

   c)  How much money was collected during the trip? (4 marks)