GCE O-LEVEL MATHEMATICS QUESTIONS

 QUESTIONS UNDER PROBABILITY

1. A coin is tossed once. Find the probability that a tail is obtained.
2. A die is thrown, find the probability that
   a) a 6 is obtained
   b) a number is divisible by 3 is obtained
   c) an odd number is obtained
   d) a factor of 12 is obtained
3. A single card is drawn from a pack of 52 playing cards. find the probability that the card drawn is  a) an ace
   b) an ace of hearts
   c) a spade
   d) a picture card
4. A bag contains 3green balls, 6red balls and 8white balls of identical sizes. A ball is drawn at random from the bag. Find the probability that the ball is 
   a) red
   b) green
   c) White
5. A fair coin is tossed and a die is thrown. Find the probability of obtaining a head and a six.
6. Two events A and B are such that P(A)=1/2, P(B)=1/3 and P(AnB)=1/4, find P(AuB) 
7. A letter is chosen at random from the english alphabet. Find the probability that it is 
   a) P
   b) M or N
   c) A vowel
   d) Either X,Y or Z

Factor and Remainder theorems

1. Find the remainder when f(x)=X square - 7X + 12 is divided by X - 2
2. Find the remainder when f(x)=X square - 5X + 6 is divided by X - 3
3. Show that (X-2) is a factor of each of the following polynomials
   a) f(x) = x square - 5x + 6
   b) g(x) = x cube - 2x square + 9x - 18
4. Given that x - 2 is a factor of f(x) where f(x) = 3x cube + Kx - 10, find the value of K and the other factor
5. Given that x - 2  is one of the factors of function p(x)= 2x square + x + k where k is a real constant. Find 
   a) the value of k
   b) The other factors of p(x)

Algebra and network

1. Expand the following
   a) (x + 4) (x + 5)
   b) (2x - 3y) square
   c) (x - 6) (x + 3)
   
2. Simplify the following
   a) 4(a - 3b) + 5b
   b) x (x + 3) - 5(x - 3)
   c) 5(2u - 3v + 4w) - 2 (u - 2v + 3w)
3. Factorize the following
   a) 15a - 10b
   b) 2zy + 12xz
4. Simplify the following
   a) X square - Y square / X + Y
   b 5/ a + 4 - 2/ a - 4
   c) 3X/ X - 1 - 2/ X - 2
   d) (a - b) - (b - a)/ (a - b)

Numbers

1. Simplify the following giving your answers a simplified fraction in each case
   a) 0.00275 X 0.0064/ 2.5 X 0.8
   b) 0.04 X 5.4 X 0.065 / 0.0936
2. Evaluate 
   a) -6 + 12 X 2 / 4
   b) 4.5 X 0.02 Living your answer in a standard form
3. Solve for X in the following equation
   a) 52x = 44 (10)
   b) 41x = 21 (10)
4. The scale of a map is 1:500000. The length of a road on this map is  240mm. Find the actual length of the road on the ground.
5. The model of transport bus is of length 20cm and its actual length is 15m, find the scale of the model.