**QUESTIONS UNDER PROBABILITY**

- A coin is tossed once. Find the probability that a tail is obtained.
- 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 - 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 - 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 - A fair coin is tossed and a die is thrown. Find the probability of obtaining a head and a six.
- Two events A and B are such that P(A)=1/2, P(B)=1/3 and P(AnB)=1/4, find P(AuB)
- 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

- Find the remainder when f(x)=X square - 7X + 12 is divided by X - 2
- Find the remainder when f(x)=X square - 5X + 6 is divided by X - 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 - 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
- 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

- Expand the following

a) (x + 4) (x + 5)

b) (2x - 3y) square

c) (x - 6) (x + 3) - Simplify the following

a) 4(a - 3b) + 5b

b) x (x + 3) - 5(x - 3)

c) 5(2u - 3v + 4w) - 2 (u - 2v + 3w) - Factorize the following

a) 15a - 10b

b) 2zy + 12xz - 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

- 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 - Evaluate

a) -6 + 12 X 2 / 4

b) 4.5 X 0.02 Living your answer in a standard form - Solve for X in the following equation

a) 52x = 44 (10)

b) 41x = 21 (10) - 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.
- The model of transport bus is of length 20cm and its actual length is 15m, find the scale of the model.