Year 11 Maths

Combinatorics, Probability

100

Susan has got a red, a white, a purple and a pink mug. How many different ways can she put them on the shelf of the cupboard?

24

200

A race has 8 participants. The best three participants will get to the final. In how many different ways can this happen?

336

300

How many odd 3-digit numbers exist?

450

400

You toss a fair coin three times. What is the probability of three heads?

1/8

500

We are rolling two fair dice at once, a black one and a white one. What is the probability that the product of the two numbers obtained is equal to 8?

1/18

Exponentials

100

2^x=64

6

200

3^x+2=243

x=3

300

8^3x=0.25

x=-2/9

400

49^x-50⋅7^x+49=0

x=0, x=2

500

2^x+2+2^x-2=68

x=4

Logarithm

100

log₂32

5

200

log₃(1/81)

-4

300

3^log100

9

400

lIf we put 500 000 ft in the bank at 6% annual interest rate, after how many years will we have 2 million fts?

23.8 years

500

A machine loses 8% of its value (previous year) every year. It is now worth half as much as when it was bought. How old can this machine be?

8.3 years

Trigonometry

100

sin²x+cos²x = ?

1

200

What is the formula for the area of a triangle using sine?

A=a⋅b⋅siny/2

300

Solve sin x = 0.5 on the interval [0; 360]. 

x= 30, x=150

400

Work out the angle of elevation of the sunbeam if on the ground a 1.8 m tall man is standing and his shadow is 1.2 m long.

56.3 degrees

500

The longer hand of a church clock is 3 m long. The shorter hand is 1 m long. How far are the end-points of the hands from each other at exactly 4 o’ clock?

3.6 m