Revision of Basic Mathematics

Question 1

Fractions can be represented with…

Answer 1

Negative powers of the base after the decimal point

For example, 10^-1, 10^-2, etc.

Question 2

Floating point (decimal)

Answer 2

Any positive number can be written as a decimal between 1 and 10 multiplied by a power of 10
e.g. 47.32 = 4.732 * 10^1

Question 3

Floating point (binary)

Answer 3

Any positive number can be written as a binary number multiplied by a power of 2
e.g. 1001.101 = 1.001101 * 2^3

Question 4

Dividend

Answer 4

The number being divided

Question 5

Divisor

Answer 5

The number the dividend is being divided by

Question 6

Quotient

Answer 6

The result of the division

Question 7

Remainder

Answer 7

What’s left over

Question 8

Prime

Answer 8

Numbers that are only divisible by 1 and itself

Question 9

Composite

Answer 9

Numbers that aren’t prime

Question 10

True or false: 1 is a prime number

Answer 10

False! Prime numbers are divisible by 2 numbers, whereas 1 is only divisible by, well, 1.

Question 11

24 as a product of prime factors

Answer 11

24 = 2 * 2 * 2 * 3 = 2^3 * 3^1

Question 12

Sieve of Eratosthenes

Answer 12

Identify a prime number, cross out all multiples of that prime, repeat

Question 13

Highest Common Factor (HCF)

Answer 13

Largest number that evenly divides (i.e. no remainder) 2 numbers

Question 14

True or false: If one number is 0, the HCF is 0

Answer 14

False! The HCF is the other number

Question 15

Lowest Common Multiple (LCM)

Answer 15

Smallest number which is a multiple of 2 numbers

Question 16

Calculating LCM

Answer 16

Multiply the product of prime factors for each number, excluding the HCF
e.g. 15 = 3 * 5, 25 = 5^2, so the LCM is 15 * 3 * 5^2 which is 75

Question 17

True or false: LCM can also be calculated by dividing the product of the numbers by their HCF.

Answer 17

True!

Question 18

a ↓ 1 = ?

Answer 18

1

Question 19

a ↑ 1 = ?

Answer 19

a

Question 20

a ↓ 0 = ?

Answer 20

a

Question 21

a ↑ 0 = ?

Answer 21

0

Question 22

(a ↑ b) * (a ↓ b) = ?

Answer 22

a * b

Question 23

Adding/subtracting fractions

Answer 23

a/b + c/d = (ad ± bc) / bd

Question 24

Multiplying fractions

Answer 24

a/b * c/d = ac / bd

Question 25

Dividing fractions

Answer 25

a/b ÷ c/d = a/b * d/c = ad / bc

Question 26

Expanding/factorising expressions

Answer 26

a(x + y) = ax + ay

(x + a)y = xy + ay

Question 27

Expanding two brackets

Answer 27

(x + a)(y + b) = xy + xb + ay + ab