Section 1: Number

Question 1

Integer meaning

Answer 1

Another name for a whole number- either a positive or negative number, or zero

Question 2

What are 3 different forms of Rational numbers

Answer 2

1. Integers
2. Fractions
3. Terminating or recurring decimals

Question 3

What are Irrational numbers

Answer 3

Numbers that can’t be written as fractions— they’re never-ending, non-repeating decimal. Square roots of +ve integers are either integers or irrational. Surds are numbers or expressions containing irrational roots

Question 4

What does BODMAS stand for and what is it used for

Answer 4

Brackets 
Other 
Division 
Multiplication 
Adding 
Subtracting 

Tells you the order in which these operations should be done

Question 5

What are multiples of a number

Answer 5

A numbers times table

Question 6

What are factors of a number

Answer 6

All the numbers that divide into the number

Question 7

What is a prime number

Answer 7

A number which doesn’t divide by anything, apart from itself and 1— i.e. It’s only factors are itself and 1. ( the only exception is 1, which is NOT a prime number)

Question 8

How to find prime factors of a number

Answer 8

Use a factor tree:

1. Start with the number at the top, and split it into factors
2. Every time you get a prime, ring it
3. Keep going until you can’t go further then write the primes out in order. If there’s more than one of the same factor, write them as powers

Question 9

What is the LCM

Answer 9

‘Least common multiple’ is the smallest number bet that will divide by all the numbers in the question.

Question 10

What is the HCF

Answer 10

‘Highest common factor’ is the biggest number that will divide into all the numbers in the question

Question 11

How do you simplify a fraction

Answer 11

Divide numerator and denominator by same number, till they won’t go further

Question 12

How to multiply fractions

Answer 12

Simplify then multiply too and bottom numbers separately

Question 13

How to divide fractions

Answer 13

Flip the second and multiply

Question 14

How to add and subtract fractions

Answer 14

Make sure denominators at the same then add/subtract numerators only

Question 15

How to find common denominator

Answer 15

Find a number that all denominators divide into- this is common denominator

Question 16

How to fraction -> decimal

Answer 16

Divide numerator by denominator

Question 17

How to decimal -> percentage

Answer 17

x100

Question 18

How to percentage -> decimal

Answer 18

Divide by 100

Question 19

How to terminating decimal -> fraction

Answer 19

The digits after the d.p go on top and a power of 10 on the bottom- with the same number of zeros as there were decimal places

Question 20

How to recurring decimal -> fraction

Answer 20

1. Name decimal x
2. Multiply x by a power of 10 to move it past the decimal point by one full repeated lump
   3 subtract x by the power of 10 x to get rid of decimal part
3. Then divide to leave x and simplify if possible

Question 21

How to fractions into recurring decimals

Answer 21

Find an equivalent fraction with all mined on denominator. The numerator will tell you the recurring part

Question 22

How to round to a given number of decimal places

Answer 22

• identify position of ‘last digit’ from the number of decimal places.
• then look at digit to the right (the decider)
• if decider 5 or above round up last digit, if decider 4 or less leave digit as is

Question 23

Rounding to significant figures

Answer 23

The first s.f of any number is the first digit which isn’t zero. The 2nd,3rd,4th,etc. s.f follow on immediately after the 1st, regardless of being zeros or not zeros

Question 24

How to estimate calculations

Answer 24

Round all numbers to 1 sig fig

Question 25

How to estimate square roots

Answer 25

Find 2 square numbers, one either side of the number you’re given. Decide which number it’s closest to, and mar a sensible estimate of the digit after the decimal point

Question 26

What are upper and lower bounds

Answer 26

When a measurement is rounded to a given unit, the actual measurement can be anything up to half a unit bigger smaller

Question 27

What are the three rules of standard form

Answer 27

A x 10^n

1. Front number (A) must always be between 1 and 10
2. The power of 10 (n) is how far the decimal point moves
3. n is positive for big numbers and negative for small numbers

Question 28

Multiplying and dividing standard form

Answer 28

1. Rearrange to put front number and powers of 10 together
2. Multiply/divide front numbers, and use the power rules to multiply/divide the powers of 10
3. Make sure answer is in standard form

Question 29

Adding and subtracting standard form

Answer 29

1. Make sure powers of 10 are same
2. Add/subtract front numbers
3. Convert answer to standard form if necessary