Edexcel GCSE June 2026
Mathematics Paper 3F Solved Paper
Integer - answer-All whole numbers (both positive and negative) and zero. E.g. 17, -
456, 0
Rational numbers - answer-Terminating or recurring numbers (numbers which end)
E.g. 2/5, 5, 1/3
Irrational numbers - answer-Numbers that can't be written as a fraction, are never
ending and non-repeating. E.g. π, √2, √5
BIDMAS - answer-The order in which processes are done within a calculation.
Multiplication and division can be done either way around, as can addition and
subtraction
Brackets, indices, divison, multiplication, addition, subtraction - answer-BIDMAS stands
for
Factor - answer-The numbers that multiply together to make a larger number E.g.
factors of 24 are 1, 24, 2, 12, 3, 8, 4, 6
Prime number - answer-A number whose only factors are itself and 1. E.g. 2, 5, 7, 13,
29, 43
Factor tree - answer-A diagram that shows how a number can be broken down into it's
prime factors
Finding prime factors of a number - answer-1. Write the number and put 2 lines coming
out under it in opposite directions
2. Write two numbers that multiply together to make that large number
3. Repeat with the new numbers until none of the numbers can be factorised any further
LCM - answer-Lowest Common Multiple. The smallest set of numbers that are factors of
the numbers given. E.g. lowest common multiple of 18 and 30 is 90
Finding LCM - answer-1. List all the prime factors of both numbers
2. If a factor appears more than once across either list, write it down
3. Multiply all these numbers together
, HCF - answer-Highest Common Factor. The largest number that divides into the
numbers given. E.g. Highest common factor of 36 and 54 is 18
Finding HCF - answer-1. List all the prime factors that appear in the numbers
2. Multiply together all the numbers that appear in all the lists
Cancelling - answer-Dividing by a number to eliminate it, or to make it simpler. E.g.
18/24 = 6/8 = 3/4
Numerator - answer-The number on top in a fraction
Denominator - answer-The number on the bottom of a fraction
Mixed number - answer-A number that has an integer part and a fraction part
Improper fraction - answer-A fraction where the numerator is larger than the
denominator (the fraction is bigger than 1)
Converting a mixed number to an improper fraction - answer-1. Multiply the
denominator by the integer
2. Add this number to the numerator
3. Replace the numerator with this number
Reciprocal - answer-Where the numerator and denominator flip. (divide by 1)
Multiplying fractions - answer-1. Multiply the numerators
2. Multiply the denominators
3. Cancel the resultant fraction into it's simplest form (if required)
Dividing fractions - answer-1. Convert any mixed numbers into improper fractions
2. Find the reciprocal of the second number (flip it over)
3. Multiply these two together
Adding fractions - answer-1. Convert any mixed numbers to proper fractions
2. Find a common denominator
3. Add the numerators together
4. Write the answer to 3. as a fraction over the answer to 2.
5. Simplify (if required)
Finding a common denominator - answer-1. Multiply the second denominator by the first
numerator
2. Multiply the first denominator by the second numerator
3. Multiply the two denominators
Answer to 1. is your first numerator
Answer to 2. is your second numerator
Answer to 3. is your common denominator
Mathematics Paper 3F Solved Paper
Integer - answer-All whole numbers (both positive and negative) and zero. E.g. 17, -
456, 0
Rational numbers - answer-Terminating or recurring numbers (numbers which end)
E.g. 2/5, 5, 1/3
Irrational numbers - answer-Numbers that can't be written as a fraction, are never
ending and non-repeating. E.g. π, √2, √5
BIDMAS - answer-The order in which processes are done within a calculation.
Multiplication and division can be done either way around, as can addition and
subtraction
Brackets, indices, divison, multiplication, addition, subtraction - answer-BIDMAS stands
for
Factor - answer-The numbers that multiply together to make a larger number E.g.
factors of 24 are 1, 24, 2, 12, 3, 8, 4, 6
Prime number - answer-A number whose only factors are itself and 1. E.g. 2, 5, 7, 13,
29, 43
Factor tree - answer-A diagram that shows how a number can be broken down into it's
prime factors
Finding prime factors of a number - answer-1. Write the number and put 2 lines coming
out under it in opposite directions
2. Write two numbers that multiply together to make that large number
3. Repeat with the new numbers until none of the numbers can be factorised any further
LCM - answer-Lowest Common Multiple. The smallest set of numbers that are factors of
the numbers given. E.g. lowest common multiple of 18 and 30 is 90
Finding LCM - answer-1. List all the prime factors of both numbers
2. If a factor appears more than once across either list, write it down
3. Multiply all these numbers together
, HCF - answer-Highest Common Factor. The largest number that divides into the
numbers given. E.g. Highest common factor of 36 and 54 is 18
Finding HCF - answer-1. List all the prime factors that appear in the numbers
2. Multiply together all the numbers that appear in all the lists
Cancelling - answer-Dividing by a number to eliminate it, or to make it simpler. E.g.
18/24 = 6/8 = 3/4
Numerator - answer-The number on top in a fraction
Denominator - answer-The number on the bottom of a fraction
Mixed number - answer-A number that has an integer part and a fraction part
Improper fraction - answer-A fraction where the numerator is larger than the
denominator (the fraction is bigger than 1)
Converting a mixed number to an improper fraction - answer-1. Multiply the
denominator by the integer
2. Add this number to the numerator
3. Replace the numerator with this number
Reciprocal - answer-Where the numerator and denominator flip. (divide by 1)
Multiplying fractions - answer-1. Multiply the numerators
2. Multiply the denominators
3. Cancel the resultant fraction into it's simplest form (if required)
Dividing fractions - answer-1. Convert any mixed numbers into improper fractions
2. Find the reciprocal of the second number (flip it over)
3. Multiply these two together
Adding fractions - answer-1. Convert any mixed numbers to proper fractions
2. Find a common denominator
3. Add the numerators together
4. Write the answer to 3. as a fraction over the answer to 2.
5. Simplify (if required)
Finding a common denominator - answer-1. Multiply the second denominator by the first
numerator
2. Multiply the first denominator by the second numerator
3. Multiply the two denominators
Answer to 1. is your first numerator
Answer to 2. is your second numerator
Answer to 3. is your common denominator
