GCSE Maths Questions and Answers
100% Solved | Graded A+
Finding the LCM of two numbers when you have the prime factors - ✔✔-
List all the prime factors out
- If a factor appears more than once, list it that many times, e.g. 2, 2, 2, 3, 4
and 2, 2, 3, 4 would be 2, 2, 2, 3, 4
- Multiply these together
Finding the HCF of two numbers when you have the prime factors - ✔✔-
List all the prime factors that appear in both numbers
- Multiply these together
Multiplying fractions - ✔✔Multiply the top and bottom separately
Dividing fractions - ✔✔Turn the second fraction upside down then multiply
Rule for terminating and recurring decimals - ✔✔If the denominator has
prime factors of only 2 or 5, it is a terminal decimal
Turning a recurring decimal into a fraction - ✔✔- Name the decimal with an
algebraic letter
1
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
,- Multiply by a power of ten to get the one loop of repeated numbers past
the decimal point
- Subtract the larger value from the single value to get an integer
- Rearrange
- *Simplify*
Turning a recurring fraction into a decimal when the recurring decimal is not
immediately after the decimal, e.g. r = 0.16666... - ✔✔- Name the decimal
with an algebraic letter e.g. r = 0.16666...
- Multiply by a power of ten to get the non-repeating part out of the bracket
e.g. 10r = 1.6666...
- Multiply to get the repeating part out of the bracket e.g. 100r = 16.6666...
- Take away the larger value from the smaller one (to get an integer) e.g.
100r - 10r = 90r = 15
r = 15/90
- *Simplify* e.g. 15/90 = 1/6
Turning a fraction into a decimal - ✔✔- Make the fraction have all nines at
the bottom
- The number on the top is the recurring part, the number of nines is the
number of recurring decimals there are
Significant figures - ✔✔The first number which isn't a zero. This is rounded.
2
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
, Rules for calculating with significant digits - ✔✔
Estimating square roots - ✔✔- Find two numbers either side of the number
in the root
- Make a sensible estimate depending on which one it is closer to
Truncated units - ✔✔When a measurement is truncated, the actual
measurement can be up to a whole unit bigger but no smaller, e.g. 2.4
truncated to 1 d.p. is 2.4 ≤ x < 2.5
Multiplying and dividing standard form - ✔✔- Convert both numbers to
standard form
- Separate the power of ten and the other number
- Do each calculation separately
Adding and subtracting standard form - ✔✔- Convert both numbers into
standard form
- Make both powers of 10 the same in each bracket
- Add the two numbers and multiply by whatever power of ten; they are to
the same power so this can be done
Negative powers - ✔✔1 over whatever the number to the power was, e.g.
7⁻² = ² =
3
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
100% Solved | Graded A+
Finding the LCM of two numbers when you have the prime factors - ✔✔-
List all the prime factors out
- If a factor appears more than once, list it that many times, e.g. 2, 2, 2, 3, 4
and 2, 2, 3, 4 would be 2, 2, 2, 3, 4
- Multiply these together
Finding the HCF of two numbers when you have the prime factors - ✔✔-
List all the prime factors that appear in both numbers
- Multiply these together
Multiplying fractions - ✔✔Multiply the top and bottom separately
Dividing fractions - ✔✔Turn the second fraction upside down then multiply
Rule for terminating and recurring decimals - ✔✔If the denominator has
prime factors of only 2 or 5, it is a terminal decimal
Turning a recurring decimal into a fraction - ✔✔- Name the decimal with an
algebraic letter
1
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
,- Multiply by a power of ten to get the one loop of repeated numbers past
the decimal point
- Subtract the larger value from the single value to get an integer
- Rearrange
- *Simplify*
Turning a recurring fraction into a decimal when the recurring decimal is not
immediately after the decimal, e.g. r = 0.16666... - ✔✔- Name the decimal
with an algebraic letter e.g. r = 0.16666...
- Multiply by a power of ten to get the non-repeating part out of the bracket
e.g. 10r = 1.6666...
- Multiply to get the repeating part out of the bracket e.g. 100r = 16.6666...
- Take away the larger value from the smaller one (to get an integer) e.g.
100r - 10r = 90r = 15
r = 15/90
- *Simplify* e.g. 15/90 = 1/6
Turning a fraction into a decimal - ✔✔- Make the fraction have all nines at
the bottom
- The number on the top is the recurring part, the number of nines is the
number of recurring decimals there are
Significant figures - ✔✔The first number which isn't a zero. This is rounded.
2
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
, Rules for calculating with significant digits - ✔✔
Estimating square roots - ✔✔- Find two numbers either side of the number
in the root
- Make a sensible estimate depending on which one it is closer to
Truncated units - ✔✔When a measurement is truncated, the actual
measurement can be up to a whole unit bigger but no smaller, e.g. 2.4
truncated to 1 d.p. is 2.4 ≤ x < 2.5
Multiplying and dividing standard form - ✔✔- Convert both numbers to
standard form
- Separate the power of ten and the other number
- Do each calculation separately
Adding and subtracting standard form - ✔✔- Convert both numbers into
standard form
- Make both powers of 10 the same in each bracket
- Add the two numbers and multiply by whatever power of ten; they are to
the same power so this can be done
Negative powers - ✔✔1 over whatever the number to the power was, e.g.
7⁻² = ² =
3
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
