Key ideas
Substitution
Replace each letter with its number, then work it out.
Write the line with the numbers in: that's usually the first mark.
Hidden multiplying
4a means 4 × a. ab means a × b.
If a = 3: 4a = 4 × 3 = 12, not 43.
Negative numbers
Put negative numbers in brackets: if c = −2, then 5c = 5 × (−2) = −10.
c² = (−2)² = 4: a negative squared is positive.
Order of operations
Use BODMAS: brackets, then powers, then × and ÷, then + and −.
2a² means 2 × a², so square first.
Substituting whole numbers
If a = 3 and b = 5, find the value of 4a + 2b.(2 marks)
Replace the letters.4a + 2b = 4 × 3 + 2 × 5✓1
In plain English4a means 4 × a, so write 4 × 3. 2b means 2 × b, so write 2 × 5.
Work it out.= 12 + 10 = 22✓2
In plain EnglishMultiply first, then add.
⚠ A common mistake: writing 4a as 43. The 4 and the a are multiplied.
Substituting negative numbers
If p = 6 and q = −4, find the value of 3p + 2q.(2 marks)
Replace the letters, using a bracket for the negative.3 × 6 + 2 × (−4)✓1
In plain EnglishPutting −4 in a bracket stops the signs getting mixed up.
Work it out.= 18 + (−8) = 18 − 8 = 10✓2
In plain English2 × −4 = −8. Adding −8 is the same as taking away 8.
If x = −3 and y = −5, find the value of xy.(1 mark)
Multiply.xy = (−3) × (−5) = 15✓1
In plain Englishxy means x × y. A negative times a negative is positive.
Squares and brackets
If m = 4, find the value of 2m² + 1.(2 marks)
Replace the letter.2 × 4² + 1✓1
In plain English2m² means 2 × m². Only the m is squared, not the 2.
Square first.= 2 × 16 + 1 = 32 + 1 = 33✓2
In plain EnglishPowers come before multiplying: 4² = 16, then × 2, then + 1.
⚠ A common mistake: working out (2 × 4)² = 64. Square the 4 first.
If a = 7 and b = 2, find the value of 5(a − b).(2 marks)
Replace the letters.5 × (7 − 2)✓1
In plain EnglishKeep the bracket.
Bracket first.= 5 × 5 = 25✓2
In plain EnglishWork out the bracket first (7 − 2 = 5), then multiply by 5.
Substituting into a formula
The formula F = 1.8C + 32 changes a temperature in °C to °F. Find F when C = 25.(2 marks)
Substitute.F = 1.8 × 25 + 32✓1
In plain EnglishReplace C with 25.
Calculate.F = 45 + 32 = 77 °F✓2
In plain EnglishMultiply first: 1.8 × 25 = 45. Then add 32.
The area of a triangle is A = bh2. Find A when b = 9 cm and h = 6 cm.(2 marks)
Substitute.A = 9 × 62✓1
In plain Englishbh means b × h.
Calculate.A = 542 = 27 cm²✓2
In plain EnglishArea is in square units.
0 of 0 complete
Your turn
Write the line with the numbers in first, then calculate. Use a minus sign for negative answers. Stuck? Tap Need a hint?