Algebra: Formulae, Sequences and Equations
Algebra: Formulae, Sequences and Equations extends Year 6 algebra beyond one-step equations, covering using a formula with more than one letter, generating a sequence from a written rule and finding a distant term without listing every value, and finding pairs of whole numbers that satisfy an equation with two unknowns.
Before you start
Make sure you're comfortable with these topics first:
Method
- When using a formula, substitute the known values into the letters carefully, keeping to the correct order of operations as you calculate.
- To find an unknown in a two-step equation, undo the operations in reverse order: undo any addition or subtraction first, then undo any multiplication or division.
- To describe a sequence, find the term-to-term rule (what is added, subtracted or multiplied each time) by comparing consecutive terms.
- To find a term further along a sequence without listing every value, use the term-to-term rule to write an expression for the nth term, then substitute the term number you need.
- For an equation with two unknowns (such as a + b = 20), remember there is more than one possible pair of answers unless another clue narrows it down, such as both numbers being equal, or one being double the other.
- When a question asks you to find all the possibilities, work systematically, for example starting with the smallest possible value, so that no pair is missed or repeated.
- Check any solution by substituting it back into the original formula, equation or sequence rule to confirm it works.
Worked example
A sequence begins 4, 9, 14, 19, ... Find an expression for the nth term, and use it to find the 20th term.
- Find the term-to-term rule by comparing consecutive terms: 9 - 4 = 5, 14 - 9 = 5, 19 - 14 = 5, so the rule is add 5 each time.
- Since the sequence goes up by 5 each time, the nth term must include 5n (5 times the term number).
- Compare 5n with the actual sequence: when n = 1, 5n = 5, but the first term is 4, which is 1 less, so the nth term is 5n - 1.
- Check the rule against another term: when n = 3, 5n - 1 = 15 - 1 = 14, which matches the third term.
- Substitute n = 20 into the rule to find the 20th term: 5 x 20 - 1 = 100 - 1 = 99.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1The formula for the perimeter of a rectangle is P = 2l + 2w. Find P when l = 9cm and w = 6cm.Show answer
Answer: 30cm
Q2Continue the sequence: 2, 6, 10, 14, ___Show answer
Answer: 18
Q3Find the nth term of the sequence 3, 8, 13, 18, ...Show answer
Answer: 5n - 2
Q4If a + b = 15 and a is double b, find the values of a and b.Show answer
Answer: a = 10, b = 5
Q5Solve 3n + 8 = 29.Show answer
Answer: n = 7
Q6A taxi charges a formula of C = 2.50 + 1.20m, where C is the cost in pounds and m is the number of miles travelled. Work out the cost of a 6 mile journey.Show answer
Answer: 9.70 pounds
Q7Find two whole numbers that multiply to give 36 and add to give 13.Show answer
Answer: 4 and 9
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
The nth term of a sequence is 4n + 3. Find the 15th term.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
The cost of hiring a bike is given by the formula C = 5 + 2h, where C is the cost in pounds and h is the number of hours. Yusuf hires a bike and pays 23 pounds in total. Work out how many hours he hired the bike for.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
The first term of a sequence is 7, and each term after that is found by adding 6 to the term before it. A pupil says that 150 will appear somewhere in the sequence. Use the nth term of the sequence to decide whether the pupil is correct, showing your working.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the algebra: formulae, sequences and equations worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
Next topics
Not quite what you needed?
Tell us what is missing on algebra: formulae, sequences and equations, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.