CEM Style Maths Mixed Section 3
Section 3 is the hardest tier of a CEM-style mixed maths section. Alongside the arithmetic and geometry drawn on by earlier sections, questions now bring in early algebra, such as function machines and simple equations, and sequences, and several items are layered, requiring two separate calculations chained together rather than a single step, so a pupil must plan the whole solution route before writing anything down.
Before you start
Make sure you're comfortable with these topics first:
Method
- For a layered question, identify every separate calculation it needs and the order they must be done in before starting the first one.
- For a function machine or simple equation, work out what operation was applied to the unknown, then apply the inverse operation to find it, for example if x + 7 = 20, subtract 7 from both sides.
- For a sequence question, find the term-to-term rule, what is added, subtracted or multiplied to get from one term to the next, using at least two consecutive terms before predicting further terms.
- Write down the result of each stage of a layered question clearly labelled, so a wrong final answer can still be checked stage by stage.
- Watch for a question that reuses an earlier answer, such as 'using your answer to part (a)'; recheck that earlier answer if the final result looks unreasonable.
- Because this is the hardest tier, budget slightly more time per question here than in Sections 1 and 2, and accept that not every question may be reached.
- If genuinely stuck, write down any partial working, such as the sequence rule or one stage of a layered calculation, rather than leaving the space blank.
Worked example
The first four terms of a sequence are 4, 9, 14, 19. (a) Find the term-to-term rule. (b) Find the 8th term of the sequence.
- (a) Find the difference between consecutive terms: 9 - 4 = 5, 14 - 9 = 5, 19 - 14 = 5, so the term-to-term rule is 'add 5'.
- (b) The 1st term is 4, so the 8th term is 7 steps on from the 1st term.
- 7 steps of adding 5 add a total of 7 x 5 = 35 to the first term.
- 8th term = 4 + 35 = 39.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Solve: x + 12 = 30.Show answer
Answer: x = 18.
Q2Solve: 3y = 27.Show answer
Answer: y = 9.
Q3A function machine multiplies a number by 4, then subtracts 6, giving an output of 26. What was the input number?Show answer
Answer: 8 (reverse the steps: 26 + 6 = 32, then 32 / 4 = 8).
Q4Find the next two terms of the sequence 3, 7, 11, 15, ...Show answer
Answer: 19 and 23 (the rule is add 4).
Q5Solve: 5x - 4 = 21.Show answer
Answer: x = 5.
Q6A sequence starts at 50, and each term is 6 less than the one before. Find the 4th term.Show answer
Answer: 32 (50, 44, 38, 32).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A function machine takes a number, doubles it, then adds 9, to give an output of 41. (a) Form an equation using x for the input number. (b) Solve the equation to find x.
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 6, and the term-to-term rule is 'multiply by 2, then subtract 1'. (a) Find the second and third terms. (b) Find the fourth term.
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 cem style maths mixed section 3 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 cem style maths mixed section 3, 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.