Maths · Topic 1: Year 10
Algebra
The index laws in algebra, expanding brackets and factorising, solving equations, using and rearranging formulae, and linear and non-linear sequences.
Lessons
Ticks are remembered on this device only.
-
1
Algebraic indices
The index laws work just as well with letters as with numbers. Deal with the numbers first, then each letter in turn, and even a long expression simplifies in…
6 terms -
2
Expanding and factorising
Expanding multiplies brackets out; factorising puts them back. They are the same skill run in opposite directions, and between them they turn up in almost…
6 terms -
3
Equations
An equation is a balance: whatever you do to one side, you do to the other. With that one rule you can solve equations with the unknown on both sides, inside…
5 terms -
4
Formulae
A formula is a rule linking several quantities. Substituting puts numbers in; changing the subject rearranges the rule so it works out a different quantity -…
5 terms -
5
Linear sequences
A linear sequence goes up or down by the same amount every time. Its nth term is a formula that gives any term straight away - the 100th as easily as the 1st -…
6 terms -
6
Non-linear sequences
Not every sequence goes up by the same amount. Square, cube and triangular numbers, Fibonacci sequences and geometric sequences all follow rules of their own -…
6 terms -
7
More expanding and factorising
Three brackets, quadratics that start with a number in front of the squared term, and the difference of two squares with coefficients - plus using factorising…
5 terms
Downloads
Free, no account needed.
- Algebraic indices.pptx Built from the lesson script on 28 September 2026. View
- Algebraic indices - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 28 September 2026. View
- Algebraic indices - Exam Questions.docx Built from the lesson script on 28 September 2026. View
- Expanding and factorising.pptx Built from the lesson script on 28 September 2026. View
- Expanding and factorising - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 28 September 2026. View
- Expanding and factorising - Exam Questions.docx Built from the lesson script on 28 September 2026. View
- Equations.pptx Built from the lesson script on 28 September 2026. View
- Equations - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 28 September 2026. View
- Equations - Exam Questions.docx Built from the lesson script on 28 September 2026. View
- Formulae.pptx Built from the lesson script on 28 September 2026. View
- Formulae - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 28 September 2026. View
- Formulae - Exam Questions.docx Built from the lesson script on 28 September 2026. View
- Linear sequences.pptx Built from the lesson script on 28 September 2026. View
- Linear sequences - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 28 September 2026. View
- Linear sequences - Exam Questions.docx Built from the lesson script on 28 September 2026. View
- Non-linear sequences.pptx Built from the lesson script on 28 September 2026. View
- Non-linear sequences - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 28 September 2026. View
- Non-linear sequences - Exam Questions.docx Built from the lesson script on 28 September 2026. View
- More expanding and factorising.pptx Built from the lesson script on 28 September 2026. View
- More expanding and factorising - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 28 September 2026. View
- More expanding and factorising - Exam Questions.docx Built from the lesson script on 28 September 2026. View
Key terms in this chapter
All 39, gathered from every lesson.
- Index (power)
- The small number showing how many times the base is multiplied by itself.
- Coefficient
- The number in front of a letter, e.g. 5 in \(5x^3\).
- Like terms
- Terms with exactly the same letters and powers, e.g. \(3x^2\) and \(7x^2\).
- Simplify
- Write an expression in its shortest form.
- Negative index (Higher)
- \(x^{-n} = \dfrac{1}{x^n}\).
- Fractional index (Higher)
- \(x^{\frac{1}{n}} = \sqrt[n]{x}\).
- Expand
- Multiply out brackets.
- Factorise
- Write an expression as a product of factors, using brackets.
- Factorise fully
- Take out the highest common factor, so no common factor is left inside.
- Quadratic expression
- An expression whose highest power is \(x^2\), such as \(x^2 + 5x + 6\).
- Difference of two squares
- An expression of the form \(x^2 - a^2\), which factorises to \((x + a)(x - a)\).
- Identity
- Two expressions that are equal for every value of \(x\), written with \(\equiv\).
- Equation
- A statement that two expressions are equal, true for particular values of the letter.
- Solve
- Find the value of the letter that makes the equation true.
- Solution
- The value that makes the equation true.
- Inverse operation
- The operation that undoes another: \(-\) undoes \(+\), \(\div\) undoes \(\times\).
- Linear equation
- An equation where the highest power of the letter is 1.
- Formula
- A rule linking two or more quantities, written with letters.
- Substitute
- Replace the letters in a formula with numbers.
- Subject
- The letter on its own on one side of a formula.
- Change the subject
- Rearrange a formula so a different letter is the subject.
- Identity
- Two expressions that are equal for every value of the letters, written with \(\equiv\).
- Sequence
- A list of numbers or patterns that follows a rule.
- Term
- One number in a sequence.
- Term-to-term rule
- The rule that gets you from one term to the next.
- nth term
- A formula that gives any term from its position, \(n\).
- Common difference
- The amount a linear sequence goes up or down by each time.
- Linear (arithmetic) sequence
- A sequence with a common difference.
- Triangular numbers
- 1, 3, 6, 10, 15, ... - the numbers of dots in triangular patterns.
- Fibonacci-type sequence
- Each term is the sum of the two terms before it.
- Geometric sequence
- Each term is multiplied by the same number to get the next.
- Common ratio
- The number a geometric sequence is multiplied by each time.
- Quadratic sequence (Higher)
- A sequence whose second differences are all the same; its nth term includes \(n^2\).
- Second difference (Higher)
- The difference between neighbouring first differences.
- Binomial
- An expression with two terms, such as \((x + 3)\).
- Product of three binomials
- Three brackets multiplied, such as \((x + 1)(x + 2)(x + 3)\).
- Splitting the middle term
- Writing \(bx\) as two terms so that \(ax^2 + bx + c\) can be factorised in pairs.
- Algebraic fraction
- A fraction with algebra on the top, the bottom or both.
- Proof
- An argument showing something is true in every case, not just the ones tested.