Maths · OCR Paper 1
Algebra
The algebra skills tested on OCR Paper 1: simplifying and expanding, factorising, solving equations and inequalities, rearranging formulae, and sequences.
Lessons
Ticks are remembered on this device only.
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1
Simplifying and Expanding Expressions
Algebraic notation, collecting like terms, and expanding single brackets, double brackets and squared brackets.
10 terms -
2
Factorising Expressions
Taking out common factors, factorising quadratics, and using the difference of two squares.
10 terms -
3
Solving Linear Equations and Inequalities
Solving equations with brackets, fractions and unknowns on both sides, forming equations, and solving inequalities.
10 terms -
4
Substitution and Rearranging Formulae
Substituting into formulae, writing your own, and changing the subject of a formula.
10 terms -
5
Sequences and the nth Term
Continuing sequences, finding the nth term of linear and quadratic sequences, and testing whether a number is in a sequence.
10 terms
Key terms in this chapter
All 50, gathered from every lesson.
- Consecutive
- Following one after another in order, such as the consecutive integers 7, 8 and 9.
- Term
- A single part of an expression, with the sign in front of it, such as \(-3x\).
- Expression
- A collection of terms with no equals sign, such as \(3x + 5\).
- Equation
- A statement that two expressions are equal, which is true only for certain values.
- Formula
- A rule that links quantities using letters, such as \(A = lw\).
- Identity
- An equation that is true for all values of the letters, written with the symbol \(\equiv\).
- Like terms
- Terms with the same letters raised to the same powers.
- Coefficient
- The number that multiplies a letter in a term.
- Expand
- Multiply out brackets to remove them.
- Simplify
- Write an expression in its shortest form by collecting like terms.
- Algebraic fraction
- A fraction whose numerator or denominator contains algebraic terms.
- Factorise
- Write an expression as a product of brackets, the reverse of expanding.
- Common factor
- A number or letter that divides exactly into every term of an expression.
- Fully factorised
- Written with the highest possible common factor taken out, with nothing common left inside the brackets.
- Quadratic expression
- An expression whose highest power is \(x^2\), such as \(x^2 + 5x + 6\).
- Coefficient
- The number multiplying a letter in a term.
- Constant term
- The term in an expression that is just a number, with no letter.
- Difference of two squares
- An expression of the form \(a^2 - b^2\), which factorises to \((a + b)(a - b)\).
- Perfect square
- A number or term that is the square of another, such as 49 or \(4x^2\).
- Factorising by grouping
- Splitting the middle term of a quadratic and factorising the terms in pairs.
- Boundary value
- The value at which an inequality changes from true to false, such as 4 in \(x < 4\).
- Equation
- A statement that two expressions are equal, which is true only for certain values of the unknown.
- Solve
- Find the value or values of the unknown that make an equation or inequality true.
- Inverse operation
- The operation that undoes another, such as subtraction undoing addition.
- Unknown
- A letter that stands for a number you need to find.
- Inequality
- A statement that compares two expressions using \(<\), \(>\), \(\leq\) or \(\geq\).
- Integer solutions
- The whole-number values that satisfy an inequality.
- Open circle
- The symbol on a number line showing that an end value is not included.
- Filled circle
- The symbol on a number line showing that an end value is included.
- Substitute
- Replace a letter with a number.
- Output
- The result of putting an input through a formula or a function machine.
- Substitute
- Replace a letter in an expression or formula with a number.
- Formula
- A rule that links quantities using letters.
- Subject of a formula
- The letter on its own on one side of the equals sign.
- Rearrange
- Change a formula so that a different letter is the subject.
- Variable
- A letter that can take different values.
- Inverse operation
- The operation that undoes another, such as division undoing multiplication.
- Function machine
- A diagram showing the operations applied to an input, in order, to give an output.
- Constant
- A quantity that has a fixed value and does not change.
- Evaluate
- Work out the numerical value of an expression.
- Common ratio
- The number that each term of a geometric sequence is multiplied by to get the next term.
- Sequence
- A list of numbers that follow a rule.
- Term
- One of the numbers in a sequence.
- Term-to-term rule
- A rule that tells you how to get from one term to the next.
- nth term
- A formula that gives the term in position \(n\) of a sequence.
- Arithmetic sequence
- A sequence that increases or decreases by the same amount each time.
- Common difference
- The constant amount added to get from one term of an arithmetic sequence to the next.
- Geometric sequence
- A sequence in which each term is multiplied by the same number to get the next.
- Fibonacci-type sequence
- A sequence in which each term is the sum of the two terms before it.
- Quadratic sequence
- A sequence whose nth term includes an \(n^2\) term, so its second difference is constant.