Like terms are terms that have the same set of variables and corresponding exponents.

Simplifying is to write an expression in a more efficient and compact form without affecting the value of the original expression. Fully simplifying means the expression cannot be simplified further.

Checking and securing understanding of simplifying

Maths

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

Algebraic manipulation

Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values.

Checking and securing understanding of substitution

A term is single number or letter, or the product of numbers and/or variables. Each term is separated by the operators + and –

Expressions contain one or more terms, where each term is separated by an operator.

An equation is used to show 2 expressions that are equal to each other.

An identity is an equation that holds true for all values of the variables. The symbol ≡ is used to show two expressions are equivalent and form an identity.

A formula is a rule linking sets of physical variables in context.

Further algebraic terminology

The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Checking and securing understanding of expanding a single bracket

A factor is a term which exactly divides another term.

To factorise is to express a term as the product of its factors.

Checking and securing understanding of factorising 

An interior angle is an angle formed inside a polygon by two of its edges.

Vertically opposite angles are pairs of opposite angles formed when two lines intersect at a point. They are equal.

Checking and securing understanding of forming linear equations

The additive inverse of a number is a number that, when added to the original number, gives the sum of 0.

The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Checking and securing understanding of solving and interpreting linear equations

The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1.

Checking and securing understanding of changing the subject

A binomial is an algebraic expression representing the sum or difference of exactly 2 unlike terms.

Any of the multiplication results that lead up to an overall multiplication result.

Checking and securing understanding of the product of two binomials

The product of three binomials

To express a term as the product of its factors.

A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2

Factorising a quadratic expression

The absolute value of a number is its distance from zero.

Factorising using the difference of two squares

Factorising quadratics of the form ax^2 + bx + c

A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.

A parabola is a curve where any point on the curve is an equal distance from: a fixed point (the focus ), and a fixed straight line (the directrix ).

Solving quadratic equations by factorising

Solving quadratic equations by factorising where rearrangement is required

Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q

Solving quadratic equations by completing the square

The quadratic formula is a formula for finding the solutions to any quadratic equation of the form ax^2 + bx + c = 0

Solving quadratic equations by using the formula

A partial product refers to any of the multiplication results that lead up to an overall multiplication result.

A binomial is an algebraic expression representing the sum or difference of exactly two unlike terms.

Algebraic manipulation

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