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Edexcel

Maths · Edexcel Paper 1

Further Algebra

The further algebra skills tested on Edexcel Paper 1: solving quadratics, simultaneous equations, inequalities and regions, surds, and algebraic fractions and proof.

  • 5 lessons
  • Edexcel
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Lessons

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Key terms in this chapter

All 45, gathered from every lesson.

Quadratic equation
An equation whose highest power of \(x\) is \(x^2\), usually with two solutions.
Factorise
Write an expression as a product of brackets.
Root
A solution of an equation, shown where its graph crosses the \(x\)-axis.
Discriminant
The expression \(b^2 - 4ac\) from the quadratic formula.
Quadratic formula
A formula that gives the solutions of any quadratic equation.
Completing the square
Rewriting \(x^2 + bx + c\) as \((x + p)^2 + q\).
Repeated root
A root that comes from a bracket squared, such as \((x - 3)^2 = 0\).
Coefficient
The number multiplying a letter, such as 2 in \(2x^2\).
Substitute
Replace a letter with its value.
Simultaneous equations
Equations that are true for the same values of the unknowns.
Elimination
Adding or subtracting equations to remove one unknown.
Substitution
Replacing a letter in one equation with its value or expression from another.
Unknown
A letter standing for a number that has to be found.
Solution pair
The values of \(x\) and \(y\) that make both equations true.
Intersection
The point where two lines or curves cross.
Linear equation
An equation whose graph is a straight line.
Coefficient
The number in front of a letter.
Equation (1) and (2)
Labels used to refer to each equation when you add or subtract them.
Inequality
A statement that one value is less than or greater than another.
Region
An area of a graph that satisfies one or more inequalities.
Boundary
The line that separates the points that satisfy an inequality from those that do not.
Solid line
A boundary that is included in the region.
Dashed line
A boundary that is not included in the region.
Integer
A whole number, positive, negative or zero.
Integer point
A point whose coordinates are both whole numbers.
Double inequality
An inequality with two parts, such as \(-2 < x \leq 3\).
Test point
A point put into an inequality to see which side of the line to shade.
Surd
A root of a number that cannot be written as a whole number or fraction.
Irrational
A number that cannot be written as a fraction, with a decimal that never ends or repeats.
Rationalise
Remove a surd from the denominator of a fraction.
Conjugate
An expression with the sign between two terms changed, such as \(2 - \sqrt{3}\) for \(2 + \sqrt{3}\).
Square factor
A factor that is a square number, such as 4 or 9.
Like surds
Surds with the same number under the root, which can be added or subtracted.
Exact value
An answer left in terms of surds or \(\pi\) rather than rounded.
Square root
The number that gives a stated number when multiplied by itself.
Denominator
The bottom of a fraction.
Algebraic fraction
A fraction whose top or bottom contains letters.
Cancel
Divide the top and bottom of a fraction by the same factor.
Common denominator
A shared multiple of the denominators, used to add or subtract fractions.
Proof
A logical argument that shows a statement is always true.
Counter-example
A single example that shows a statement is false.
Identity
An equation that is true for all values, written with \(\equiv\).
Consecutive
Following one after another, such as \(n\) and \(n + 1\).
Factor
An expression that divides exactly into another.
Multiple
A number in the times table of another number.