Maths · Topic 1: Year 10
Equations and inequalities
Solving linear inequalities, quadratic equations by factorising, the formula and completing the square, and solving simultaneous equations, including linear with quadratic.
Lessons
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1
Solving linear inequalities
Solve linear inequalities, show solutions on a number line, list integer solutions, and at Higher tier show regions on a graph.
6 terms -
2
Solving quadratic equations 1
Solve quadratic equations by factorising, including the difference of two squares and equations that need rearranging first.
6 terms -
3
Solving quadratic equations 2
Solve harder quadratics by factorising when the coefficient of x squared is not 1, and use the quadratic formula when they do not factorise.
6 terms -
4
Completing the square
Write quadratic expressions in the form (x + a) squared plus b, solve equations by completing the square, and find the turning point of a quadratic graph.
6 terms -
5
Solving simple simultaneous equations
Solve pairs of linear equations with two unknowns by elimination and substitution, and read the solution from a graph.
6 terms -
6
More simultaneous equations
Solve simultaneous equations when neither pair of coefficients matches, by multiplying one or both equations first, and solve worded problems.
6 terms -
7
Solving linear and quadratic simultaneous equations
Solve a linear equation and a quadratic equation together by substitution, find the points where a line meets a curve or circle, and show that a line is a…
6 terms
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- Solving linear inequalities.pptx Built from the lesson script on 30 September 2026. View
- Solving linear inequalities - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Solving linear inequalities - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Solving quadratic equations 1.pptx Built from the lesson script on 30 September 2026. View
- Solving quadratic equations 1 - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Solving quadratic equations 1 - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Solving quadratic equations 2.pptx Built from the lesson script on 30 September 2026. View
- Solving quadratic equations 2 - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Solving quadratic equations 2 - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Completing the square.pptx Built from the lesson script on 30 September 2026. View
- Completing the square - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Completing the square - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Solving simple simultaneous equations.pptx Built from the lesson script on 30 September 2026. View
- Solving simple simultaneous equations - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Solving simple simultaneous equations - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- More simultaneous equations.pptx Built from the lesson script on 30 September 2026. View
- More simultaneous equations - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- More simultaneous equations - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Solving linear and quadratic simultaneous equations.pptx Built from the lesson script on 30 September 2026. View
- Solving linear and quadratic simultaneous equations - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Solving linear and quadratic simultaneous equations - Exam Questions.docx Built from the lesson script on 30 September 2026. View
Key terms in this chapter
All 42, gathered from every lesson.
- Inequality
- A statement that compares two values using \(<\), \(>\), \(\le\) or \(\ge\).
- Integer
- A whole number, positive, negative or zero.
- Solution set
- All the values that make an inequality true.
- Boundary line
- The line that separates a region on a graph.
- Region
- An area of a graph that satisfies one or more inequalities.
- Strict inequality
- One with \(<\) or \(>\), not including the boundary.
- Quadratic equation
- An equation whose highest power is \(x^2\).
- Root
- A solution of an equation; where a graph crosses the x-axis.
- Factorise
- Write as a product of brackets.
- Null factor law
- If \(ab = 0\), then \(a = 0\) or \(b = 0\).
- Difference of two squares
- \(a^2 - b^2 = (a - b)(a + b)\).
- Perfect square
- A quadratic that is a bracket squared.
- Coefficient
- The number multiplying a variable, such as the 2 in \(2x^2\).
- Quadratic formula
- \(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
- Discriminant
- The expression \(b^2 - 4ac\) under the square root.
- Surd
- A root that cannot be simplified to a whole number, such as \(\sqrt{7}\).
- Root
- A solution of an equation.
- Substitute
- Replace letters with numbers.
- Completing the square
- Rewriting a quadratic as a squared bracket plus a constant.
- Turning point
- The lowest or highest point of a quadratic graph.
- Minimum value
- The smallest value a function can take.
- Line of symmetry
- The vertical line through the turning point.
- Surd
- A root left in exact form, such as \(\sqrt{11}\).
- Coefficient
- The number multiplying a variable.
- Simultaneous equations
- Two or more equations that are true at the same time.
- Unknown
- A letter standing for a number to be found.
- Elimination
- Removing one unknown by adding or subtracting equations.
- Substitution
- Replacing an unknown with an expression.
- Solution
- The pair of values that satisfies both equations.
- Coefficient
- The number multiplying an unknown.
- Simultaneous equations
- Equations that must both be true for the same unknown values.
- Elimination
- Removing an unknown by adding or subtracting.
- Lowest common multiple
- The smallest number that is a multiple of two numbers.
- Coefficient
- The number multiplying an unknown.
- Substitute
- Replace an unknown by its value.
- Check
- Put the answers back into both equations.
- Tangent
- A line that touches a curve at exactly one point.
- Repeated root
- A solution that occurs twice, such as \(x = 1\) in \((x - 1)^2 = 0\).
- Intersection
- A point where a line and a curve meet.
- Substitution
- Replacing a letter with an expression.
- Circle equation
- \(x^2 + y^2 = r^2\) for a circle centred on the origin.
- Discriminant
- \(b^2 - 4ac\); it shows the number of real roots.