Maths · Topic 2: Year 11
Equations and graphs
Solving simultaneous equations and inequalities graphically, quadratic equations and graphs, cubic equations and using iteration.
Lessons
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1
Solving simultaneous equations graphically
Draw two straight lines on the same grid and read off the point where they cross to solve a pair of simultaneous equations.
6 terms -
2
Representing inequalities graphically
Shade the region that satisfies one or more inequalities on a graph, use solid and dashed boundaries, and write inequalities for a given region.
6 terms -
3
Quadratic equations
Solve quadratic equations by factorising, by using the quadratic formula and by completing the square, and choose a suitable method.
6 terms -
4
Using quadratic graphs
Draw quadratic graphs from a table, find roots, the turning point and the line of symmetry, and use a graph to solve related equations.
6 terms -
5
Cubic equations
Draw and recognise cubic graphs, find their roots and turning points, and use a graph to estimate solutions of cubic equations.
6 terms -
6
Using iteration to solve equations
Show that a root lies in an interval using a change of sign, use decimal search, and use iteration formulae x_(n+1) = f(x_n) to find roots to a given accuracy.
6 terms
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- Solving simultaneous equations graphically.pptx Built from the lesson script on 30 September 2026. View
- Solving simultaneous equations graphically - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Solving simultaneous equations graphically - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Representing inequalities graphically.pptx Built from the lesson script on 30 September 2026. View
- Representing inequalities graphically - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Representing inequalities graphically - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Quadratic equations.pptx Built from the lesson script on 30 September 2026. View
- Quadratic equations - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Quadratic equations - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Using quadratic graphs.pptx Built from the lesson script on 30 September 2026. View
- Using quadratic graphs - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Using quadratic graphs - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Cubic equations.pptx Built from the lesson script on 30 September 2026. View
- Cubic equations - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Cubic equations - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Using iteration to solve equations.pptx Built from the lesson script on 30 September 2026. View
- Using iteration to solve equations - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Using iteration to solve equations - Exam Questions.docx Built from the lesson script on 30 September 2026. View
Key terms in this chapter
All 36, gathered from every lesson.
- Simultaneous equations
- Equations that are both true for the same values.
- Intersection
- The point where two lines cross.
- Gradient
- How steep a line is.
- Intercept
- Where a line crosses an axis.
- Parallel
- Lines with the same gradient.
- Solution
- The values of \(x\) and \(y\) that satisfy both equations.
- Inequality
- A statement using \(<\), \(>\), \(\le\) or \(\ge\).
- Boundary
- The line separating the region from the rest.
- Region
- The set of points that satisfy the inequalities.
- Integer
- A whole number.
- Test point
- A point used to decide which side to shade.
- Solid line
- Boundary included.
- Quadratic
- An equation with a highest power of \(x^2\).
- Factorise
- Write as a product of brackets.
- Root
- A solution of an equation.
- Discriminant
- \(b^2 - 4ac\).
- Completing the square
- Writing \(x^2 + bx + c\) as \((x + p)^2 + q\).
- Surd
- A root that cannot be simplified to a whole number, e.g. \(\sqrt{11}\).
- Parabola
- The U-shaped graph of a quadratic.
- Root
- A value of \(x\) where \(y = 0\).
- Turning point
- The lowest or highest point of the curve.
- Line of symmetry
- The vertical line through the turning point.
- \(y\)-intercept
- Where the graph crosses the y-axis.
- Minimum
- The lowest point of a U-shaped curve.
- Cubic
- An expression or equation with a highest power of \(x^3\).
- Root
- A solution of \(f(x) = 0\).
- Local maximum
- A turning point at the top of a hill.
- Local minimum
- A turning point at the bottom of a valley.
- Intersection
- Where two graphs meet.
- Estimate
- An approximate value from a graph.
- Iteration
- Repeating a calculation using the previous answer.
- Iteration formula
- A rule \(x_{n+1} = f(x_n)\).
- Starting value
- The first value, \(x_0\).
- Change of sign
- \(f(a)\) and \(f(b)\) have opposite signs.
- Root
- A value of \(x\) where \(f(x) = 0\).
- Convergence
- The values getting closer to a limit.