GCSE Mathematics (Foundation) OCR
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62 topics in 5 modules
☑️ Algebra 4 topics
- Inequalities
- Quadratic Equations
- Simultaneous Equations
- Proof
☑️ Graphs 11 topics
- Coordinates and Midpoints
- Straight Line Graphs
- Drawing Straight Line Graphs
- Straight Line Graphs- Gradients
- Straight Line Graphs- y = mx + c
- Using y = mx + c
- Quadratic Graphs
- Harder Graphs
- Solving Equations using Graphs
- Distance-Time Graphs
- Real-Life Graphs
☑️ Ratio, Proportion and Rates of Change 9 topics
- Ratios
- Direct and Inverse Proportion
- Inverse and Proportion Problems
- Percentages
- Compound Growth and Decay
- Unit Conversions
- Area and Volume Conversions
- Time Intervals
- Speed, Density and Pressure
☑️ Angles and Geometry 23 topics
- Properties of 2D Shapes
- Congruent Shapes
- Similiar Shapes
- The Four Transformations
- Perimeter and Area
- Perimeter and Area- Circles
- 3D Shapes
- 3D Shapes- Surface Area
- 3D Shapes- Volume
- Projections
- Angle Basics
- Five Angle Rules
- Parallel Lines
- Geometry Problems
- Angles in Polygons
- Triangle Construction
- Loci and Construction
- Bearings
- Maps and Scale Drawings
- Pythagoras' theorem
- Trigonometry- Sin, Cos and Tan
- Trigonometry- Common Values
- Vectors
☑️ Probability and Statistics 15 topics
- Probability
- Probability Experiements
- The AND/OR Rules
- Tree Diagrams
- Sets and Venn Diagrams
- Sampling and Bias
- Collecting Data
- Mean, Median, Mode and Range
- Simple Charts and Graphs
- Pie Charts
- Scatter Graphs
- Frequency Tables
- Grouped Frequency Tables
- Interpreting Data
- Comparing Data Sets
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GCSE Mathematics (Foundation) OCR Revision Content
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GCSE Mathematics (Foundation) OCR - Algebra - Inequalities Content Preview
Algebra
Inequalities
Understanding Inequalities
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An inequality shows the relationship between two expressions that may not be equal.
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The symbols used in inequalities are > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), ≠ (not equal to).
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A number line can be used to visualise an inequality.
Solving Inequalities
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You can solve inequalities in the same way you solve equations.
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When solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number.
Graphical Representation of Inequalities
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Inequalities can be represented graphically on number lines or coordinate grids.
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An open circle on a number line represents a 'less than' or 'greater than' inequality.
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A closed circle on a number line represents a 'less than or equal to' or 'greater than or equal to' inequality.
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To represent an inequality on a coordinate grid, use a dashed line for 'less than' or 'greater than', and a solid line for 'less than or equal to' or 'greater than or equal to'.
Inequalities with More Than One Variable
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When dealing with inequalities with more than one variable, use similar techniques as with equations.
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Remember to make one variable the subject first if the inequality does not involve a straight-line equation.
Solving Inequalities Involving Absolute Values
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The absolute value of a number is its distance from zero.
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Solving inequalities involving absolute values consists of two steps: solving the equation where the absolute value is greater, then where it is less.
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Simplification methods are used to split the inequality into two separate inequalities based on the absolute value.
Inequalities and Real-Life Situations
- Inequalities are widely used to represent real-life situations. For example, they can be used to describe the minimum or maximum limits on things like speed, weight, costs, etc.
Question: What step must you take when solving an inequality if you are required to multiply or divide by a negative number?
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