2.9.3
Solving Quadratic Inequalities
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Quadratic Inequalities
Find inequalities for x when x² > 9 and for x² < 9:
x² > 9
- Square root both sides.
- If x² is more than the answer, x must be smaller than the negative or larger than the positive.
x² < 9
- Square root both sides.
- If x² is less than the answer, x must be in between the two values.
- A useful check is to see if x = 0 satisfies the inequality.
- If it does x must be in between the two square roots.
1Number
1.1Using Numbers
1.1.1Equal Symbols1.1.2Negative Numbers1.1.3BIDMAS1.1.4Inverse Operations1.1.5End of Topic Test- Ordering1.1.6Factors1.1.7Multiples1.1.8Highest Common Factor1.1.9Lowest Common Multiple1.1.10Number of Ways to Do a Task1.1.11Number of Combinations1.1.12Number of Ways To Arrange Objects1.1.13End of Topic Test - Factors, Multiples & Combos1.1.14Standard Form1.1.15Ordinary Numbers to Standard Form1.1.16Addition in Standard Form1.1.17Subtraction in Standard Form1.1.18Multiplication in Standard Form1.1.19Division in Standard Form1.1.20Exam-Style Questions - Standard Form & Primes1.1.21Long Division1.1.22Prime Numbers1.1.23End of Topic Test - Standard Form & Long Division1.1.24Diagnostic Misconceptions - 1 NOT a Prime Number1.1.25Diagnostic Misconceptions - BIDMAS1.1.26Diagnostic Misconceptions - Adding Negatives
1.2Fractions, Decimals & Percentages
1.2.1Adding Fractions1.2.2Subtracting Fractions1.2.3Multiplying Fractions1.2.4Dividing Fractions1.2.5Mixed Fractions1.2.6Calculating Percentages of Numbers1.2.7Calculating Fractions of Numbers1.2.8Multiply Decimals1.2.9Place Value1.2.10Recurring Decimals1.2.11Exam-Style Questions - Recurring Decimals1.2.12Convert Fractions & Terminating Decimals1.2.13Convert Recurring Decimals1.2.14Convert Decimals & Percentages1.2.15Compare Decimals1.2.16Compare Fractions1.2.17Exam-Style Questions - Percentages1.2.18End of Topic Test - Fractions & Decimals1.2.19Diagnostic Misconceptions - Adding Fractions
1.3Powers & Roots
1.3.1Powers1.3.2Roots1.3.3Indices Advanced1.3.4Estimating Powers1.3.5Estimating Roots1.3.6Multiplying Powers1.3.7Dividing Powers1.3.8Power Raised to Power1.3.9Fractions Raised to a Power1.3.10Numbers Raised to Negative Powers1.3.11Roots of Numbers1.3.12Numbers to the Power of 1 & 01.3.13Surds1.3.14Simplify Surds1.3.15Rationalise Denominator1.3.16Exam-Style Questions - Indices1.3.17End of Topic Test - Powers & Roots1.3.18Diagnostic Misconceptions - Squaring1.3.19Diagnostic Misconceptions - Simplifying Surds
2Algebra
2.1Introduction to Algebra
2.1.1Algebra Basics2.1.2Substituting Values2.1.3Algebraic Vocabulary2.1.4Collecting Terms2.1.5End of Topic Test - Algebra Basics & Power Rules2.1.6Expanding Brackets I2.1.7Common Factors2.1.8Expanding Brackets II2.1.9Rearrange For x2.1.10Rearrange with Powers2.1.11Exam-Style Questions - Basics of Algebra2.1.12End of Topic Test - Expanding & Rearranging
2.2Manipulating Algebra
2.2.1How to Factorise2.2.2Factorising Quadratics2.2.3Algebraic Fractions - Addition & Subtraction2.2.4Algebraic Fractions - Multiplication & Division2.2.5Diagnostic Misconceptions - Common Denominators2.2.6Factorising Quadratics (tt)2.2.7Simplify algebraic fractions - cancelling factors2.2.8Simplify algebraic fractions - factorisation
2.3Proofs & Functions
2.4Straight Line Graphs
2.5Common Graphs
2.6Transformations & Tangents
2.7Properties of Graphs
2.8Solving Equations
2.8.1Solve Linear Equations2.8.2Linear Equations with Fractions2.8.3Solve Linear Equations Graphically2.8.4Quadratic ±2.8.5Factorise Quadratics2.8.6Quadratic Formula2.8.7Complete the Square2.8.8Solve Quadratics Graphically2.8.9End of Topic Test - Solving Equations2.8.10Simultaneous Equations2.8.11Quadratic Simultaneous Equations2.8.12Simultaneous Equations - Graphs2.8.13Simultaneous Equations - Word Problems2.8.14Approximate Solutions - Number of Iterations2.8.15Approximate Solutions - Iterations to 1 DP2.8.16Approximate Solutions - Iteration Formula2.8.17Exam-Style Questions - Simultaneous Equations2.8.18End of Topic Test - Simultaneous Equations2.8.19Diagnostic Misconceptions - Solving Quadratics
2.9Inequalities
2.10Sequences
2.10.1Nth Term Rules2.10.2Recurrence Relationships2.10.3Find Nth Term in Linear Sequence2.10.4Check If a Number is In a Sequence2.10.5Exam-Style Questions - Sequences2.10.6Arithmetic & Geometric Progressions2.10.7Key Sequences2.10.8Quadratic Sequences2.10.9Find Nth Term in Quadratic Sequence2.10.10Exam-Style Questions - Geometric Series2.10.11End of Topic Test - Sequences2.10.12Nth Term Rules (tt)
3Ratio
3.1Ratios in Practice
3.2Manipulating Ratios
3.2.1Simplifying Ratios3.2.2Turn Ratios into Equations3.2.3Ratio Notation & Reduction3.2.4End of Topic Test - Units & Ratios3.2.5Part : Part Ratio3.2.6Part : Whole Ratio3.2.7Two Ratios3.2.8Differences in Ratios3.2.9Fractions in Ratios3.2.10Numbers as Fractions3.2.11Ratios to Fractions3.2.12Exam-Style Questions - Ratios3.2.13End of Topic Test - Fractions & Ratios3.2.14Diagnostic Misconceptions - Combining Ratios
3.3Percentage & Interest
3.3.1Convert Percentages to Decimals3.3.2Convert Percentages to Fractions3.3.3Find the Percentage3.3.4More/Less Percentage3.3.5Price from Percentage Change3.3.6Calculate Percentage Change from Price3.3.7End of Topic Test - Percentages3.3.8Profit & Interest & Discount3.3.9Original Price after Discounts3.3.10Simple Interest3.3.11Compound Growth & Decay3.3.12Compound Interest3.3.13Compound Interest - After How Many Days?3.3.14End of Topic Test - Percentages in Finance
3.4Proportion
4Geometry
4.1Introduction to Geometry
4.1.1Geometry Basics4.1.2Geometry Basics 24.1.3Regular Polygons4.1.4Triangles & Angles4.1.5Midpoint4.1.6Bisectors & Perpendiculars4.1.7Locus4.1.8Angle rules4.1.9Parallel Angle Rules4.1.10Angles in a Polygon4.1.11Angles in a Triangle4.1.12Exam-Style Questions - Angles in Shapes4.1.13End of Topic Test - Geometry
4.2Triangles & Quadrilaterals
4.3Transformations
4.4Circle Basics
4.5Circle Theorems
4.5.1Perpendicular Bisector of a Chord4.5.2Angle at the Centre4.5.3Angle of a Semicircle4.5.4Opposite Angles in Cyclic Quadrilaterals4.5.5Tangent Lengths4.5.6Angle in the Same Segment4.5.7Alternate Segment Theorem4.5.8Exam-Style Questions - Circle Theorems4.5.9Diagnostic Misconceptions - Circumference & Radius
4.6Measurements & Units
4.7Calculating Area
4.8Triangle Formulae
4.93D Shapes
4.9.1Types of 3D Shape4.9.2Plans & Elevations4.9.3Nets4.9.4Volume of 3D Shapes4.9.5Volume of a Cuboid4.9.6Volume of a Cylinder4.9.7Volume of a Sphere4.9.8Volume of a Hemisphere4.9.9Volume of a Cone4.9.10Volume of a Pyramid4.9.11Surface Area & Composite Shapes4.9.12Surface Area of a Cuboid4.9.13Surface Area of a Cylinder4.9.14Surface Area of a Sphere/Hemisphere4.9.15Surface Area of a Cone4.9.16Exam-Style Questions - Volume
5Probability
5.1Introduction to Probability
5.2Representing Probabilities
5.3Probability Calculations
5.3.1Theoretical Probabilities5.3.2Multiple Events5.3.3Probability Calculations5.3.4Dependent Events5.3.5Independent Events5.3.6Probability Tree Diagram5.3.7Complex Tree Diagrams5.3.8Conditional Probability5.3.9Conditional Probability From a Two Way Table5.3.10Conditional Probability Venn Diagrams5.3.11Conditional Probability Tree Diagrams5.3.12Exam-Style Questions - Probability5.3.13End of Topic Test - Probability5.3.14Diagnostic Misconceptions - Denominator
6Statistics
6.1Introduction to Statistics
6.2Charts & Diagrams
6.2.1Bar Charts6.2.2Pie Charts6.2.3Stem & Leaf Diagrams6.2.4Back to Back Stem & Leaf Diagrams6.2.5End of Topic Test - Statistics6.2.6Pictograms6.2.7Time Series Graphs6.2.8Histograms6.2.9Histograms 26.2.10Frequency Polygons6.2.11Cumulative Frequency6.2.12Cumulative Frequency 26.2.13Scatter Graphs6.2.14Scatter Graphs - Predictions6.2.15Correlation & Causation6.2.16Exam-Style Questions - Cumulative Frequency
6.3Comparing Datasets
Jump to other topics
1Number
1.1Using Numbers
1.1.1Equal Symbols1.1.2Negative Numbers1.1.3BIDMAS1.1.4Inverse Operations1.1.5End of Topic Test- Ordering1.1.6Factors1.1.7Multiples1.1.8Highest Common Factor1.1.9Lowest Common Multiple1.1.10Number of Ways to Do a Task1.1.11Number of Combinations1.1.12Number of Ways To Arrange Objects1.1.13End of Topic Test - Factors, Multiples & Combos1.1.14Standard Form1.1.15Ordinary Numbers to Standard Form1.1.16Addition in Standard Form1.1.17Subtraction in Standard Form1.1.18Multiplication in Standard Form1.1.19Division in Standard Form1.1.20Exam-Style Questions - Standard Form & Primes1.1.21Long Division1.1.22Prime Numbers1.1.23End of Topic Test - Standard Form & Long Division1.1.24Diagnostic Misconceptions - 1 NOT a Prime Number1.1.25Diagnostic Misconceptions - BIDMAS1.1.26Diagnostic Misconceptions - Adding Negatives
1.2Fractions, Decimals & Percentages
1.2.1Adding Fractions1.2.2Subtracting Fractions1.2.3Multiplying Fractions1.2.4Dividing Fractions1.2.5Mixed Fractions1.2.6Calculating Percentages of Numbers1.2.7Calculating Fractions of Numbers1.2.8Multiply Decimals1.2.9Place Value1.2.10Recurring Decimals1.2.11Exam-Style Questions - Recurring Decimals1.2.12Convert Fractions & Terminating Decimals1.2.13Convert Recurring Decimals1.2.14Convert Decimals & Percentages1.2.15Compare Decimals1.2.16Compare Fractions1.2.17Exam-Style Questions - Percentages1.2.18End of Topic Test - Fractions & Decimals1.2.19Diagnostic Misconceptions - Adding Fractions
1.3Powers & Roots
1.3.1Powers1.3.2Roots1.3.3Indices Advanced1.3.4Estimating Powers1.3.5Estimating Roots1.3.6Multiplying Powers1.3.7Dividing Powers1.3.8Power Raised to Power1.3.9Fractions Raised to a Power1.3.10Numbers Raised to Negative Powers1.3.11Roots of Numbers1.3.12Numbers to the Power of 1 & 01.3.13Surds1.3.14Simplify Surds1.3.15Rationalise Denominator1.3.16Exam-Style Questions - Indices1.3.17End of Topic Test - Powers & Roots1.3.18Diagnostic Misconceptions - Squaring1.3.19Diagnostic Misconceptions - Simplifying Surds
2Algebra
2.1Introduction to Algebra
2.1.1Algebra Basics2.1.2Substituting Values2.1.3Algebraic Vocabulary2.1.4Collecting Terms2.1.5End of Topic Test - Algebra Basics & Power Rules2.1.6Expanding Brackets I2.1.7Common Factors2.1.8Expanding Brackets II2.1.9Rearrange For x2.1.10Rearrange with Powers2.1.11Exam-Style Questions - Basics of Algebra2.1.12End of Topic Test - Expanding & Rearranging
2.2Manipulating Algebra
2.2.1How to Factorise2.2.2Factorising Quadratics2.2.3Algebraic Fractions - Addition & Subtraction2.2.4Algebraic Fractions - Multiplication & Division2.2.5Diagnostic Misconceptions - Common Denominators2.2.6Factorising Quadratics (tt)2.2.7Simplify algebraic fractions - cancelling factors2.2.8Simplify algebraic fractions - factorisation
2.3Proofs & Functions
2.4Straight Line Graphs
2.5Common Graphs
2.6Transformations & Tangents
2.7Properties of Graphs
2.8Solving Equations
2.8.1Solve Linear Equations2.8.2Linear Equations with Fractions2.8.3Solve Linear Equations Graphically2.8.4Quadratic ±2.8.5Factorise Quadratics2.8.6Quadratic Formula2.8.7Complete the Square2.8.8Solve Quadratics Graphically2.8.9End of Topic Test - Solving Equations2.8.10Simultaneous Equations2.8.11Quadratic Simultaneous Equations2.8.12Simultaneous Equations - Graphs2.8.13Simultaneous Equations - Word Problems2.8.14Approximate Solutions - Number of Iterations2.8.15Approximate Solutions - Iterations to 1 DP2.8.16Approximate Solutions - Iteration Formula2.8.17Exam-Style Questions - Simultaneous Equations2.8.18End of Topic Test - Simultaneous Equations2.8.19Diagnostic Misconceptions - Solving Quadratics
2.9Inequalities
2.10Sequences
2.10.1Nth Term Rules2.10.2Recurrence Relationships2.10.3Find Nth Term in Linear Sequence2.10.4Check If a Number is In a Sequence2.10.5Exam-Style Questions - Sequences2.10.6Arithmetic & Geometric Progressions2.10.7Key Sequences2.10.8Quadratic Sequences2.10.9Find Nth Term in Quadratic Sequence2.10.10Exam-Style Questions - Geometric Series2.10.11End of Topic Test - Sequences2.10.12Nth Term Rules (tt)
3Ratio
3.1Ratios in Practice
3.2Manipulating Ratios
3.2.1Simplifying Ratios3.2.2Turn Ratios into Equations3.2.3Ratio Notation & Reduction3.2.4End of Topic Test - Units & Ratios3.2.5Part : Part Ratio3.2.6Part : Whole Ratio3.2.7Two Ratios3.2.8Differences in Ratios3.2.9Fractions in Ratios3.2.10Numbers as Fractions3.2.11Ratios to Fractions3.2.12Exam-Style Questions - Ratios3.2.13End of Topic Test - Fractions & Ratios3.2.14Diagnostic Misconceptions - Combining Ratios
3.3Percentage & Interest
3.3.1Convert Percentages to Decimals3.3.2Convert Percentages to Fractions3.3.3Find the Percentage3.3.4More/Less Percentage3.3.5Price from Percentage Change3.3.6Calculate Percentage Change from Price3.3.7End of Topic Test - Percentages3.3.8Profit & Interest & Discount3.3.9Original Price after Discounts3.3.10Simple Interest3.3.11Compound Growth & Decay3.3.12Compound Interest3.3.13Compound Interest - After How Many Days?3.3.14End of Topic Test - Percentages in Finance
3.4Proportion
4Geometry
4.1Introduction to Geometry
4.1.1Geometry Basics4.1.2Geometry Basics 24.1.3Regular Polygons4.1.4Triangles & Angles4.1.5Midpoint4.1.6Bisectors & Perpendiculars4.1.7Locus4.1.8Angle rules4.1.9Parallel Angle Rules4.1.10Angles in a Polygon4.1.11Angles in a Triangle4.1.12Exam-Style Questions - Angles in Shapes4.1.13End of Topic Test - Geometry
4.2Triangles & Quadrilaterals
4.3Transformations
4.4Circle Basics
4.5Circle Theorems
4.5.1Perpendicular Bisector of a Chord4.5.2Angle at the Centre4.5.3Angle of a Semicircle4.5.4Opposite Angles in Cyclic Quadrilaterals4.5.5Tangent Lengths4.5.6Angle in the Same Segment4.5.7Alternate Segment Theorem4.5.8Exam-Style Questions - Circle Theorems4.5.9Diagnostic Misconceptions - Circumference & Radius
4.6Measurements & Units
4.7Calculating Area
4.8Triangle Formulae
4.93D Shapes
4.9.1Types of 3D Shape4.9.2Plans & Elevations4.9.3Nets4.9.4Volume of 3D Shapes4.9.5Volume of a Cuboid4.9.6Volume of a Cylinder4.9.7Volume of a Sphere4.9.8Volume of a Hemisphere4.9.9Volume of a Cone4.9.10Volume of a Pyramid4.9.11Surface Area & Composite Shapes4.9.12Surface Area of a Cuboid4.9.13Surface Area of a Cylinder4.9.14Surface Area of a Sphere/Hemisphere4.9.15Surface Area of a Cone4.9.16Exam-Style Questions - Volume
5Probability
5.1Introduction to Probability
5.2Representing Probabilities
5.3Probability Calculations
5.3.1Theoretical Probabilities5.3.2Multiple Events5.3.3Probability Calculations5.3.4Dependent Events5.3.5Independent Events5.3.6Probability Tree Diagram5.3.7Complex Tree Diagrams5.3.8Conditional Probability5.3.9Conditional Probability From a Two Way Table5.3.10Conditional Probability Venn Diagrams5.3.11Conditional Probability Tree Diagrams5.3.12Exam-Style Questions - Probability5.3.13End of Topic Test - Probability5.3.14Diagnostic Misconceptions - Denominator
6Statistics
6.1Introduction to Statistics
6.2Charts & Diagrams
6.2.1Bar Charts6.2.2Pie Charts6.2.3Stem & Leaf Diagrams6.2.4Back to Back Stem & Leaf Diagrams6.2.5End of Topic Test - Statistics6.2.6Pictograms6.2.7Time Series Graphs6.2.8Histograms6.2.9Histograms 26.2.10Frequency Polygons6.2.11Cumulative Frequency6.2.12Cumulative Frequency 26.2.13Scatter Graphs6.2.14Scatter Graphs - Predictions6.2.15Correlation & Causation6.2.16Exam-Style Questions - Cumulative Frequency
6.3Comparing Datasets
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