Form 4 Mathematics
Contents
Chapter 1: Algebra 4 (Inequalities and Linear Programming)
1.1. Introduction
1.2. Solving Inequalities
1.2.1. Solving simple linear inequalities
1.2.2. Solving simultaneous inequalities
1.3. Graphical Representation of Inequalities
1.3.1. Representing inequalities on a number line
1.3.2. Illustrating an inequality on the Cartesian plane
1.4. Linear Programming
1.5. Summary
1.6. Further Reading
1.7. Assessment Test
Chapter 2: Trigonometry Ratios 1
2.1. Introduction
2.2. Pythagoras’ Theorem
2.2.1. Pythagorean Triples
2.3. Trigonometric Ratios
2.3.1. Tangent
2.3.2. Sine
2.3.3. Cosine
2.4. Angles of Elevation and Depression
2.5. Summary
2.6. Further Reading
2.7. Assessment Test
Chapter 3: Variation
3.1. Introduction
3.2. Direct Variation
3.3. Inverse Variation / Indirect Variation
3.4. Joint Variation
3.5. Partial Variation
3.6. Summary
3.7. Further Reading
3.8. Assessment Test
Chapter 4: Trigonometry 2
4.1. Introduction
4.2. Area of a Triangle using the Sine Ratio
4.3. The Sine Rule
4.4. Sine Rule with Bearing
4.5. The Cosine Rule
4.6. Cosine Rule with Bearing
4.7. Summary
4.8. Further Reading
4.9. Assessment Test
Chapter 5: Travel Graphs
5.1. Introduction
5.2. Speed Time Graphs
5.3. Velocity Time Graphs
5.4. Distance Time Graphs
5.5. Summary
5.6. Further Reading
5.7. Assessment Test
Chapter 6: Probability
6.1. Introduction
6.2. Probability Definition
6.3. Experimental Probability
6.4. Theoretical Probability
6.5. Mutually Exclusive Events
6.6. Independent Events
6.7. Combined Events
6.8. Outcome Tables
6.9. Tree Diagram
6.10. Summary
6.11. Further Reading
6.12. Assessment Test
Chapter 7: Vectors
7.1. Introduction
7.2. Types of Vectors
7.2.1. Vector Notation
7.2.2. Translation Vectors
7.2.3. Equal Vectors
7.2.4. Negative Vectors
7.2.5. Parallel Vectors
7.2.6. Position Vectors
7.3. Magnitude of Vectors
7.4. Combined Vectors
7.4.1. Sum of Vectors
7.5. Vector Properties of Plane Shapes
7.6. Vector Algebra (Finding Scalars)
7.7. Summary
7.8. Further Reading
7.9. Assessment Test
Chapter 8: Transformation 1
8.1. Introduction
8.2. Translation
8.2.1. Vector notation of a translation vector
8.3. Rotation
8.3.1. 90° rotation
8.3.2. 180° rotation
8.3.3. 270° rotation
8.4. Reflection
8.5. Enlargement
8.5.1. Positive enlargement scale factor
8.5.2. Negative enlargement scale factor
8.5.3. Fractional scale factor
8.6. Summary
8.7. Further Reading
8.8. Assessment Test
Chapter 9: Functional Graphs 2
9.1. Introduction
9.2. Quadratic Function / Graphs
9.2.1. Examples of Quadratic Functions
9.2.2. Plotting Quadratic Graphs / Functions
9.2.3. Area under the Curve (under the Quadratic Graph)
9.2.4. Gradient of a Quadratic Function
9.2.5. Roots of a Quadratic Function
9.2.6. Maximum and Minimum
9.2.7. Line of Symmetry
9.3. Inverse Graph / Function
9.3.1. Plotting an Inverse Function
9.3.2. Area Under the Inverse Function / Curve / Graph
9.3.3. Gradient of an Inverse Function
9.3.4. Intersection of a Line and the Inverse Function
9.4. Summary
9.5. Further Reading
9.6. Assessment Test
Chapter 10: Geometry
10.1. Introduction
10.2. Geometrical Construction
10.2.1. Construction of Quadrilaterals
10.2.2. Construction of a Perpendicular Line from a Point to a Line
10.2.3. Construction of an Inscribed Circle of a Triangle
10.2.4. Construction of a Circumscribed Circle of a Triangle
10.3. Locus
10.3.1. The Locus of Points Equidistant from a Fixed Point
10.3.2. The Locus of Points Equidistant from two Fixed Points
10.3.3. The Locus of Points Equidistant from a Straight Line
10.3.4. The Locus of Points Equidistant from two Intersecting Straight Lines
10.4. Summary
10.5. Further Reading
10.6. Assessment Test
Chapter 11: Statistics
11.1. Introduction
11.2. Statistics – Data Collection
11.3. Data Classification
11.4. Histogram and Frequency Polygon
11.4.1. Histogram with Equal Class Width
11.4.2. Frequency Polygon
11.4.3. Histogram with Unequal Width
11.5. Cumulative Curve
11.6. Measures of Dispersion
11.7. Summary
11.8. Further Reading
11.9. Assessment Test
Chapter 12: Transformation 2
12.1. Introduction
12.2. Reflection in any Line and use of Matrices
12.2.1. Reflection in any Line (Geometrical Solution)
12.2.2. Use of Matrices in Reflections
12.3. Rotation by Drawing and use of Matrices
12.3.1. Rotation by Drawing (Geometrical Construction)
12.3.2. Matrices in Rotation Transformation
12.4. Enlargement using Matrices
12.5. Stretch (One Way and Two Way)
12.6. Shear using Matrices and Geometrical Methods
12.7. Combination of Transformations
12.8. Summary
12.9. Further Reading
12.10. Assessment Test