Form 3 Mathematics
Contents
Chapter 1: Real Numbers
1.1. Introduction
1.2. Number concepts and operations
1.3. Ratios, rates and proportions
1.4. Irrational numbers
1.5. Approximations, estimations and limits of accuracy
1.6. Ordinary and standard form
1.7. Number bases
1.8. Scale and simple map problems
1.9. Number patterns and sequences
1.10. Summary
1.11. Further reading
1.12. Test 1
Chapter 2: Algebra 1
2.1. Introduction
2.2. Lowest common multiple (LCM) and highest common factor (HCF)
2.2.1. Lowest common multiple (LCM)
2.2.2. Highest common factor (HCF)
2.3. Algebraic manipulations
2.3.1. Linear expressions
2.3.1.1. Expressions with brackets
2.3.1.2. Expressions with fractions
2.3.2. Factorisation
2.3.2.1. Factorising two terms
2.3.2.2. Factorising four terms
2.3.2.3. Factorising three terms (quadratic expressions)
2.3.3. Substitution
2.4. Algebraic fractions
2.4.1. Lowest terms
2.4.2. Addition and subtraction of algebraic fractions
2.4.3. Multiplication and division of algebraic fractions
2.5. Summary
2.6. Further reading
2.7. Test 2
Chapter 3: Sets
3.1. Introduction
3.2. Set builder notation
3.3. Venn diagrams with two subsets
3.4. Venn diagrams with three subsets
3.5. Summary
3.6. Further reading
3.7. Test 3
Chapter 4: Algebra 2
4.1. Introduction
4.2. Linear equations
4.2.1. Simple linear equations
4.2.2. Equations with fractions
4.3. Substitution of values
4.4. Changing the subject of the formula
4.4.1. Formula with brackets
4.4.2. Formula with squares and square roots
4.5. Simultaneous equations
4.5.1. Solving simultaneous equations by elimination
4.5.2. Solving simultaneous equations by substitution
4.6. Quadratic equations
4.6.1. Solving quadratic equations by factorisation
4.6.2. Solving quadratic equations using the perfect square case
4.6.3. Solving quadratic equations using the quadratic formula
4.7. Summary
4.8. Further reading
4.9. Test 4
Chapter 5: Functional Graphs
5.1. Introduction
5.2. Functional notation
5.2.1. Formation of the functional notation
5.2.2. Calculations in functional notation
5.3. Linear functions/graphs
5.3.1. Plotting a linear function/graph
5.3.2. Gradient of linear functions
5.3.3. Finding the gradient from the equation of a straight line
5.4. Cubic function/graph
5.4.1. Plotting the cubic function
5.4.2. Area under the curve
5.4.3. Gradient on a cubic function
5.4.4. Roots of a cubic function
5.4.5. Turning points of the cubic function
5.5. Summary
5.6. Further reading
5.7. Test 5
Chapter 6: Matrices
6.1. Introduction
6.2. Order of a matrix
6.3. Addition and subtraction of matrices
6.4. Scalar multiplication and equal matrices
6.5. Multiplication of matrices
6.6. Determinant of 2 × 2 matrices
6.7. Inverse of 2 × 2 matrices
6.8. Identity matrices
6.9. Singular and non-singular matrices
6.10. Simultaneous linear equations in two variables
6.11. Summary
6.12. Further reading
6.13. Test 6
Chapter 7: Geometry 1
7.1. Introduction
7.2. Points, lines and angles
7.2.1. A right angle is equal to 90°
7.2.2. Vertically opposite angles are equal
7.2.3. Angles on a straight line add up to 180°
7.2.4. The sum of all angles in a triangle is 180°
7.2.5. The sum of all angles around a point is 360°
7.2.6. Corresponding angles are equal
7.2.7. Alternate angles are equal
7.3. Lines of symmetry
7.3.1. Rotational or point symmetry
7.4. Polygons
7.4.1. Properties of some common polygons
7.4.2. Regular polygons
7.4.3. Sum of interior and exterior angles of polygons
7.4.3.1. Interior angles of a polygon
7.4.3.2. Exterior angles of a polygon
7.5. Summary
7.6. Further reading
7.7. Test 7
Chapter 8: Geometry 2
8.1. Introduction
8.2. Parts of a circle
8.3. Circle theorems
8.3.1. Angles in the semicircle are right angle
8.3.2. Angle on a straight line is 180°
8.3.3. Angles in the same segment are equal
8.3.4. The angle subtended at the centre of the circle by an arc is twice the size of the angle on the circumference subtended by the same arc
8.3.5. Opposite angles of a cyclic quad add up to 180°
8.3.6. Exterior angle of a cyclic quad is equal to the interior opposite angle
8.3.7. The angle between a tangent at a point and the radius to the same point on the circle is a right angle
8.3.8. Angles in the alternate segments are equal
8.3.9. Equal chords subtend equal angles
8.3.10. Tangents from same external point to a circle are equal
8.4. Summary
8.5. Further reading
8.6. Test 8
Chapter 9: Financial Mathematics 1
9.1. Introduction
9.2. Bank statement
9.3. Simple interest
9.4. Compound interest
9.5. Commission
9.6. Hire purchase
9.7. Summary
9.8. Further reading
9.9. Test 9
Chapter 10: Geometry 3
10.1. Introduction
10.2. Similarity
10.3. Scale factor
10.4. The area factor
10.5. The volume factor
10.6. Summary
10.7. Further reading
10.8. Test 10
Chapter 11: Geometry 4 (Geometrical Construction)
11.1. Introduction
11.2. Constructing a straight line
11.3. Bisection of straight lines
11.4. Construction of angles
11.4.1. Construction of a 60° angle
11.4.2. Construction of a 120° angle
11.4.3. Construction of a 90° angle
11.5. Bisection of angles
11.6. Construction of plane shapes
11.6.1. Construction of triangles
11.7. Summary
11.8. Further reading
11.9. Test 11
Chapter 12: Financial Mathematics 2
12.1. Introduction
12.2. Foreign exchange
12.3. Conversion of rates and calculations
12.4. Sales and income tax rates
12.4.1. P.A.Y.E (Pay As You Earn)
12.5. VAT
12.6. Customs and excise duty
12.7. Summary
12.8. Further reading
12.9. Test 12
Chapter 13: Measures and Mensuration 1
13.1. Introduction
13.2. Perimeter of combined shapes
13.3. Area of combined shapes
13.3.1. Parallelograms and triangles between parallel lines
13.3.2. Arcs, sectors and segments of circles
13.3.3. Perimeter of a sector
13.3.4. Area of sector
13.3.5. Area of segment
13.4. Volume of cones, cylinders and pyramids
13.4.1. Volume of cones and pyramids
13.4.2. Volume of pyramids
13.4.3. Volume of cylinders
13.5. Density
13.6. Summary
13.7. Further reading
13.8. Test 13
Chapter 14: Measures and Mensuration 2
14.1. Introduction
14.2. Surface area
14.2.1. Total surface area of a cone
14.2.2. Total surface area of a cylinder
14.2.3. Surface area of a sphere
14.3. Volume of prisms
14.3.1. Capacity
14.3.2. Volume of a sphere
14.4. Volume of frustums
14.5. Area and volume of solid shapes (composite and hollow shapes)
14.5.1. Surface and exposed surface areas of combined solid shapes
14.5.2. Composite solids
14.5.3. Hollow solids (shapes)
14.6. Summary
14.7. Further reading
14.8. Test 14
Chapter 15: Indices and Logarithms
15.1. Introduction
15.2. Indices
15.2.1. Evaluation
15.2.2. Equations
15.3. Logarithms
15.3.1. Theory of logarithms
15.4. Summary
15.5. Further reading
15.6. Test 15