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Secondary 4 Maths Topics

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1. Number System and Radicals

1.1 Understanding the number systems
1.2 Prime factorization
1.3 Greatest Common Factors (GCF)
1.4 Least Common Multiple (LCM)
1.5 Rational vs. Irrational numbers
1.6 Converting repeating decimals to fractions

2. Rational Numbers

2.1 Comparing and ordering rational numbers
2.2 Solving problems with rational numbers in decimal form
2.3 Solving problems with rational numbers in fraction form
2.4 Determine square roots of rational numbers

3. Solving Linear Equations

3.1 Solving linear equations using multiplication and division
3.2 Solving two-step linear equations: ax + b = c, x/a + b = c
3.3 Solving linear equations using distributive property: a(x + b) = c
3.4 Solving linear equations with variables on both sides
3.5 Solving literal equations

4. Linear Inequalities

4.1 Express linear inequalities graphically and algebraically
4.2 Solving one-step linear inequalities
4.3 Solving multi-step linear inequalities
4.4 Compound inequalities

5. Introduction to Relations and Functions

5.1 Relationship between two variables
5.2 Understand relations between x- and y-intercepts
5.3 Domain and range of a function
5.4 Identifying functions
5.5 Function notation

6. Linear Functions

6.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
6.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
6.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
6.4 Gradient intercept form: y = mx + b
6.5 General form: Ax + By + C = 0
6.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
6.7 Rate of change
6.8 Graphing linear functions using table of values
6.9 Graphing linear functions using x- and y-intercepts
6.10 Graphing from gradient-intercept form y=mx+b
6.11 Graphing linear functions using a single point and gradient
6.12 Word problems of graphing linear functions
6.13 Parallel and perpendicular lines in linear functions
6.14 Applications of linear relations

7. Linear Equations (Advanced)

7.1 Introduction to linear equations
7.2 Introduction to nonlinear equations
7.3 Special case of linear equations: Horizontal lines
7.4 Special case of linear equations: Vertical lines
7.5 Parallel line equation
7.6 Perpendicular line equation
7.7 Combination of both parallel and perpendicular line equations
7.8 Applications of linear equations

8. Solving Simultaneous Equations

8.1 Determining number of solutions to linear equations
8.2 Solving simultaneous equations by graphing
8.3 Solving simultaneous equations by elimination
8.4 Solving simultaneous equations by substitution
8.5 Money related questions in linear equations
8.6 Unknown number related questions in linear equations
8.7 Distance and time related questions in linear equations
8.8 Rectangular shape related questions in linear equations

9. Exponents

9.1 Product rule of exponents
9.2 Quotient rule of exponents
9.3 Power of a product rule
9.4 Power of a quotient rule
9.5 Power of a power rule
9.6 Negative exponent rule
9.7 Combining the exponent rules
9.8 Scientific notation
9.9 Convert between radicals and rational exponents
9.10 Solving for exponents

10. Exponential Functions

10.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
10.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
10.3 Exponents: Power rule (a^x)^y = a^(x * y)
10.4 Exponents: Negative exponents
10.5 Exponents: Zero exponent: a^0 = 1
10.6 Exponents: Rational exponents
10.7 Graphing exponential functions
10.8 Graphing transformations of exponential functions
10.9 Finding an exponential function given its graph

11. Exponential Growth and Decay

11.1 Exponential growth and decay by a factor
11.2 Exponential decay: Half-life
11.3 Exponential growth and decay by percentage
11.4 Continuous growth and decay

12. Operations of Polynomials

12.1 What is a polynomial?
12.2 Polynomial components
12.3 Multiplying monomial by monomial
12.4 Multiplying monomial by binomial
12.5 Multiplying binomial by binomial
12.6 Multiplying polynomial by polynomial
12.7 Applications of polynomials
12.8 Pascal's triangle
12.9 Binomial theorem

13. Factorising Quadratic Equations

13.1 Factorise by taking out the greatest common factor
13.2 Factorise by grouping
13.3 Factorising difference of squares: x^2 - y^2
13.4 Factorising trinomials
13.5 Factoring difference of cubes
13.6 Factoring sum of cubes

14. Quadratic Functions

14.1 Characteristics of quadratic functions
14.2 Transformations of quadratic functions
14.3 Quadratic function in general form: y = ax^2 + bx + c
14.4 Quadratic function in vertex form: y = a(x-p)^2 + q
14.5 Completing the square
14.6 Converting from general to vertex form by completing the square
14.7 Shortcut: Vertex formula
14.8 Graphing parabolas for given quadratic functions
14.9 Finding the quadratic functions for given parabolas
14.10 Applications of quadratic functions

15. Quadratic Equations and Inequalities

15.1 Solving quadratic equations by factorising
15.2 Solving quadratic equations by completing the square
15.3 Using quadratic formula to solve quadratic equations
15.4 Nature of roots of quadratic equations: The discriminant
15.5 Applications of quadratic equations
15.6 Solving quadratic inequalities

16. Pythagorean Theorem

16.1 Squares and square roots
16.2 Pythagorean theorem
16.3 Estimating square roots
16.4 Using the pythagorean relationship
16.5 Applications of pythagorean theorem

17. Angles, Lines and Transversals

17.1 Pairs of lines and angles
17.2 Parallel lines and transversals
17.3 Parallel line proofs
17.4 Perpendicular line proofs
17.5 Parallel and perpendicular line segments
17.6 Perpendicular bisectors
17.7 Angle Bisectors

18. Properties of Triangles

18.1 Classifying Triangles
18.2 Isosceles and Equilateral Triangles

19. Congruent Triangles

19.1 Congruence and Congruent Triangles
19.2 Triangles Congruent by SSS Proofs
19.3 Triangles Congruent by SAS and HL Proofs
19.4 Triangles Congruent by ASA and AAS Proofs

20. Symmetry and Surface Area

20.1 Line symmetry
20.2 Rotational symmetry and transformations
20.3 Surface area of 3-dimensional shapes

21. Circle Geometry

21.1 Angles in a circle
21.2 Chord properties
21.3 Tangent properties
21.4 Circles and circumference
21.5 Arcs of a circle
21.6 Areas and sectors of circles
21.7 Inscribed Angles and Proofs
21.8 Central and inscribed angles in circles

22. Scale Factors and Similarity

22.1 Enlargements and reductions with scale factors
22.2 Scale diagrams
22.3 Similar triangles
22.4 Similar polygons

23. Surface Area and Volume

23.1 Surface area and volume of prisms
23.2 Surface area and volume of pyramids
23.3 Surface area and volume of cylinders
23.4 Surface area and volume of cones
23.5 Surface area and volume of spheres

24. Algebraic Fractions

24.1 Simplifying algebraic fractions and restrictions
24.2 Adding and subtracting algebraic fractions
24.3 Multiplying algebraic fractions
24.4 Dividing algebraic fractions
24.5 Solving equations with algebraic fractions
24.6 Applications of equations with algebraic fractions
24.7 Simplifying complex fractions
24.8 Partial fraction decomposition

25. Reciprocal Functions

25.1 Graphing reciprocals of linear functions
25.2 Graphing reciprocals of quadratic functions

26. Introduction to Trigonometry

26.1 Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
26.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
26.3 Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
26.4 Combination of SohCahToa questions
26.5 Solving expressions using 45-45-90 special right triangles
26.6 Solving expressions using 30-60-90 special right triangles
26.7 Word problems relating ladder in trigonometry
26.8 Word problems relating guy wire in trigonometry
26.9 Other word problems relating angles in trigonometry

27. Trigonometry

27.1 Angle in standard position
27.2 Coterminal angles
27.3 Reference angle
27.4 Find the exact value of trigonometric ratios
27.5 ASTC rule in trigonometry (All Students Take Calculus)
27.6 Unit circle
27.7 Converting between degrees and radians
27.8 Trigonometric ratios of angles in radians
27.9 Radian measure and arc length
27.10 Law of sines
27.11 Law of cosines
27.12 Applications of the sine law and cosine law

28. Bearings

28.1 Introduction to bearings
28.2 Bearings and direction word problems
28.3 Angle of elevation and depression

29. Vectors

29.1 Introduction to vectors
29.2 Magnitude of a vector
29.3 Direction angle of a vector
29.4 Scalar multiplication
29.5 Equivalent vectors
29.6 Adding and subtracting vectors in component form
29.7 Operations on vectors in magnitude and direction form
29.8 Unit Vector
29.9 Word problems on vectors

30. Probability

30.1 Determining probabilities using tree diagrams and tables
30.2 Probability of independent events
30.3 Probability with Venn diagrams

31. Statistics

31.1 Median and mode
31.2 Mean
31.3 Range and outliers
31.4 Application of averages

32. Data and Graphs

32.1 Reading and drawing histograms
32.2 Box-and-whisker plots and scatter plots

33. Derivatives

33.1 Definition of derivative
33.2 Power rule
33.3 Chain rule
33.4 Derivative of exponential functions
33.5 Product rule
33.6 Quotient rule

34. Introduction to Matrices

34.1 Notation of matrices
34.2 Adding and subtracting matrices
34.3 Scalar multiplication
34.4 Matrix multiplication
34.5 The three types of matrix row operations
34.6 Representing a linear system as a matrix
34.7 Solving a linear system with matrices using Gaussian elimination

34 Chapters · 211 Topics · 1452 Videos

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Yes — all Secondary 4 Maths lessons align with the Singapore O Level Additional Mathematics and Elementary Mathematics syllabuses, covering every required topic.

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