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Secondary 4 Maths Topics

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1.Number System and Radicals

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

2.Rational Numbers

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

3.Solving Linear Equations

3.1Solving linear equations using multiplication and division (free lessons)
3.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
3.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
3.4Solving linear equations with variables on both sides
3.5Solving literal equations

4.Linear Inequalities

4.1Express linear inequalities graphically and algebraically (free lessons)
4.2Solving one-step linear inequalities
4.3Solving multi-step linear inequalities

5.Introduction to Relations and Functions

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

6.Linear Functions

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

7.Linear equations (Advanced)

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

8.Solving Simultaneous Equations

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

9.Exponents

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

10.Exponential Functions

10.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
10.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
10.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
10.4Exponents: Negative exponents
10.5Exponents: Zero exponent: a0=1 a^0 = 1
10.6Exponents: Rational exponents
10.7Graphing exponential functions
10.8Graphing transformations of exponential functions
10.9Finding an exponential function given its graph

11.Exponential Growth and Decay

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

12.Operations of polynomials

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

13.Factorising Quadratic Equations

13.1Factorise by taking out the greatest common factor (free lessons)
13.2Factorise by grouping
13.3Factorising difference of squares: x2−y2x^2 - y^2
13.4Factorising trinomials
13.5Factoring difference of cubes
13.6Factoring sum of cubes

14.Quadratic Functions

14.1Characteristics of quadratic functions (free lessons)
14.2Transformations of quadratic functions
14.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
14.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
14.5Completing the square
14.6Converting from general to vertex form by completing the square
14.7Shortcut: Vertex formula (free lessons)
14.8Finding the quadratic functions for given parabolas (free lessons)
14.9Applications of quadratic functions

15.Quadratic Equations and Inequalities

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

16.Pythagorean Theorem

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

17.Angles, Lines and Transversals

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

18.Properties of Triangles

18.1Classifying Triangles
18.2Isosceles and Equilateral Triangles

19.Congruent Triangles

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

20.Symmetry and Surface Area

20.1Line symmetry (free lessons)
20.2Rotational symmetry and transformations
20.3Surface area of 3-dimensional shapes (free lessons)

21.Circle Geometry

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

22.Scale Factors and Similarity

22.1Enlargements and reductions with scale factors (free lessons)
22.2Scale diagrams
22.3Similar triangles
22.4Similar polygons

23.Surface Area and Volume

23.1Surface area and volume of prisms (free lessons)
23.2Surface area and volume of pyramids
23.3Surface area and volume of cylinders
23.4Surface area and volume of cones (free lessons)
23.5Surface area and volume of spheres

24.Algebraic Fractions

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

25.Introduction to Trigonometry

25.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
25.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
25.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
25.4Combination of SohCahToa questions (free lessons)
25.5Solving expressions using 45-45-90 special right triangles (free lessons)
25.6Solving expressions using 30-60-90 special right triangles
25.7Word problems relating ladder in trigonometry
25.8Word problems relating guy wire in trigonometry
25.9Other word problems relating angles in trigonometry

26.Trigonometry

26.1Angle in standard position
26.2Coterminal angles (free lessons)
26.3Reference angle
26.4Find the exact value of trigonometric ratios
26.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
26.6Unit circle (free lessons)
26.7Converting between degrees and radians
26.8Trigonometric ratios of angles in radians
26.9Radian measure and arc length
26.10Law of sines
26.11Law of cosines
26.12Applications of the sine law and cosine law

27.Vectors

27.1Introduction to vectors
27.2Magnitude of a vector
27.3Direction angle of a vector
27.4Scalar multiplication
27.5Equivalent vectors
27.6Adding and subtracting vectors in component form
27.7Operations on vectors in magnitude and direction form

28.Probability

28.1Determining probabilities using tree diagrams and tables (free lessons)
28.2Probability of independent events
28.3Probability with Venn diagrams

29.Statistics

29.1Median and mode
29.2Mean
29.3Range and outliers
29.4Application of averages

30.Data and Graphs

30.1Reading and drawing histograms
30.2Box-and-whisker plots and scatter plots

31.Derivatives

31.1Definition of derivative
31.2Power rule
31.3Chain rule
31.4Derivative of exponential functions
31.5Product rule
31.6Quotient rule

32.Introduction to Matrices

32.1Notation of matrices
32.2Adding and subtracting matrices
32.3Multiplying a matrix by a scalar
32.4Multiplying a matrix by another matrix
32.5The three types of matrix row operations
32.6Representing a linear system as a matrix
32.7Solving a linear system with matrices using Gaussian elimination
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