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Secondary 4 Maths topics

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1Number 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

2Rational 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

3Solving 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

4Linear Inequalities

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

5Introduction 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)

6Linear 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

7Linear 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

8Solving 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

9Exponents

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

10Exponential 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

11Exponential 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

12Operations 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

13Factorising 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

14Quadratic 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 (free lessons)
14.6Converting from general to vertex form by completing the square
14.7Shortcut: Vertex formula (free lessons)
14.8Graphing parabolas for given quadratic functions
14.9Finding the quadratic functions for given parabolas (free lessons)
14.10Applications of quadratic functions

15Quadratic 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

16Pythagorean 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

17Angles, 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

18Properties of Triangles

18.1Classifying Triangles
18.2Isosceles and Equilateral Triangles

19Congruent 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

20Symmetry and Surface Area

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

21Circle 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

22Scale Factors and Similarity

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

23Surface 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

24Algebraic 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

25Reciprocal Functions

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

26Introduction to Trigonometry

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

27Trigonometry

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

28Bearings

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

29Vectors

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

30Probability

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

31Statistics

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

32Data and Graphs

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

33Derivatives

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

34Introduction to Matrices

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