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Higher 1 Maths Topics

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1. Solving Linear Equations

1.1 Solving linear equations using multiplication and division
1.2 Solving two-step linear equations: ax + b = c, x/a + b = c
1.3 Solving linear equations using distributive property: a(x + b) = c
1.4 Solving linear equations with variables on both sides
1.5 Solving literal equations

2. Linear Inequalities

2.1 Express linear inequalities graphically and algebraically
2.2 Solving one-step linear inequalities
2.3 Solving multi-step linear inequalities
2.4 Compound inequalities

3. Factorising Quadratic Equations

3.1 Factorise by taking out the greatest common factor
3.2 Factorise by grouping
3.3 Factorising difference of squares: x^2 - y^2
3.4 Factorising trinomials
3.5 Factoring difference of cubes
3.6 Factoring sum of cubes

4. Quadratic Functions

4.1 Characteristics of quadratic functions
4.2 Transformations of quadratic functions
4.3 Quadratic function in general form: y = ax^2 + bx + c
4.4 Quadratic function in vertex form: y = a(x-p)^2 + q
4.5 Completing the square
4.6 Converting from general to vertex form by completing the square
4.7 Shortcut: Vertex formula
4.8 Graphing parabolas for given quadratic functions
4.9 Finding the quadratic functions for given parabolas
4.10 Applications of quadratic functions

5. Quadratic Equations and Inequalities

5.1 Solving quadratic equations by factorising
5.2 Solving quadratic equations by completing the square
5.3 Using quadratic formula to solve quadratic equations
5.4 Nature of roots of quadratic equations: The discriminant
5.5 Applications of quadratic equations
5.6 Solving quadratic inequalities

6. Introduction to Relations and Functions

6.1 Relationship between two variables
6.2 Understand relations between x- and y-intercepts
6.3 Domain and range of a function
6.4 Identifying functions
6.5 Function notation

7. Linear Functions

7.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
7.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
7.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
7.4 Gradient intercept form: y = mx + b
7.5 General form: Ax + By + C = 0
7.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
7.7 Rate of change
7.8 Graphing linear functions using table of values
7.9 Graphing linear functions using x- and y-intercepts
7.10 Graphing from gradient-intercept form y=mx+b
7.11 Graphing linear functions using a single point and gradient
7.12 Word problems of graphing linear functions
7.13 Parallel and perpendicular lines in linear functions
7.14 Applications of linear relations

8. Linear equations (Advanced)

8.1 Introduction to linear equations
8.2 Introduction to nonlinear equations
8.3 Special case of linear equations: Horizontal lines
8.4 Special case of linear equations: Vertical lines
8.5 Parallel line equation
8.6 Perpendicular line equation
8.7 Combination of both parallel and perpendicular line equations
8.8 Applications of linear equations

9. Solving Simultaneous Equations

9.1 Determining number of solutions to linear equations
9.2 Solving simultaneous equations by graphing
9.3 Solving simultaneous equations by elimination
9.4 Solving simultaneous equations by substitution
9.5 Money related questions in linear equations
9.6 Unknown number related questions in linear equations
9.7 Distance and time related questions in linear equations
9.8 Rectangular shape related questions in linear equations

10. Imaginary and Complex Numbers

10.1 Introduction to imaginary numbers
10.2 Complex numbers and complex planes
10.3 Adding and subtracting complex numbers
10.4 Complex conjugates
10.5 Multiplying and dividing complex numbers
10.6 Distance and midpoint of complex numbers
10.7 Angle and absolute value of complex numbers
10.8 Polar form of complex numbers
10.9 Operations on complex numbers in polar form

11. Operations of polynomials

11.1 What is a polynomial?
11.2 Polynomial components
11.3 Multiplying monomial by monomial
11.4 Multiplying monomial by binomial
11.5 Multiplying binomial by binomial
11.6 Multiplying polynomial by polynomial
11.7 Applications of polynomials
11.8 Fundamental theorem of algebra
11.9 Pascal's triangle
11.10 Binomial theorem

12. Radicals

12.1 Operations with radicals
12.2 Conversion between entire radicals and mixed radicals
12.3 Adding and subtracting radicals
12.4 Multiplying radicals
12.5 Solving radical equations

13. Radical Functions

13.1 Basic radical functions
13.2 Transformations of radical functions
13.3 Square root of a function

14. Algebraic Fractions

14.1 Simplifying algebraic fractions and restrictions
14.2 Adding and subtracting algebraic fractions
14.3 Multiplying algebraic fractions
14.4 Dividing algebraic fractions
14.5 Solving equations with algebraic fractions
14.6 Applications of equations with algebraic fractions
14.7 Simplifying complex fractions
14.8 Partial fraction decomposition

15. Reciprocal Functions

15.1 Graphing reciprocals of linear functions
15.2 Graphing reciprocals of quadratic functions

16. Rational Functions

16.1 What is a rational function?
16.2 Point of discontinuity
16.3 Vertical asymptote
16.4 Horizontal asymptote
16.5 Slant asymptote
16.6 Graphs of rational functions
16.7 Solving rational inequalities

17. Operations of Functions

17.1 Function notation
17.2 Operations with functions
17.3 Adding functions
17.4 Subtracting functions
17.5 Multiplying functions
17.6 Dividing functions
17.7 Composite functions
17.8 Inequalities of combined functions
17.9 Inverse functions
17.10 One to one functions
17.11 Difference quotient: applications of functions

18. Transformations of Functions

18.1 Transformations of functions: Horizontal translations
18.2 Transformations of functions: Vertical translations
18.3 Reflection across the y-axis: y = f(-x)
18.4 Reflection across the x-axis: y = -f(x)
18.5 Transformations of functions: Horizontal stretches
18.6 Transformations of functions: Vertical stretches
18.7 Combining transformations of functions
18.8 Even and odd functions

19. Exponential Functions

19.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
19.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
19.3 Exponents: Power rule (a^x)^y = a^(x * y)
19.4 Exponents: Negative exponents
19.5 Exponents: Zero exponent: a^0 = 1
19.6 Exponents: Rational exponents
19.7 Graphing exponential functions
19.8 Graphing transformations of exponential functions
19.9 Finding an exponential function given its graph

20. Applications of Exponential Functions

20.1 Exponential growth and decay by a factor
20.2 Exponential decay: Half-life
20.3 Exponential growth and decay by percentage
20.4 Finance: Compound interest
20.5 Continuous growth and decay

21. Logarithmic Functions

21.1 What is a logarithm?
21.2 Converting from logarithmic form to exponential form
21.3 Evaluating logarithms without a calculator
21.4 Common logarithms
21.5 Natural log: ln
21.6 Evaluating logarithms using change-of-base formula
21.7 Converting from exponential form to logarithmic form
21.8 Solving exponential equations with logarithms
21.9 Product rule of logarithms
21.10 Quotient rule of logarithms
21.11 Combining product rule and quotient rule in logarithms
21.12 Evaluating logarithms using logarithm rules
21.13 Solving logarithmic equations
21.14 Graphing logarithmic functions
21.15 Finding a logarithmic function given its graph

22. Conics

22.1 Conics - Parabola
22.2 Conics - Ellipse
22.3 Conics - Circle
22.4 Conics - Hyperbola

23. Introduction to Trigonometry

23.1 Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
23.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
23.3 Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
23.4 Combination of SohCahToa questions
23.5 Solving expressions using 45-45-90 special right triangles
23.6 Solving expressions using 30-60-90 special right triangles
23.7 Word problems relating ladder in trigonometry
23.8 Word problems relating guy wire in trigonometry
23.9 Other word problems relating angles in trigonometry

24. Trigonometry

24.1 Angle in standard position
24.2 Coterminal angles
24.3 Reference angle
24.4 Find the exact value of trigonometric ratios
24.5 ASTC rule in trigonometry (All Students Take Calculus)
24.6 Unit circle
24.7 Converting between degrees and radians
24.8 Trigonometric ratios of angles in radians
24.9 Radian measure and arc length
24.10 Law of sines
24.11 Law of cosines
24.12 Applications of the sine law and cosine law

25. Bearings

25.1 Introduction to bearings
25.2 Bearings and direction word problems
25.3 Angle of elevation and depression

26. Graphing Trigonometric Functions

26.1 Sine graph: y = sin x
26.2 Cosine graph: y = cos x
26.3 Tangent graph: y = tan x
26.4 Cotangent graph: y = cot x
26.5 Secant graph: y = sec x
26.6 Cosecant graph: y = csc x
26.7 Graphing transformations of trigonometric functions
26.8 Determining trigonometric functions given their graphs

27. Trigonometric Identities

27.1 Quotient identities and reciprocal identities
27.2 Pythagorean identities
27.3 Sum and difference identities
27.4 Cofunction identities
27.5 Double-angle identities

28. Sequences

28.1 Arithmetic sequences
28.2 Geometric sequences
28.3 Sigma notation

29. Derivatives

29.1 Definition of derivative
29.2 Power rule
29.3 Chain rule
29.4 Derivative of exponential functions
29.5 Product rule
29.6 Quotient rule
29.7 Derivative of logarithmic functions

30. Probability

30.1 Determining probabilities using tree diagrams and tables
30.2 Probability of independent events
30.3 Probability with Venn diagrams
30.4 Addition rule for "OR"
30.5 Multiplication rule for "AND"
30.6 Conditional probability

31. Statistics

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

32. Introduction to Matrices

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

33. Determinants and Inverses of Matrices

33.1 The determinant of a 2 x 2 matrix
33.2 The determinant of a 3 x 3 matrix (General & Shortcut Method)
33.3 The inverse of a 2 x 2 matrix
33.4 The inverse of 3 x 3 matrices with matrix row operations
33.5 The inverse of 3 x 3 matrix with determinants and adjugate
33.6 2 x 2 invertible matrix
33.7 Solving linear systems using Cramer's Rule
33.8 Solving linear systems using 2 x 2 inverse matrices

33 Chapters · 234 Topics · 1510 Videos

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