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Higher 1 Maths Topics

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1Solving Linear Equations

1.1Solving linear equations using multiplication and division (free lessons)
1.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
1.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
1.4Solving linear equations with variables on both sides
1.5Solving literal equations

2Linear Inequalities

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

3Factorising Quadratic Equations

3.1Factorise by taking out the greatest common factor (free lessons)
3.2Factorise by grouping
3.3Factorising difference of squares: x2−y2x^2 - y^2
3.4Factorising trinomials
3.5Factoring difference of cubes
3.6Factoring sum of cubes

4Quadratic Functions

4.1Characteristics of quadratic functions (free lessons)
4.2Transformations of quadratic functions
4.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
4.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
4.5Completing the square (free lessons)
4.6Converting from general to vertex form by completing the square
4.7Shortcut: Vertex formula (free lessons)
4.8Graphing parabolas for given quadratic functions
4.9Finding the quadratic functions for given parabolas (free lessons)
4.10Applications of quadratic functions

5Quadratic Equations and Inequalities

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

6Introduction to Relations and Functions

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

7Linear Functions

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

8Linear equations (Advanced)

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

9Solving Simultaneous Equations

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

10Imaginary and Complex Numbers

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

11Operations of polynomials

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

12Radicals

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

13Radical Functions

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

14Algebraic Fractions

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

15Reciprocal Functions

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

16Rational Functions

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

17Operations of Functions

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

18Transformations of Functions

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

19Exponential Functions

19.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
19.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
19.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
19.4Exponents: Negative exponents
19.5Exponents: Zero exponent: a0=1 a^0 = 1
19.6Exponents: Rational exponents
19.7Graphing exponential functions
19.8Graphing transformations of exponential functions
19.9Finding an exponential function given its graph

20Applications of Exponential Functions

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

21Logarithmic Functions

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

22Conics

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

23Introduction to Trigonometry

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

24Trigonometry

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

25Bearings

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

26Graphing Trigonometric Functions

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

27Trigonometric Identities

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

28Sequences

28.1Arithmetic sequences (free lessons)
28.2Geometric sequences
28.3Sigma notation

29Derivatives

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

30Probability

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

31Statistics

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

32Introduction to Matrices

32.1Notation of matrices
32.2Adding and subtracting matrices
32.3Scalar multiplication
32.4Matrix multiplication
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

33Determinants and Inverses of Matrices

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