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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)

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

15Rational Functions

15.1What is a rational function? (free lessons)
15.2Point of discontinuity
15.3Vertical asymptote
15.4Horizontal asymptote
15.5Slant asymptote
15.6Graphs of rational functions
15.7Solving rational inequalities

16Operations of Functions

16.1Function notation (free lessons)
16.2Operations with functions
16.3Adding functions
16.4Subtracting functions
16.5Multiplying functions
16.6Dividing functions
16.7Composite functions (free lessons)
16.8Inequalities of combined functions
16.9Inverse functions (free lessons)
16.10One to one functions
16.11Difference quotient: applications of functions

17Transformations of Functions

17.1Transformations of functions: Horizontal translations
17.2Transformations of functions: Vertical translations
17.3Reflection across the y-axis: y=f(−x)y = f(-x) (free lessons)
17.4Reflection across the x-axis: y=−f(x)y = -f(x)
17.5Transformations of functions: Horizontal stretches
17.6Transformations of functions: Vertical stretches
17.7Combining transformations of functions
17.8Even and odd functions

18Exponential Functions

18.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
18.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
18.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
18.4Exponents: Negative exponents
18.5Exponents: Zero exponent: a0=1 a^0 = 1
18.6Exponents: Rational exponents
18.7Graphing exponential functions
18.8Graphing transformations of exponential functions
18.9Finding an exponential function given its graph

19Applications of Exponential Functions

19.1Exponential growth and decay by a factor
19.2Exponential decay: Half-life (free lessons)
19.3Exponential growth and decay by percentage
19.4Finance: Compound interest
19.5Continuous growth and decay

20Logarithmic Functions

20.1What is a logarithm?
20.2Converting from logarithmic form to exponential form (free lessons)
20.3Evaluating logarithms without a calculator
20.4Common logarithms
20.5Natural log: ln
20.6Evaluating logarithms using change-of-base formula
20.7Converting from exponential form to logarithmic form (free lessons)
20.8Solving exponential equations with logarithms
20.9Product rule of logarithms (free lessons)
20.10Quotient rule of logarithms
20.11Combining product rule and quotient rule in logarithms
20.12Evaluating logarithms using logarithm rules
20.13Solving logarithmic equations (free lessons)
20.14Graphing logarithmic functions
20.15Finding a logarithmic function given its graph

21Conics

21.1Conics - Parabola
21.2Conics - Ellipse
21.3Conics - Circle
21.4Conics - Hyperbola

22Introduction to Trigonometry

22.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
22.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
22.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
22.4Combination of SohCahToa questions (free lessons)
22.5Solving expressions using 45-45-90 special right triangles (free lessons)
22.6Solving expressions using 30-60-90 special right triangles
22.7Word problems relating ladder in trigonometry
22.8Word problems relating guy wire in trigonometry
22.9Other word problems relating angles in trigonometry

23Trigonometry

23.1Angle in standard position
23.2Coterminal angles (free lessons)
23.3Reference angle
23.4Find the exact value of trigonometric ratios
23.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
23.6Unit circle (free lessons)
23.7Converting between degrees and radians
23.8Trigonometric ratios of angles in radians
23.9Radian measure and arc length
23.10Law of sines
23.11Law of cosines
23.12Applications of the sine law and cosine law

24Graphing Trigonometric Functions

24.1Sine graph: y = sin x
24.2Cosine graph: y = cos x
24.3Tangent graph: y = tan x
24.4Cotangent graph: y = cot x
24.5Secant graph: y = sec x
24.6Cosecant graph: y = csc x
24.7Graphing transformations of trigonometric functions
24.8Determining trigonometric functions given their graphs

25Trigonometric Identities

25.1Quotient identities and reciprocal identities (free lessons)
25.2Pythagorean identities
25.3Sum and difference identities
25.4Cofunction identities
25.5Double-angle identities (free lessons)

26Sequences

26.1Arithmetic sequences (free lessons)
26.2Geometric sequences
26.3Sigma notation

27Derivatives

27.1Definition of derivative
27.2Power rule
27.3Chain rule
27.4Derivative of exponential functions
27.5Product rule
27.6Quotient rule
27.7Derivative of logarithmic functions

28Probability

28.1Determining probabilities using tree diagrams and tables (free lessons)
28.2Probability of independent events
28.3Probability with Venn diagrams
28.4Addition rule for "OR"
28.5Multiplication rule for "AND"
28.6Conditional probability

29Statistics

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

30Introduction to Matrices

30.1Notation of matrices
30.2Adding and subtracting matrices
30.3Scalar multiplication
30.4Matrix multiplication
30.5The three types of matrix row operations
30.6Representing a linear system as a matrix
30.7Solving a linear system with matrices using Gaussian elimination

31Determinants and Inverses of Matrices

31.1The determinant of a 2 x 2 matrix
31.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
31.3The inverse of a 2 x 2 matrix
31.4The inverse of 3 x 3 matrices with matrix row operations
31.5The inverse of 3 x 3 matrix with determinants and adjugate
31.62 x 2 invertible matrix
31.7Solving linear systems using Cramer's Rule
31.8Solving linear systems using 2 x 2 inverse matrices
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