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AU Year 11 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)

3Quadratic Equations and Inequalities

3.1Solving quadratic equations by factoring
3.2Solving quadratic equations by completing the square
3.3Solving quadratic equations using the quadratic formula
3.4Nature of roots of quadratic equations: The discriminant
3.5Applications of quadratic equations
3.6Solving quadratic inequalities

4Solving Simultaneous Equations

4.1Determining number of solutions to linear equations (free lessons)
4.2Solving simultaneous equations by graphing
4.3Solving simultaneous equations by elimination
4.4Solving simultaneous equations by substitution
4.5Money related questions in linear equations (free lessons)
4.6Unknown number related questions in linear equations
4.7Distance and time related questions in linear equations
4.8Rectangular shape related questions in linear equations

5Linear programming

5.1What is linear programming?
5.2Linear programming word problems

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)

7Direct Variation

7.1Writing and solving for proportions
7.2Understanding graphs of proportional relationships (free lessons)
7.3Graphing and writing equations of proportional relationships
7.4Applications of proportional relationships (free lessons)

8Imaginary and Complex Numbers

8.1Introduction to imaginary numbers (free lessons)
8.2Complex numbers and complex planes (free lessons)
8.3Adding and subtracting complex numbers
8.4Complex conjugates
8.5Multiplying and dividing complex numbers
8.6Distance and midpoint of complex numbers
8.7Angle and absolute value of complex numbers
8.8Polar form of complex numbers
8.9Operations on complex numbers in polar form

9Factorising Polynomial

9.1Factorise by taking out the greatest common factor (free lessons)
9.2Factorise by grouping
9.3Factorising difference of squares: x2−y2x^2 - y^2
9.4Factorising trinomials
9.5Factoring difference of cubes
9.6Factoring sum of cubes

10Quadratic Functions

10.1Characteristics of quadratic functions (free lessons)
10.2Transformations of quadratic functions
10.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
10.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
10.5Completing the square (free lessons)
10.6Converting from general to vertex form by completing the square
10.7Shortcut: Vertex formula (free lessons)
10.8Graphing parabolas for given quadratic functions
10.9Finding the quadratic functions for given parabolas (free lessons)
10.10Applications of quadratic functions

11Polynomial Functions

11.1What is a polynomial function? (free lessons)
11.2Polynomial long division (free lessons)
11.3Polynomial synthetic division
11.4Remainder theorem
11.5Factor theorem
11.6Rational zero theorem
11.7Characteristics of polynomial graphs
11.8Multiplicities of polynomials
11.9Imaginary zeros of polynomials
11.10Determining the equation of a polynomial function
11.11Applications of polynomial functions
11.12Solving polynomial inequalities
11.13Fundamental theorem of algebra
11.14Descartes’ rule of signs

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

14Exponents

14.1Product rule of exponents (free lessons)
14.2Quotient rule of exponents
14.3Power of a product rule
14.4Power of a quotient rule
14.5Power of a power rule (free lessons)
14.6Negative exponent rule
14.7Combining the exponent rules
14.8Scientific notation
14.9Convert between radicals and rational exponents (free lessons)
14.10Solving for exponents

15Exponential Functions

15.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
15.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
15.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
15.4Exponents: Negative exponents
15.5Exponents: Zero exponent: a0=1 a^0 = 1
15.6Exponents: Rational exponents
15.7Graphing exponential functions
15.8Graphing transformations of exponential functions
15.9Finding an exponential function given its graph

16Logarithmic Functions

16.1What is a logarithm?
16.2Converting from logarithmic form to exponential form (free lessons)
16.3Evaluating logarithms without a calculator
16.4Common logarithms
16.5Natural log: ln
16.6Evaluating logarithms using change-of-base formula
16.7Converting from exponential form to logarithmic form (free lessons)
16.8Solving exponential equations with logarithms
16.9Product rule of logarithms (free lessons)
16.10Quotient rule of logarithms
16.11Combining product rule and quotient rule in logarithms
16.12Evaluating logarithms using logarithm rules
16.13Solving logarithmic equations (free lessons)
16.14Graphing logarithmic functions
16.15Finding a logarithmic function given its graph

17Applications of Exponential and Logarithmic Functions

17.1Exponential growth and decay by a factor
17.2Exponential decay: Half-life (free lessons)
17.3Exponential growth and decay by percentage
17.4Finance: Compound interest
17.5Continuous growth and decay
17.6Logarithmic scale: Richter scale (earthquake)
17.7Logarithmic scale: pH scale
17.8Logarithmic scale: dB scale
17.9Finance: Future value and present value

18Conics

18.1Conics - Parabola
18.2Conics - Ellipse
18.3Conics - Circle
18.4Conics - Hyperbola

19Introduction to Trigonometry

19.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
19.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
19.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
19.4Combination of SohCahToa questions (free lessons)
19.5Solving expressions using 45-45-90 special right triangles (free lessons)
19.6Solving expressions using 30-60-90 special right triangles
19.7Word problems relating ladder in trigonometry
19.8Word problems relating guy wire in trigonometry
19.9Other word problems relating angles in trigonometry

20Trigonometric Ratios and Angle Measure

20.1Standard angle
20.2Coterminal angles (free lessons)
20.3Reference angles
20.4Find the exact value of trigonometric ratios
20.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
20.6Unit circle (free lessons)
20.7Sine rule
20.8Cosine rule
20.9Applications of the sine rule and cosine rule

21Graphing Trigonometric Functions

21.1Sine graph: y = sin x
21.2Cosine graph: y = cos x
21.3Tangent graph: y = tan x
21.4Cotangent graph: y = cot x
21.5Secant graph: y = sec x
21.6Cosecant graph: y = csc x
21.7Graphing transformations of trigonometric functions
21.8Determining trigonometric functions given their graphs

22Applications of Trigonometric Functions

22.1Ferris wheel trig problems
22.2Tides and water depth trig problems
22.3Spring (simple harmonic motion) trig problems

23Trigonometric Identities

23.1Quotient identities and reciprocal identities (free lessons)
23.2Pythagorean identities
23.3Sum and difference identities
23.4Cofunction identities
23.5Double-angle identities (free lessons)

24Circle Geometry

24.1Angles in a circle (free lessons)
24.2Chord properties
24.3Tangent properties
24.4Circles and circumference
24.5Arcs of a circle
24.6Areas and sectors of circles
24.7Inscribed Angles and Proofs
24.8Central and inscribed angles in circles

25Sequences and Series

25.1Arithmetic sequences (free lessons)
25.2Arithmetic series (free lessons)
25.3Geometric sequences
25.4Geometric series
25.5Infinite geometric series
25.6Sigma notation
25.7Arithmetic mean vs. Geometric mean

26Introduction to Probability

26.1Introduction to probability
26.2Organizing outcomes
26.3Probability of independent events
26.4Comparing experimental and theoretical probability

27Probability

27.1Determining probabilities using tree diagrams and tables (free lessons)
27.2Probability of independent events
27.3Probability with Venn diagrams

28Statistics

28.1Median and mode
28.2Mean
28.3Range and outliers
28.4Application of averages

29Limits

29.1Finding limits from graphs
29.2Continuity
29.3Finding limits algebraically - direct substitution
29.4Finding limits algebraically - when direct substitution is not possible
29.5Infinite limits - vertical asymptotes
29.6Limits at infinity - horizontal asymptotes
29.7Intermediate value theorem
29.8Squeeze theorem

30Derivatives

30.1Definition of derivative
30.2Power rule
30.3Gradient and equation of tangent line
30.4Chain rule
30.5Derivative of trigonometric functions
30.6Derivative of exponential functions
30.7Product rule
30.8Quotient rule
30.9Implicit differentiation
30.10Derivative of inverse trigonometric functions
30.11Derivative of logarithmic functions
30.12Higher order derivatives
30.13Position velocity acceleration

31Introduction to Matrices

31.1Notation of matrices
31.2Adding and subtracting matrices
31.3Scalar multiplication
31.4Matrix multiplication
31.5The three types of matrix row operations
31.6Representing a linear system as a matrix
31.7Solving a linear system with matrices using Gaussian elimination

32Determinants and Inverses of Matrices

32.1The determinant of a 2 x 2 matrix
32.2The determinant of a 3 x 3 matrix (General & Shortcut Method)
32.3The inverse of a 2 x 2 matrix
32.4The inverse of 3 x 3 matrices with matrix row operations
32.5The inverse of 3 x 3 matrix with determinants and adjugate
32.62 x 2 invertible matrix
32.7Solving linear systems using Cramer's Rule
32.8Solving linear systems using 2 x 2 inverse matrices
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