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Fifth Year Maths Topics

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1Number System and Radicals

1.1Understanding the number systems (free lessons)
1.2Prime factorisation
1.3Greatest Common Factors (GCF)
1.4Least Common Multiple (LCM) (free lessons)
1.5Rational vs. Irrational numbers
1.6Converting repeating decimals to fractions

2Exponents

2.1Product rule of exponents (free lessons)
2.2Quotient rule of exponents
2.3Power of a product rule
2.4Power of a quotient rule
2.5Power of a power rule (free lessons)
2.6Negative exponent rule
2.7Combining the exponent rules
2.8Scientific notation
2.9Convert between radicals and rational exponents (free lessons)
2.10Solving for exponents

3Linear Inequalities

3.1Express linear inequalities graphically and algebraically (free lessons)
3.2Solving one-step linear inequalities (free lessons)
3.3Solving multi-step linear inequalities (free lessons)

4Quadratic Equations and Inequalities

4.1Solving quadratic equations by factorising
4.2Solving quadratic equations by completing the square
4.3Using quadratic formula to solve quadratic equations
4.4Nature of roots of quadratic equations: The discriminant
4.5Applications of quadratic equations
4.6Solving quadratic 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)

6Solving Simultaneous Equations

6.1Determining number of solutions to linear equations (free lessons)
6.2Solving simultaneous equations by graphing
6.3Solving simultaneous equations by elimination
6.4Solving simultaneous equations by substitution
6.5Money related questions in linear equations (free lessons)
6.6Unknown number related questions in linear equations
6.7Distance and time related questions in linear equations
6.8Rectangular shape related questions in linear equations

7Inequalities in two variables

7.1Graphing linear inequalities in two variables (free lessons)
7.2Graphing simultaneous linear inequalities (free lessons)
7.3Graphing quadratic inequalities in two variables
7.4Graphing simultaneous quadratic inequalities
7.5Applications of inequalities
7.6What is linear programming?
7.7Linear programming word problems

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 Quadratic Functions

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

11Operations of Polynomials

11.1What is a polynomial? (free lessons)
11.2Using algebra tiles to solve polynomials

12Polynomial Functions

12.1What is a polynomial function? (free lessons)
12.2Polynomial long division (free lessons)
12.3Polynomial synthetic division
12.4Remainder theorem
12.5Factor theorem
12.6Rational zero theorem
12.7Characteristics of polynomial graphs
12.8Multiplicities of polynomials
12.9Imaginary zeros of polynomials
12.10Determining the equation of a polynomial function
12.11Applications of polynomial functions
12.12Solving polynomial inequalities
12.13Fundamental theorem of algebra
12.14Descartes’ rule of signs

13Radicals

13.1Operations with radicals (free lessons)
13.2Conversion between entire radicals and mixed radicals
13.3Adding and subtracting radicals (free lessons)
13.4Multiplying radicals
13.5Solving radical equations

14Radical Functions

14.1Basic radical functions
14.2Transformations of radical functions
14.3Square root of a function

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

16Rational Expressions

16.1Simplifying rational expressions and restrictions
16.2Adding and subtracting rational expressions (free lessons)
16.3Multiplying rational expressions
16.4Dividing rational expressions
16.5Solving rational equations
16.6Applications of rational equations
16.7Simplifying complex fractions
16.8Partial fraction decomposition

17Function Operations

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

18Logarithmic Functions

18.1What is a logarithm?
18.2Converting from logarithmic form to exponential form (free lessons)
18.3Evaluating logarithms without a calculator
18.4Common logarithms
18.5Natural log: ln
18.6Evaluating logarithms using change-of-base formula
18.7Converting from exponential form to logarithmic form (free lessons)
18.8Solving exponential equations with logarithms
18.9Product rule of logarithms (free lessons)
18.10Quotient rule of logarithms
18.11Combining product rule and quotient rule in logarithms
18.12Evaluating logarithms using logarithm rules
18.13Solving logarithmic equations (free lessons)
18.14Graphing logarithmic functions
18.15Finding a logarithmic function given its graph

19Exponential Growth and Decay

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

20Trigonometry

20.1Angle in standard position
20.2Coterminal angles (free lessons)
20.3Reference angle
20.4Find the exact value of trigonometric ratios
20.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
20.6Unit circle (free lessons)
20.7Converting between degrees and radians
20.8Trigonometric ratios of angles in radians
20.9Radian measure and arc length
20.10Law of sines
20.11Law of cosines
20.12Applications of the sine law and cosine law

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)

24Scale Factors and Similarity

24.1Enlargements and reductions with scale factors (free lessons)
24.2Scale diagrams
24.3Similar triangles
24.4Similar polygons

25Circle Geometry

25.1Angles in a circle (free lessons)
25.2Chord properties
25.3Tangent properties
25.4Circles and circumference
25.5Arcs of a circle
25.6Areas and sectors of circles
25.7Inscribed Angles and Proofs
25.8Central and inscribed angles in circles

26Conics

26.1Conics - Parabola
26.2Conics - Ellipse
26.3Conics - Circle
26.4Conics - Hyperbola

27Surface Area and Volume

27.1Surface area and volume of prisms (free lessons)
27.2Surface area and volume of pyramids
27.3Surface area and volume of cylinders
27.4Surface area and volume of cones (free lessons)
27.5Surface area and volume of spheres

28Sequences and series

28.1Arithmetic sequences (free lessons)
28.2Arithmetic series (free lessons)
28.3Geometric sequences
28.4Geometric series
28.5Infinite geometric series
28.6Sigma notation
28.7Arithmetic mean vs. Geometric mean

29Probability

29.1Determining probabilities using tree diagrams and tables (free lessons)
29.2Probability of independent events
29.3Probability with Venn diagrams

30Permutations and Combinations

30.1Fundamental counting principle
30.2Factorial notation
30.3Path counting problems
30.4Permutation vs. Combination
30.5Permutations
30.6Combinations
30.7Problems involving both permutations and combinations
30.8Pascal's triangle
30.9Binomial theorem

31Statistics

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

32Data and Graphs

32.1Reading and drawing histograms
32.2Reading and drawing line graphs
32.3Box-and-whisker plots and scatter plots
32.4Stem-and-leaf plots
32.5Reading and drawing Venn diagrams
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