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Transition Year Maths Topics

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1.Number 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

2.Adding and Subtracting Integers

2.1Introduction to integer addition
2.2Adding integers
2.3Introduction to integer subtraction
2.4Subtracting integers
2.5Application of integer operations

3.Multiplying and Dividing Integers

3.1Understanding integer multiplication
3.2Multiplying integers
3.3Understanding integer division
3.4Dividing integers
3.5Applications of integer operations

4.Rational Numbers

4.1Comparing and ordering rational numbers (free lessons)
4.2Solving problems with rational numbers in decimal form
4.3Solving problems with rational numbers in fraction form
4.4Determine square roots of rational numbers

5.Solving Linear Equations

5.1Solving linear equations using multiplication and division (free lessons)
5.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
5.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
5.4Solving linear equations with variables on both sides
5.5Solving literal equations

6.Linear Inequalities

6.1Express linear inequalities graphically and algebraically (free lessons)
6.2Solving one-step linear inequalities
6.3Solving multi-step linear inequalities

7.Solving Simultaneous Equations

7.1Determining number of solutions to linear equations (free lessons)
7.2Solving simultaneous linear equations by graphing
7.3Solving simultaneous linear equations by elimination
7.4Solving simultaneous linear equations by substitution
7.5Money related questions in linear equations (free lessons)
7.6Unknown number related questions in linear equations
7.7Distance and time related questions in linear equations
7.8Rectangular shape related questions in linear equations

8.Exponents

8.1Product rule of exponents (free lessons)
8.2Quotient rule of exponents
8.3Power of a product rule
8.4Power of a quotient rule
8.5Power of a power rule (free lessons)
8.6Negative exponent rule
8.7Combining the exponent rules
8.8Scientific notation
8.9Convert between radicals and rational exponents (free lessons)
8.10Solving for exponents

9.Exponential Functions

9.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
9.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
9.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
9.4Exponents: Negative exponents
9.5Exponents: Zero exponent: a0=1 a^0 = 1
9.6Exponents: Rational exponents
9.7Graphing exponential functions
9.8Graphing transformations of exponential functions
9.9Finding an exponential function given its graph

10.Exponential Growth and Decay

10.1Exponential growth and decay by a factor
10.2Exponential decay: Half-life (free lessons)
10.3Exponential growth and decay by percentage
10.4Continuous growth and decay

11.Operations 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

12.Factorising Polynomial expressions

12.1Common factors of polynomials (free lessons)
12.2Factorising polynomials by grouping
12.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
12.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
12.5Factorising polynomials: x2+bx+cx^2 + bx + c (free lessons)
12.6Applications of polynomials: x2+bx+cx^2 + bx + c
12.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
12.8Factorising polynomials: ax2+bx+cax^2 + bx + c
12.9Factorising perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
12.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
12.11Evaluating polynomials
12.12Using algebra tiles to solve polynomials
12.13Solving polynomial equations (free lessons)
12.14Word problems of polynomials

13.Factorising Quadratic Functions

13.1Factorise by taking out the greatest common factor (free lessons)
13.2Factorise by grouping
13.3Factorising difference of squares: x2−y2x^2 - y^2
13.4Factorising trinomials
13.5Factoring difference of cubes
13.6Factoring sum of cubes

14.Quadratic Functions

14.1Characteristics of quadratic functions (free lessons)
14.2Transformations of quadratic functions
14.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
14.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
14.5Completing the square
14.6Converting from general to vertex form by completing the square
14.7Shortcut: Vertex formula (free lessons)
14.8Finding the quadratic functions for given parabolas (free lessons)
14.9Applications of quadratic functions

15.Radicals

15.1Square and square roots (free lessons)
15.2Cubic and cube roots
15.3Evaluating and simplifying radicals
15.4Converting radicals to mixed radicals
15.5Converting radicals to entire radicals (free lessons)
15.6Adding and subtracting radicals
15.7Multiplying and dividing radicals
15.8Rationalize the denominator

16.Rational 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

17.Coordinates, Quadrants, and Transformations

17.1Cartesian plane
17.2Draw on coordinate planes
17.3Introduction to transformations
17.4Horizontal and vertical distances

18.Angles, Lines and Transversals

18.1Pairs of lines and angles
18.2Parallel lines and transversals
18.3Parallel line proofs
18.4Perpendicular line proofs (free lessons)

19.Properties of Triangles

19.1Classifying triangles
19.2Isosceles and equilateral triangles

20.Circles

20.1Circles and circumference
20.2Angles in a circle (free lessons)
20.3Arcs of a circle
20.4Areas and sectors of circles

21.Congruent Triangles

21.1Congruence and congruent triangles
21.2Triangles congruent by SSS proofs
21.3Triangles congruent by SAS and HL proofs
21.4Triangles congruent by ASA and AAS proofs

22.Scale Factors and Similarity

22.1Enlargements and reductions with scale factors (free lessons)
22.2Scale diagrams
22.3Similar triangles
22.4Similar polygons

23.Pythagorean Theorem

23.1Squares and square roots (free lessons)
23.2Pythagorean theorem (free lessons)
23.3Estimating square roots (free lessons)
23.4Using the pythagorean relationship
23.5Applications of pythagorean theorem

24.Introduction to Trigonometry

24.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
24.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
24.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
24.4Combination of SohCahToa questions (free lessons)
24.5Solving expressions using 45-45-90 special right triangles (free lessons)
24.6Solving expressions using 30-60-90 special right triangles
24.7Word problems relating ladder in trigonometry
24.8Word problems relating guy wire in trigonometry
24.9Other word problems relating angles in trigonometry

25.Surface Area and Volume

25.1Surface area and volume of prisms (free lessons)
25.2Surface area and volume of pyramids
25.3Surface area and volume of cylinders
25.4Surface area and volume of cones (free lessons)
25.5Surface area and volume of spheres

26.Probability

26.1Determining probabilities using tree diagrams and tables (free lessons)
26.2Probability of independent events
26.3Fundamental counting principle
26.4Factorial notation
26.5Probability with Venn diagrams

27.Data and Graphs

27.1Reading and drawing histograms
27.2Reading and drawing line graphs
27.3Box-and-whisker plots and scatter plots
27.4Stem-and-leaf plots
27.5Reading and drawing Venn diagrams

28.Statistics

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