Master Transition Year Maths

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Transition Year Maths Topics

ax^2 + bx + c

Factorising polynomials:

ax^2 + bx + c

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Evaluating polynomials

Using algebra tiles to factorise polynomials

Solving polynomial equations

Word problems of polynomials

Factorising Quadratic Functions

Factorise by taking out the greatest common factor

Factorise by grouping

Factorising difference of squares: x^2 - y^2

Factorising trinomials

Factoring difference of cubes

Factoring sum of cubes

Quadratic Functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing parabolas for given quadratic functions

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Radicals

Square and square roots

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Rational Expressions

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

Reciprocal Functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Coordinates, Quadrants, and Transformations

Cartesian plane

Draw on coordinate planes

Introduction to transformations

Horizontal and vertical distances

Angles, Lines and Transversals

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Properties of Triangles

Classifying triangles

Isosceles and equilateral triangles

Circles

Circles and circumference

Angles in a circle

Arcs of a circle

Areas and sectors of circles

Congruent Triangles

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Pythagorean Theorem

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Introduction to Trigonometry

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Fundamental counting principle

Factorial notation

Probability with Venn diagrams

Data and Graphs

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Pie charts

Reading and drawing Venn diagrams

Frequency tables and dot plots

Statistics

Median and mode

Mean

Range and outliers

Application of averages

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