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Year 12 Maths Topics

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1. Solving Linear Equations

1.1 Solving linear equations using multiplication and division
1.2 Solving two-step linear equations: ax + b = c, x/a + b = c
1.3 Solving linear equations using distributive property: a(x + b) = c
1.4 Solving linear equations with variables on both sides
1.5 Solving literal equations

2. Linear Inequalities

2.1 Express linear inequalities graphically and algebraically
2.2 Solving one-step linear inequalities
2.3 Solving multi-step linear inequalities
2.4 Compound inequalities

3. Linear Functions

3.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
3.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
3.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
3.4 Gradient intercept form: y = mx + b
3.5 General form: Ax + By + C = 0
3.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
3.7 Rate of change
3.8 Graphing linear functions using table of values
3.9 Graphing linear functions using x- and y-intercepts
3.10 Graphing from gradient-intercept form y=mx+b
3.11 Graphing linear functions using a single point and gradient
3.12 Word problems of graphing linear functions
3.13 Parallel and perpendicular lines in linear functions
3.14 Applications of linear relations

4. Factorising

4.1 Factorise by taking out the greatest common factor
4.2 Factorise by grouping
4.3 Factorising difference of squares: x^2 - y^2
4.4 Factorising trinomials: ax2+bx+cax^2 + bx + c

5. Quadratic Functions

5.1 Characteristics of quadratic functions
5.2 Transformations of quadratic functions
5.3 Quadratic function in general form: y = ax^2 + bx + c
5.4 Quadratic function in vertex form: y = a(x-p)^2 + q
5.5 Completing the square
5.6 Converting from general to vertex form by completing the square
5.7 Shortcut: Vertex formula
5.8 Graphing parabolas for given quadratic functions
5.9 Finding the quadratic functions for given parabolas
5.10 Applications of quadratic functions

6. Quadratic Equations and Inequalities

6.1 Solving quadratic equations by factorising
6.2 Solving quadratic equations by completing the square
6.3 Using quadratic formula to solve quadratic equations
6.4 Nature of roots of quadratic equations: The discriminant
6.5 Applications of quadratic equations
6.6 Solving quadratic inequalities

7. Solving Simultaneous Equations

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

8. Simultaneous Equations (Advanced)

8.1 Simultaneous linear equations
8.2 Simultaneous linear-quadratic equations
8.3 Simultaneous quadratic-quadratic equations
8.4 Solving 3 variable simultaneous equations by substitution
8.5 Solving 3 variable simultaneous equations by elimination
8.6 Solving 3 variable simultaneous equations with no or infinite solutions
8.7 Word problems relating 3 variable simultaneous equations

9. Inequalities in two variables (Advanced)

9.1 Graphing linear inequalities in two variables
9.2 Graphing simultaneous linear inequalities
9.3 Graphing quadratic inequalities in two variables
9.4 Graphing simultaneous quadratic inequalities
9.5 Applications of inequalities
9.6 What is linear programming?
9.7 Linear programming word problems

10. Imaginary and Complex Numbers

10.1 Introduction to imaginary numbers
10.2 Complex numbers and complex planes
10.3 Adding and subtracting complex numbers
10.4 Complex conjugates
10.5 Multiplying and dividing complex numbers
10.6 Distance and midpoint of complex numbers
10.7 Angle and absolute value of complex numbers
10.8 Polar form of complex numbers
10.9 Operations on complex numbers in polar form

11. Polynomial Functions

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

12. Radicals

12.1 Operations with radicals
12.2 Conversion between entire radicals and mixed radicals
12.3 Adding and subtracting radicals
12.4 Multiplying radicals
12.5 Solving radical equations

13. Exponents

13.1 Product rule of exponents
13.2 Quotient rule of exponents
13.3 Power of a product rule
13.4 Power of a quotient rule
13.5 Power of a power rule
13.6 Negative exponent rule
13.7 Combining the exponent rules
13.8 Scientific notation
13.9 Convert between radicals and rational exponents
13.10 Solving for exponents

14. Algebraic Fractions

14.1 Simplifying algebraic fractions and restrictions
14.2 Adding and subtracting algebraic fractions
14.3 Multiplying algebraic fractions
14.4 Dividing algebraic fractions
14.5 Solving equations with algebraic fractions
14.6 Applications of equations with algebraic fractions
14.7 Simplifying complex fractions
14.8 Partial fraction decomposition

15. Reciprocal Functions

15.1 Graphing reciprocals of linear functions
15.2 Graphing reciprocals of quadratic functions

16. Rational Functions

16.1 What is a rational function?
16.2 Point of discontinuity
16.3 Vertical asymptote
16.4 Horizontal asymptote
16.5 Slant asymptote
16.6 Graphs of rational functions
16.7 Solving rational inequalities

17. Operations of Functions

17.1 Function notation
17.2 Operations with functions
17.3 Adding functions
17.4 Subtracting functions
17.5 Multiplying functions
17.6 Dividing functions
17.7 Composite functions
17.8 Inequalities of combined functions
17.9 Inverse functions
17.10 One to one functions
17.11 Difference quotient: applications of functions

18. Transformations of Functions

18.1 Transformations of functions: Horizontal translations
18.2 Transformations of functions: Vertical translations
18.3 Reflection across the y-axis: y = f(-x)
18.4 Reflection across the x-axis: y = -f(x)
18.5 Transformations of functions: Horizontal stretches
18.6 Transformations of functions: Vertical stretches
18.7 Combining transformations of functions
18.8 Even and odd functions

19. Exponential Functions

19.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
19.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
19.3 Exponents: Power rule (a^x)^y = a^(x * y)
19.4 Exponents: Negative exponents
19.5 Exponents: Zero exponent: a^0 = 1
19.6 Exponents: Rational exponents
19.7 Graphing exponential functions
19.8 Graphing transformations of exponential functions
19.9 Finding an exponential function given its graph

20. Logarithmic Functions

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

21. Applications of Exponential and Logarithmic Functions

21.1 Exponential growth and decay by a factor
21.2 Exponential decay: Half-life
21.3 Exponential growth and decay by percentage
21.4 Finance: Compound interest
21.5 Continuous growth and decay
21.6 Logarithmic scale: Richter scale (earthquake)
21.7 Logarithmic scale: pH scale
21.8 Logarithmic scale: dB scale
21.9 Finance: Future value and present value

22. Introduction to Trigonometry

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

23. Trigonometric Ratios and Angle Measure

23.1 Standard angle
23.2 Coterminal angles
23.3 Reference angles
23.4 Find the exact value of trigonometric ratios
23.5 ASTC rule in trigonometry (All Students Take Calculus)
23.6 Unit circle
23.7 Law of sines
23.8 Law of cosines
23.9 Applications of the sine law and cosine law

24. Bearings

24.1 Introduction to bearings
24.2 Bearings and direction word problems
24.3 Angle of elevation and depression

25. Graphing Trigonometric Functions

25.1 Sine graph: y = sin x
25.2 Cosine graph: y = cos x
25.3 Tangent graph: y = tan x
25.4 Cotangent graph: y = cot x
25.5 Secant graph: y = sec x
25.6 Cosecant graph: y = csc x
25.7 Graphing transformations of trigonometric functions
25.8 Determining trigonometric functions given their graphs

26. Trigonometric Identities

26.1 Quotient identities and reciprocal identities
26.2 Pythagorean identities
26.3 Sum and difference identities
26.4 Cofunction identities
26.5 Double-angle identities

27. Conics

27.1 Conics - Parabola
27.2 Conics - Ellipse
27.3 Conics - Circle
27.4 Conics - Hyperbola

28. Surface Area and Volume

28.1 Surface area and volume of prisms
28.2 Surface area and volume of pyramids
28.3 Surface area and volume of cylinders
28.4 Surface area and volume of cones
28.5 Surface area and volume of spheres

29. Sequences and Series

29.1 Arithmetic sequences
29.2 Arithmetic series
29.3 Geometric sequences
29.4 Geometric series
29.5 Infinite geometric series
29.6 Sigma notation
29.7 Arithmetic mean vs. Geometric mean

30. Probability

30.1 Determining probabilities using tree diagrams and tables
30.2 Probability of independent events
30.3 Probability with Venn diagrams

31. Permutations and Combinations

31.1 Fundamental counting principle
31.2 Factorial notation
31.3 Path counting problems
31.4 Permutation vs. Combination
31.5 Permutations
31.6 Combinations
31.7 Problems involving both permutations and combinations
31.8 Pascal's triangle
31.9 Binomial theorem

32. Statistics

32.1 Median and mode
32.2 Mean
32.3 Range and outliers
32.4 Application of averages

33. Data and Graphs

33.1 Reading and drawing bar graphs
33.2 Reading and drawing histograms
33.3 Reading and drawing line graphs
33.4 Box-and-whisker plots and scatter plots
33.5 Stem-and-leaf plots
33.6 Reading and drawing Venn diagrams
33.7 Frequency tables and dot plots

33 Chapters · 245 Topics · 1501 Videos

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Yes — our Year 12 Maths content covers all major topics regardless of textbook, aligned to NCEA Level 2 standards for New Zealand.

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Absolutely. Our Year 12 Maths course is specifically designed to cover all NCEA Level 2 Mathematics achievement standards and exam requirements.

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