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Year 11 Maths Topics

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1. Rational Numbers

1.1 Comparing and ordering rational numbers
1.2 Solving problems with rational numbers in decimal form
1.3 Solving problems with rational numbers in fraction form
1.4 Determine square roots of rational numbers

2. Ratios, Rates, and Proportions

2.1 Ratios
2.2 Rates
2.3 Proportions

3. Direct variation

3.1 Identifying proportional relationships
3.2 Understanding graphs of proportional relationships
3.3 Graphing and writing equations of proportional relationships
3.4 Applications of proportional relationships

4. Introduction to Relations and Functions

4.1 Relationship between two variables
4.2 Understand relations between x- and y-intercepts
4.3 Domain and range of a function
4.4 Identifying functions
4.5 Function notation

5. Linear Functions

5.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
5.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
5.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
5.4 Gradient intercept form: y = mx + b
5.5 General form: Ax + By + C = 0
5.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
5.7 Rate of change
5.8 Graphing linear functions using table of values
5.9 Graphing linear functions using x- and y-intercepts
5.10 Graphing from gradient-intercept form y=mx+b
5.11 Graphing linear functions using a single point and gradient
5.12 Word problems of graphing linear functions
5.13 Parallel and perpendicular lines in linear functions
5.14 Applications of linear relations

6. Linear Inequalities

6.1 Express linear inequalities graphically and algebraically
6.2 Solving one-step linear inequalities
6.3 Solving multi-step linear inequalities
6.4 Compound 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. Exponents

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

9. Exponential Functions

9.1 Exponents: Product rule (a^x)(a^y) = a^(x+y)
9.2 Exponents: Division rule (a^x / a^y) = a^(x-y)
9.3 Exponents: Power rule (a^x)^y = a^(x * y)
9.4 Exponents: Negative exponents
9.5 Exponents: Zero exponent: a^0 = 1
9.6 Exponents: Rational exponents
9.7 Graphing exponential functions
9.8 Graphing transformations of exponential functions
9.9 Finding an exponential function given its graph

10. Logarithmic Functions

10.1 What is a logarithm?
10.2 Converting from logarithmic form to exponential form
10.3 Evaluating logarithms without a calculator
10.4 Common logarithms
10.5 Natural log: ln
10.6 Evaluating logarithms using change-of-base formula
10.7 Converting from exponential form to logarithmic form
10.8 Solving exponential equations with logarithms
10.9 Product rule of logarithms
10.10 Quotient rule of logarithms
10.11 Combining product rule and quotient rule in logarithms
10.12 Evaluating logarithms using logarithm rules
10.13 Solving logarithmic equations
10.14 Graphing logarithmic functions
10.15 Finding a logarithmic function given its graph

11. Introduction to Polynomials

11.1 Characteristics of polynomials
11.2 Equivalent expressions of polynomials
11.3 Adding and subtracting polynomials

12. Operations of Polynomials

12.1 What is a polynomial?
12.2 Polynomial components
12.3 Multiplying monomial by monomial
12.4 Multiplying monomial by binomial
12.5 Multiplying binomial by binomial
12.6 Multiplying polynomial by polynomial
12.7 Applications of polynomials

13. Factorising Polynomial Expressions

13.1 Common factors of polynomials
13.2 Factorising polynomials by grouping
13.3 Solving polynomials with the unknown "b" from x^2 + bx + c
13.4 Solving polynomials with the unknown "c" from x^2 + bx + c
13.5 Factorising polynomials: x^2 + bx + c
13.6 Applications of polynomials: x^2 + bx + c
13.7 Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
13.8 Factorising polynomials: ax2+bx+cax^2 + bx + c
13.9 Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
13.10 Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
13.11 Evaluating polynomials
13.12 Using algebra tiles to factorise polynomials
13.13 Solving polynomial equations
13.14 Word problems of polynomials

14. Quadratic Functions

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

15. Conics

15.1 Conics - Parabola
15.2 Conics - Ellipse
15.3 Conics - Circle
15.4 Conics - Hyperbola

16. Radicals

16.1 Operations with radicals
16.2 Conversion between entire radicals and mixed radicals
16.3 Adding and subtracting radicals
16.4 Multiplying radicals
16.5 Solving radical equations

17. Algebraic Fractions

17.1 Simplifying algebraic fractions and restrictions
17.2 Adding and subtracting algebraic fractions
17.3 Multiplying algebraic fractions
17.4 Dividing algebraic fractions
17.5 Solving equations with algebraic fractions
17.6 Applications of equations with algebraic fractions
17.7 Simplifying complex fractions
17.8 Partial fraction decomposition

18. Reciprocal Functions

18.1 Graphing reciprocals of linear functions
18.2 Graphing reciprocals of quadratic functions

19. Rational Functions

19.1 What is a rational function?
19.2 Point of discontinuity
19.3 Vertical asymptote
19.4 Horizontal asymptote
19.5 Slant asymptote
19.6 Graphs of rational functions
19.7 Solving rational inequalities

20. Sequences and Series

20.1 Arithmetic sequences
20.2 Arithmetic series
20.3 Geometric sequences
20.4 Geometric series
20.5 Infinite geometric series
20.6 Sigma notation
20.7 Arithmetic mean vs. Geometric mean

21. Angles, Lines and Transversals

21.1 Pairs of lines and angles
21.2 Parallel lines and transversals
21.3 Parallel line proofs
21.4 Perpendicular line proofs

22. Symmetry and Surface Area

22.1 Line symmetry
22.2 Rotational symmetry and transformations
22.3 Surface area of 3-dimensional shapes

23. Properties of triangles

23.1 Classifying Triangles
23.2 Isosceles and Equilateral Triangles

24. Pythagorean Theorem

24.1 Squares and square roots
24.2 Pythagorean theorem
24.3 Estimating square roots
24.4 Using the pythagorean relationship
24.5 Applications of pythagorean theorem

25. Circle Geometry

25.1 Angles in a circle
25.2 Chord properties
25.3 Tangent properties
25.4 Circles and circumference
25.5 Arcs of a circle
25.6 Areas and sectors of circles

26. Scale Factors and Similarity

26.1 Enlargements and reductions with scale factors
26.2 Scale diagrams
26.3 Similar triangles
26.4 Similar polygons

27. Congruent Triangles

27.1 Congruence and Congruent Triangles
27.2 Triangles Congruent by SSS Proofs
27.3 Triangles Congruent by SAS and HL Proofs
27.4 Triangles Congruent by ASA and AAS Proofs

28. Introduction to volume

28.1 Introduction to volume
28.2 Volume of prisms
28.3 Volume of cylinders
28.4 Word problems relating volume of prisms and cylinders

29. Surface Area and Volume

29.1 Surface area and volume of prisms
29.2 Surface area and volume of pyramids
29.3 Surface area and volume of cylinders
29.4 Surface area and volume of cones
29.5 Surface area and volume of spheres

30. Introduction to Trigonometry

30.1 Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
30.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
30.3 Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
30.4 Combination of SohCahToa questions
30.5 Solving expressions using 45-45-90 special right triangles
30.6 Solving expressions using 30-60-90 special right triangles
30.7 Word problems relating ladder in trigonometry
30.8 Word problems relating guy wire in trigonometry
30.9 Other word problems relating angles in trigonometry

31. Trigonometric Ratios and Angle Measure

31.1 Standard angle
31.2 Coterminal angles
31.3 Reference angles
31.4 Find the exact value of trigonometric ratios
31.5 ASTC rule in trigonometry (All Students Take Calculus)
31.6 Unit circle
31.7 Law of sines
31.8 Law of cosines
31.9 Applications of the sine law and cosine law

32. Bearings

32.1 Introduction to bearings
32.2 Bearings and direction word problems
32.3 Angle of elevation and depression

33. Statistics

33.1 Median and mode
33.2 Mean
33.3 Range and outliers
33.4 Application of averages

34. Probability

34.1 Determining probabilities using tree diagrams and tables
34.2 Probability of independent events
34.3 Probability with Venn diagrams

35. Data and Graphs

35.1 Reading and drawing bar graphs
35.2 Reading and drawing histograms
35.3 Reading and drawing line graphs
35.4 Box-and-whisker plots and scatter plots
35.5 Stem-and-leaf plots
35.6 Reading and drawing Venn diagrams
35.7 Frequency tables and dot plots

35 Chapters · 215 Topics · 1504 Videos

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Yes — all content is specifically aligned to NCEA Level 1 achievement standards, covering algebra, trigonometry, calculus, and statistics.

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