📘 Year 11 Maths – FULL Curriculum

A. Numbers

1. Prime or composite

2. Identify rational and irrational numbers

3. Compare and order rational numbers

4. Write a recurring decimal as a fraction

5. Square roots

6. Estimate square roots

7. Cube roots

8. Estimate cube roots

9. Add, subtract, multiply and divide rational numbers

10. Evaluate numerical expressions involving rational numbers

B. Percents

1. Percent of change

2. Percent of change: word problems

3. Percent of change: find the original amount word problems

4. Sale prices and VAT: find the original price

5. Multi-step problems with percents

C. Expressions and Properties

1. Properties of addition and multiplication

2. Distributive property

3. Write equivalent expressions using properties

4. Simplify variable expressions involving like terms and the distributive property

5. Identify equivalent linear expressions

D. Solve Equations

1. Solve one- and two-step linear equations

2. Solve advanced linear equations

3. Solve equations with variables on both sides

4. Solve equations: complete the solution

5. Find the number of solutions

6. Create equations with no solutions or infinitely many solutions

7. Solve linear equations: word problems

8. Solve linear equations: mixed review

9. Rearrange multi-variable equations

E. Problem Solving

1. Consecutive integer problems

2. Rate of travel: word problems

3. Weighted averages: word problems

F. Single-Variable Inequalities

1. Solve one- and two-step linear inequalities

2. Graph solutions to one- and two-step linear inequalities

3. Solve advanced linear inequalities

4. Graph solutions to advanced linear inequalities

5. Graph compound inequalities

6. Write compound inequalities from graphs

7. Solve compound inequalities

8. Graph solutions to compound inequalities

G. Relations and Functions

1. Relations: convert between tables, graphs, mappings and lists of points

2. Domain and range of relations

3. Find values using function graphs

4. Identify independent and dependent variables

5. Identify functions

6. Evaluate a function

7. Complete a function table from a graph

8. Complete a function table from an equation

9. Find solutions using a table

10. Approximate solutions using a table

11. Interpret functions using everyday language

12. Rate of change: tables

13. Rate of change: graphs

H. Direct and Inverse Variation

1. Identify proportional relationships

2. Find the constant of variation

3. Graph a proportional relationship

4. Write direct variation equations

5. Write and solve direct variation equations

6. Write inverse variation equations

7. Write and solve inverse variation equations

8. Identify direct variation and inverse variation

I. Linear Functions

1. Identify linear functions

2. Interpret points on the graph of a linear function

3. Find the gradient of a graph

4. Find the gradient from two points

5. Find a missing coordinate using gradient

6. Find the gradient and y-intercept of a linear equation

7. Graph an equation in y = mx + c form

8. Write an equation in y = mx + c form from a graph

9. Write an equation in y = mx + c form

10. Linear equations: solve for y

11. Write an equation in y = mx + c form from a table

12. Write an equation in y = mx + c form from a word problem

13. Write linear functions to solve word problems

14. Complete a table and graph a linear function

15. Compare linear functions: graphs, tables and equations

16. Find x- and y-intercepts for equations in ax + by = c form

17. Graph an equation in ax + by = c form

18. Equations of horizontal and vertical lines

19. Graph a horizontal or vertical line

20. Point-gradient form: graph an equation

21. Point-gradient form: write an equation

22. Point-gradient form: write an equation from a graph

23. Gradients of parallel lines

24. Gradients of perpendicular lines

25. Gradients of parallel and perpendicular lines

26. Write an equation for a parallel line

27. Write an equation for a perpendicular line

28. Write an equation for a parallel or perpendicular line

29. Transformations of linear functions

J. Simultaneous Equations

1. Is (x, y) a solution to the simultaneous equations?

2. Solve simultaneous equations by graphing

3. Solve simultaneous equations by graphing: word problems

4. Find the number of solutions to simultaneous equations by graphing

5. Find the number of solutions to simultaneous equations

6. Solve simultaneous equations using substitution

7. Solve simultaneous equations using substitution: word problems

8. Solve simultaneous equations using elimination

9. Solve simultaneous equations using elimination: word problems

10. Solve simultaneous equations using any method

11. Solve simultaneous equations using any method: word problems

K. Linear Inequalities

1. Does (x, y) satisfy the inequality?

2. Linear inequalities: solve for y

3. Graph a linear inequality in the coordinate plane

4. Linear inequalities: word problems

5. Is (x, y) a solution to the simultaneous inequalities?

6. Solve simultaneous linear inequalities by graphing

L. Indices

1. Indices review

2. Negative indices

3. Multiplication with indices

4. Division with indices

5. Multiplication and division with indices

6. Power rule

7. Evaluate expressions using properties of indices

8. Identify equivalent expressions involving indices

M. Number Sequences

1. Identify arithmetic and geometric sequences

2. Arithmetic sequences

3. Geometric sequences

4. Evaluate variable expressions for number sequences

5. Write variable expressions for arithmetic sequences

6. Write variable expressions for geometric sequences

7. Sequences of square and cube numbers

8. Fibonacci-type sequences

9. Number sequences: mixed review

N. Standard Form

1. Convert between ordinary numbers and standard form

2. Compare numbers written in standard form

3. Add and subtract numbers written in standard form

4. Multiply and divide numbers written in standard form

O. Exponential Functions

1. Evaluate an exponential function

2. Write exponential functions: word problems

3. Match exponential functions and graphs I

4. Match exponential functions and graphs II

5. Graph exponential functions

6. Domain and range of exponential functions

7. Exponential growth and decay: word problems

8. Compound interest

P. Monomials

1. Identify monomials

2. Multiply monomials

3. Divide monomials

4. Multiply and divide monomials

5. Powers of monomials

Q. Polynomials

1. Polynomial vocabulary

2. Model polynomials with algebra tiles

3. Add and subtract polynomials using algebra tiles

4. Add and subtract polynomials

5. Add polynomials to find perimeter

6. Multiply a polynomial by a monomial

7. Multiply two polynomials using algebra tiles

8. Multiply two binomials

9. Multiply two binomials: special cases

10. Multiply polynomials

R. Factorising

1. HCF of monomials

2. Factorise out a monomial

3. Factorise quadratics using algebra tiles

4. Factorise quadratics with leading coefficient 1

5. Factorise quadratics with other leading coefficients

6. Factorise quadratics: special cases

7. Factorise by grouping

8. Factorise polynomials

S. Quadratic Equations and Inequalities

1. Characteristics of quadratic functions: graphs

2. Characteristics of quadratic functions: equations

3. Complete a function table: quadratic functions

4. Match quadratic functions and graphs

5. Graph a quadratic function

6. Solve a quadratic equation using square roots

7. Solve a quadratic equation using the zero product property

8. Solve a quadratic equation with leading coefficient 1 by factorising

9. Solve a quadratic equation with other leading coefficients by factorising

10. Complete the square

11. Solve a quadratic equation by completing the square

12. Solve a quadratic equation using the quadratic formula

13. Solve simultaneous quadratic and linear equations by graphing

14. Solve simultaneous quadratic and linear equations

15. Graph solutions to quadratic inequalities

16. Solve quadratic inequalities

T. Function Types

1. Identify linear, quadratic and cubic functions from graphs

2. Identify linear, quadratic, cubic and exponential functions from graphs

3. Identify linear, quadratic and exponential functions from tables

4. Write linear, quadratic and exponential functions

5. Linear functions over unit intervals

6. Exponential functions over unit intervals

7. Describe linear and exponential growth and decay

U. Function Operations

1. Composition of linear functions: find a value

2. Composition of linear functions: find an equation

3. Composition of linear and quadratic functions: find a value

4. Composition of linear and quadratic functions: find an equation

5. Identify inverse functions

6. Find values of inverse functions from tables

7. Find values of inverse functions from graphs

8. Find inverse functions and relations

V. Function Transformations

1. Translation and reflection rules

2. Translations of functions

3. Reflections of functions

4. Translations and reflections of functions

W. Radical Expressions

1. Simplify radical expressions

2. Simplify radical expressions involving fractions

3. Multiply radical expressions

4. Add and subtract radical expressions

5. Simplify radical expressions using the distributive property

6. Simplify radical expressions using conjugates

7. Simplify radical expressions: mixed review

X. Fractional Indices

1. Evaluate fractional indices

2. Multiplication with fractional indices

3. Division with fractional indices

4. Power rule with fractional indices

5. Simplify expressions involving fractional indices I

6. Simplify expressions involving fractional indices II

Y. Rational Functions and Expressions

1. Rational functions: asymptotes and excluded values

2. Simplify complex fractions

3. Simplify rational expressions

4. Multiply and divide rational expressions

5. Divide polynomials

6. Add and subtract rational expressions

7. Solve rational equations

Z. Midpoints and Distance

1. Midpoints

2. Distance between two points

3. Distance to the origin in three dimensions

AA. Transformations

1. Identify translations, reflections and rotations

2. Translations: graph the image

3. Translations: find the coordinates

4. Translations: write the rule

5. Reflections: graph the image

6. Reflections: find the coordinates

7. Rotate polygons about a point

8. Rotations: graph the image

9. Rotations: find the coordinates

10. Describe transformations

11. Reflections and rotations: write the rule

12. Sequences of translations, reflections and rotations: graph the image

13. Sequences of congruence transformations: choose the sequence

14. Transformations that carry a polygon onto itself

15. Translations, reflections and rotations: mixed review

16. Dilations: graph the image

17. Dilations: find the coordinates

18. Dilations: find length, perimeter and area

19. Dilations: scale factor and classification

20. Dilations: find the scale factor and center of the dilation

21. Dilations and parallel lines

BB. Congruence

1. Identify congruent figures

2. Congruence statements and corresponding parts

3. Solve problems involving corresponding parts

4. Determine if two figures are congruent: justify your answer

5. SSS and SAS Theorems

6. ASA and AAS Theorems

7. SSS, SAS, ASA and AAS Theorems

8. SSS Theorem in the coordinate plane

9. Congruency in isosceles and equilateral triangles

10. Hypotenuse-Leg Theorem

CC. Similarity

1. Identify similar figures

2. Ratios in similar figures

3. Similarity statements

4. Side lengths and angle measures in similar figures

5. Similar triangles and indirect measurement

6. Perimeters of similar figures

7. Similarity rules for triangles

8. Similar triangles and transformations

9. Determine if two figures are similar: justify your answer

10. Areas of similar figures

DD. Right Triangles

1. Pythagoras’ Theorem

2. Pythagoras’ theorem: word problems

3. Converse of Pythagoras’ theorem

4. Pythagoras’ Inequality Theorems

5. Special right triangles

EE. Trigonometry

1. Trigonometric ratios: sin, cos and tan

2. Trigonometric ratios: csc, sec and cot

3. Find trigonometric functions of special angles: sin, cos and tan

4. Find trigonometric functions of special angles: csc, sec and cot

5. Find trigonometric functions using a calculator

6. Inverses of trigonometric functions

7. Trigonometric ratios: find a side length

8. Trigonometric ratios: find an angle measure

9. Solve a right triangle

10. Law of Sines

11. Law of Cosines

12. Solve a triangle

13. Area of a triangle: sine formula

14. Graph sine functions

15. Graph cosine functions

16. Graph sine and cosine functions

FF. Perimeter and Area

1. Perimeter

2. Area of triangles and quadrilaterals

3. Area and perimeter in the coordinate plane I

4. Area and perimeter in the coordinate plane II

5. Area and circumference of circles

6. Area of compound figures

7. Area between two shapes

8. Area and perimeter of similar figures

GG. Three-Dimensional Figures

1. Parts of three-dimensional figures

2. Three-dimensional figure vocabulary

3. Front, side and top view

4. Base plans

5. Nets of three-dimensional figures

6. Cross-sections of three-dimensional figures

7. Solids of revolution

HH. Surface Area and Volume

1. Surface area and volume of cuboids

2. Surface area of prisms and cylinders

3. Surface area of pyramids and cones

4. Surface area of spheres

5. Surface area: mixed review

6. Volume of prisms and cylinders

7. Volume of pyramids and cones

8. Volume of spheres

9. Volume of compound figures

10. Volume: mixed review

11. Similar solids

12. Surface area of similar solids

13. Volume of similar solids

14. Surface area and volume of similar solids

II. Circles

1. Parts of a circle

2. Central angles

3. Understand arc length and sector area of a circle

4. Arc measure and arc length

5. Area of sectors

6. Circle measurements: mixed review

7. Arcs and chords

8. Tangent lines

9. Angles formed by chords, secants, and tangents

10. Segments formed by chords, secants, and tangents

11. Perimeter of polygons with an inscribed circle

12. Inscribed angles

13. Angles in inscribed right triangles

14. Angles in inscribed quadrilaterals I

15. Angles in inscribed quadrilaterals II

16. Write equations of circles centered at the origin from graphs

17. Write equations of circles centered at the origin from properties

18. Find properties of circles from equations

19. Graph circles centered at the origin

JJ. Vectors

1. Compass directions and vectors

2. Find the magnitude of a vector

3. Find the component form of a vector

4. Find the component form of a vector given its magnitude and direction angle

5. Graph a resultant vector using the triangle method

6. Graph a resultant vector using the parallelogram method

7. Add vectors

8. Subtract vectors

9. Multiply a vector by a scalar

10. Find the magnitude of a vector scalar multiple

11. Determine the direction of a vector scalar multiple

12. Linear combinations of vectors

KK. Measurement

1. Convert rates and measurements: metric units

2. Metric mixed units

3. Convert rates and measurements: imperial units

4. Imperial mixed units

5. Convert between metric and imperial units

6. Precision

7. Greatest possible error

8. Minimum and maximum area and volume

9. Percent error

10. Percent error: area and volume

LL. Data and Graphs

1. Interpret tables

2. Interpret line graphs

3. Create line graphs

4. Interpret bar graphs for grouped data

5. Create bar graphs for grouped data

6. Interpret pie charts

7. Interpret stem-and-leaf plots

8. Choose the best type of graph

9. Box plots

MM. Statistics

1. Mean, median, mode and range

2. Quartiles and interquartile range

3. Variance and standard deviation

4. Describe distributions in line plots

5. Populations and samples

6. Identify biased samples

7. Create scatter plots

8. Identify trends with scatter plots

9. Make predictions with scatter plots

10. Outliers in scatter plots

11. Write an equation for a line of best fit

12. Correlation and causation

NN. Probability

1. Theoretical probability

2. Experimental probability

3. Make predictions

4. Sample spaces for compound events

5. Compound events: find the number of outcomes

6. Probability of compound events

7. Find the number of outcomes: word problems

8. Find probabilities using two-way frequency tables

9. Identify independent and dependent events

10. Probability of independent and dependent events

11. Find conditional probabilities

12. Independence and conditional probability

13. Find conditional probabilities using two-way frequency tables

14. Geometric probability