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📘 Year 10 Maths – FULL Curriculum

A. Numbers

  1. Prime or composite

  2. Prime factorisation

  3. Highest common factor

  4. Lowest common multiple

  5. HCF and LCM: word problems

  6. Compare and order rational numbers

  7. Number lines

  8. Write a recurring decimal as a fraction

  9. Convert between decimals and fractions

  10. Square roots

  11. Estimate square roots

  12. Cube roots

  13. Estimate cube roots

  14. Classify numbers

B. Operations

  1. Add, subtract, multiply and divide integers

  2. Evaluate numerical expressions involving integers

  3. Evaluate variable expressions involving integers

  4. Add and subtract rational numbers

  5. Multiply and divide rational numbers

  6. Evaluate numerical expressions involving rational numbers

  7. Evaluate variable expressions involving rational numbers

C. Ratios, Rates and Proportions

  1. Identify equivalent ratios

  2. Write an equivalent ratio

  3. Unit rates

  4. Unit rates with fractions

  5. Unit prices

  6. Solve proportions

  7. Solve proportions: word problems

  8. Estimate population size using proportions

  9. Scale drawings: word problems

D. Percents

  1. Convert between percents, fractions and decimals

  2. Solve percent equations

  3. Percent word problems

  4. Percent of change

  5. Percent of change: word problems

  6. Percent of a number: VAT, discount and more

  7. Find the percent: discount and mark-up

  8. Multi-step problems with percents

E. Expressions and Properties

  1. Write variable expressions

  2. Properties of addition and multiplication

  3. Distributive property

  4. Simplify variable expressions using properties

  5. Write equivalent expressions using properties

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

  7. Identify equivalent linear expressions

F. Solve Equations

  1. Write variable equations

  2. Identify expressions and equations

  3. Properties of equality

  4. Identify equivalent equations

  5. Does x satisfy the equation?

  6. Solve equations using order of operations

  7. Model and solve equations using algebra tiles

  8. Write and solve equations that represent diagrams

  9. Solve one-step linear equations

  10. Solve two-step linear equations

  11. Solve advanced linear equations

  12. Solve equations with variables on both sides

  13. Solve equations: complete the solution

  14. Find the number of solutions

  15. Create equations with no solutions or infinitely many solutions

  16. Solve linear equations: word problems

  17. Solve linear equations: mixed review

  18. Rearrange multi-variable equations

G. Problem Solving

  1. Word problems: mixed review

  2. Word problems with money

  3. Consecutive integer problems

  4. Rate of travel: word problems

  5. Weighted averages: word problems

H. Single-Variable Inequalities

  1. Graph inequalities

  2. Write inequalities from graphs

  3. Identify solutions to inequalities

  4. Solve one-step linear inequalities: addition and subtraction

  5. Solve one-step linear inequalities: multiplication and division

  6. Solve one-step linear inequalities

  7. Graph solutions to one-step linear inequalities

  8. Solve two-step linear inequalities

  9. Graph solutions to two-step linear inequalities

  10. Solve advanced linear inequalities

  11. Graph solutions to advanced linear inequalities

  12. Graph compound inequalities

  13. Write compound inequalities from graphs

  14. Solve compound inequalities

  15. Graph solutions to compound inequalities

I. Relations and Functions

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

  2. Domain and range of relations

  3. Identify independent and dependent variables

  4. Identify functions

  5. Identify functions: vertical line test

  6. Identify types of functions from graphs

  7. Find values using function graphs

  8. Evaluate a function

  9. Evaluate a function: plug in an expression

  10. Complete a function table from a graph

  11. Complete a function table from an equation

  12. Find solutions using a table

  13. Approximate solutions using a table

  14. Interpret functions using everyday language

J. 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. Identify direct variation and inverse variation

  7. Write inverse variation equations

  8. Write and solve inverse variation equations

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

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

  12. Linear equations: solve for y

  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. Write an equation for a parallel line

  25. Transformations of linear functions

L. 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: matching coefficients

  9. Solve simultaneous equations using elimination

  10. Solve simultaneous equations using elimination: word problems

  11. Solve simultaneous equations using any method

  12. Solve simultaneous equations using any method: word problems

M. 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

N. Indices

  1. Indices with integer bases

  2. Indices with decimal and fractional bases

  3. Multiplication with positive indices

  4. Power rule with positive indices

  5. Evaluate expressions using properties of indices: positive indices

  6. Negative indices

  7. Multiplication with integer indices

  8. Division with integer indices

  9. Multiplication and division with integer indices

  10. Power rule with integer indices

  11. Evaluate expressions using properties of indices: integer indices

  12. Identify equivalent expressions involving integer indices

  13. Evaluate integers raised to positive unit fractions

  14. Multiplication with positive unit fraction indices

O. 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

P. 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 numbers written in standard form

  5. Divide numbers written in standard form

Q. 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. Domain and range of exponential functions

  6. Exponential growth and decay: word problems

  7. Compound interest

R. Monomials

  1. Identify monomials

  2. Multiply monomials

  3. Divide monomials

  4. Multiply and divide monomials

  5. Powers of monomials

S. 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

T. 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

U. Quadratic Equations

  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

V. 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

W. Coordinate Plane

  1. Coordinate plane review

  2. Quadrants and axes

  3. Midpoint formula: find the midpoint

  4. Midpoint formula: find the endpoint

  5. Distance between two points

X. Transformations

  1. Identify reflections, rotations and translations

  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. Reflections and rotations: write the rule

  11. Reflections, rotations and translations: graph the image

  12. Reflections, rotations and translations: find the coordinates

  13. Dilations: graph the image

  14. Dilations: find the coordinates

  15. Dilations and scale factors

Y. Logic

  1. Identify hypotheses and conclusions

  2. Counterexamples

Z. Congruence

  1. Identify congruent figures

  2. Congruence statements and corresponding parts

  3. Congruent figures: side lengths and angle measures

  4. SSS and SAS Theorems

  5. ASA and AAS Theorems

  6. SSS, SAS, ASA and AAS Theorems

  7. Hypotenuse-Leg Theorem

AA. Similarity

  1. Identify similar figures

  2. Ratios in similar figures

  3. Similarity statements

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

  5. Similar figures: side lengths and angle measures

  6. Similar triangles and indirect measurement

BB. Triangles and Trigonometry

  1. Pythagoras’ theorem

  2. Pythagoras’ theorem: word problems

  3. Converse of Pythagoras’ theorem: is it a right triangle?

  4. Trigonometric ratios: sin, cos and tan

  5. Trigonometric ratios: csc, sec and cot

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

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

  8. Find trigonometric functions using a calculator

  9. Inverses of trigonometric functions

  10. Trigonometric ratios: find a side length

  11. Trigonometric ratios: find an angle measure

  12. Solve a right triangle

CC. Perimeter and Area

  1. Perimeter

  2. Circumference of circles

  3. Perimeter of semicircles and quarter circles

  4. Area of triangles and quadrilaterals

  5. Area of circles

  6. Area of semicircles and quarter circles

  7. Area of compound figures with triangles, semicircles and quarter circles

  8. Area between two shapes

  9. Area and perimeter of similar figures

DD. 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

EE. 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. Volume and surface area of similar solids

  13. Perimeter, area and volume: changes in scale

FF. 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

GG. Geometric Constructions

  1. Construct the midpoint or perpendicular bisector of a segment

  2. Construct an angle bisector

  3. Construct a perpendicular line

  4. Construct parallel lines

  5. Construct an equilateral triangle or regular hexagon

  6. Construct a square

HH. Vectors

  1. Compass directions and vectors

  2. Find the component form of a vector

  3. Graph a resultant vector using the triangle method

  4. Graph a resultant vector using the parallelogram method

  5. Add vectors

  6. Subtract vectors

II. 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 square metres and hectares

  6. Convert square units of length

  7. Convert between cubic metres and litres

  8. Convert cubic units of length

  9. Convert between metric and imperial units

  10. Precision

  11. Greatest possible error

  12. Minimum and maximum area and volume

  13. Percent error

  14. Percent error: area and volume

  15. Calculate density, mass and volume

JJ. Data and Graphs

  1. Interpret tables

  2. Interpret line graphs

  3. Create line graphs

  4. Interpret bar graphs for categorical data

  5. Create bar graphs for categorical data

  6. Interpret bar graphs for grouped data

  7. Create bar graphs for grouped data

  8. Interpret line plots

  9. Create line plots

  10. Interpret pie charts

  11. Interpret stem-and-leaf plots

  12. Box plots

KK. Statistics

  1. Calculate mean, median, mode and range

  2. Interpret charts to find mean, median, mode and range

  3. Mean, median, mode and range: find the missing number

  4. Calculate quartiles and interquartile range

  5. Identify an outlier

  6. Identify an outlier and describe the effect of removing it

  7. Describe distributions in line plots

  8. Populations and samples

  9. Identify biased samples

  10. Create scatter plots

  11. Identify trends with scatter plots

  12. Make predictions with scatter plots

  13. Outliers in scatter plots

  14. Write an equation for a line of best fit

  15. Correlation and causation

LL. Probability

  1. Probability of simple events

  2. Probability of simple events and opposite events

  3. Probability of mutually exclusive events and overlapping events

  4. Experimental probability

  5. Make predictions using experimental probability

  6. Make predictions using theoretical probability

  7. Sample spaces for compound events

  8. Compound events: find the number of outcomes

  9. Probability of compound events

  10. Find the number of outcomes: word problems

  11. Find probabilities using two-way frequency tables

  12. Identify independent and dependent events

  13. Probability of independent and dependent events

  14. Find conditional probabilities using two-way frequency tables

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