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First Year Maths Topics

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1. Number Theory

1.1

Divisibility Rules

1.2

Determining Common Factors

1.3

Determining Common Multiples

1.4

Introduction to exponents

2. Adding and Subtracting Integers

2.1

Introduction to integer addition

2.2

Adding integers

2.3

Introduction to integer subtraction

2.4

Subtracting integers

2.5

Application of integer operations

3. Multiplying and Dividing Integers

3.1

Understanding integer multiplication

3.2

Multiplying integers

3.3

Understanding integer division

3.4

Dividing integers

3.5

Applications of integer operations

4. Operations with Decimals

4.1

Adding and subtracting decimals

4.2

Multiplying decimals

4.3

Dividing decimals

4.4

Order of operations (BIDMAS)

5. Adding and Subtracting Fractions

5.1

Using models to add and subtract fractions

5.2

Adding fractions with like denominators

5.3

Subtracting fractions with like denominators

5.4

Adding and subtracting fractions with unlike denominators

5.5

Adding and subtracting mixed numbers

6. Multiplying and Dividing Fractions

6.1

Multiplying fractions and whole numbers

6.2

Dividing fractions with whole numbers

6.3

Multiplying proper fractions

6.4

Multiplying improper fractions and mixed numbers

6.5

Dividing fractions and mixed numbers

6.6

Applications of fraction operations

7. Rational Numbers

7.1

Comparing and ordering rational numbers

7.2

Solving problems with rational numbers in decimal form

7.3

Solving problems with rational numbers in fraction form

7.4

Determine square roots of rational numbers

8. Powers, and Exponents

8.1

Using exponents to describe numbers

8.2

Exponent rules

8.3

Order of operations with exponents

8.4

Using exponents to solve problems

9. Number System and Radicals

9.1

Understanding the number systems

9.2

Prime factorization

9.3

Greatest Common Factors (GCF)

9.4

Least Common Multiple (LCM)

9.5

Rational vs. Irrational numbers

9.6

Converting repeating decimals to fractions

10. Ratios, Rates, and Proportions

10.1

Ratios

10.2

Rates

10.3

Proportions

11. Pythagorean Theorem

11.1

Squares and square roots

11.2

Pythagorean theorem

11.3

Estimating square roots

11.4

Using the pythagorean relationship

11.5

Applications of pythagorean theorem

12. Proportional Relationships

12.1

Identifying proportional relationships

12.2

Understanding graphs of proportional relationships

12.3

Graphing and writing equations of proportional relationships

12.4

Applications of proportional relationships

13. Fractions, Decimals, and Percents

13.1

Representing percents

13.2

Percent of a number

13.3

Converting among fractions, decimals, and percents

13.4

Applications of percents

13.5

Taxes, discounts, tips and more

13.6

Simple interest

14. Measuring Systems

14.1

Metric systems

14.2

Imperial systems

14.3

Conversions between metric and imperial systems

14.4

Conversions involve squares and cubic

15. Coordinates, Quadrants, and Transformations

15.1

Cartesian plane

15.2

Draw on coordinate planes

15.3

Introduction to transformations

15.4

Horizontal and vertical distances

16. Linear Equations

16.1

Model and solve one-step linear equations: ax = b, x/a = b

16.2

Solving two-step linear equations using addition and subtraction: ax + b = c

16.3

Solving two-step linear equations using multiplication and division: x/a + b = c

16.4

Solving two-step linear equations using distributive property: a(x + b) = c

17. Linear Inequalities

17.1

Express linear inequalities graphically and algebraically

17.2

Solving one-step linear inequalities

17.3

Solving multi-step linear inequalities

17.4

Compound inequalities

18. Linear Functions

18.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

18.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

18.3

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

18.4

Gradient intercept form: y = mx + b

18.5

General form: Ax + By + C = 0

18.6

Gradient-point form:

y - y_1 = m (x - x_1)

18.7

Rate of change

18.8

Graphing linear functions using table of values

18.9

Graphing linear functions using x- and y-intercepts

18.10

Graphing from gradient-intercept form y=mx+b

18.11

Graphing linear functions using a single point and gradient

18.12

Word problems of graphing linear functions

18.13

Parallel and perpendicular lines in linear functions

18.14

Applications of linear relations

19. Geometry and Measurement

19.1

Parallel and perpendicular line segments

19.2

Perpendicular bisectors

19.3

Angle bisectors

20. Angles, Lines, and Transversals

20.1

Pairs of lines and angles

20.2

Parallel lines and transversals

20.3

Parallel line proofs

20.4

Perpendicular line proofs

21. Properties of triangles

21.1

Classifying triangles

21.2

Isosceles and equilateral triangles

22. Circles

22.1

Circles and circumference

22.2

Arcs of a circle

22.3

Areas and sectors of circles

23. Symmetry and Surface Area

23.1

Line symmetry

23.2

Rotational symmetry and transformations

23.3

Surface area of 3-dimensional shapes

24. Introduction to 3-Dimensional Figures

24.1

Introduction to surface area of 3-dimensional shapes

24.2

Nets of 3-dimensional shapes

24.3

Surface area of prisms

24.4

Surface area of cylinders

25. Volume

25.1

Introduction to volume

25.2

Volume of prisms

25.3

Volume of cylinders

25.4

Word problems relating volume of prisms and cylinders

26. Data and Graphs

26.1

Reading and drawing bar graphs

26.2

Reading and drawing histograms

26.3

Reading and drawing line graphs

26.4

Box-and-whisker plots and scatter plots

26.5

Stem-and-leaf plots

26.6

Pie charts

26.7

Reading and drawing Venn diagrams

26.8

Frequency tables and dot plots

27. Statistics

27.1

Median and mode

27.2

Mean

27.3

Range and outliers

27.4

Application of averages

28. Introduction to Probability

28.1

Introduction to probability

28.2

Organizing outcomes

28.3

Probability of independent events

28.4

Comparing experimental and theoretical probability

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