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First Year Maths Topics

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1.Number Theory

1.1Divisibility Rules

1.2Prime factors

1.3Determining Common Factors

1.4Determining Common Multiples

1.5Introduction to exponents

2.Adding and Subtracting Integers

2.1Introduction to integer addition

2.2Adding integers

2.3Introduction to integer subtraction

2.4Subtracting integers

2.5Application of integer operations

3.Multiplying and Dividing Integers

3.1Understanding integer multiplication

3.2Multiplying integers

3.3Understanding integer division

3.4Dividing integers

3.5Applications of integer operations

4.Operations with Decimals

4.1Adding and subtracting decimals

4.2Multiplying decimals

4.3Dividing decimals

4.4Order of operations (PEMDAS)

5.Adding and Subtracting Fractions

5.1Using models to add and subtract fractions

5.2Adding fractions with like denominators

5.3Subtracting fractions with like denominators

5.4Adding and subtracting fractions with unlike denominators

5.5Adding and subtracting mixed numbers

6.Multiplying and Dividing Fractions

6.1Multiplying fractions and whole numbers (free lessons)

6.2Dividing fractions with whole numbers

6.3Multiplying proper fractions

6.4Multiplying improper fractions and mixed numbers

6.5Dividing fractions and mixed numbers

6.6Applications of fraction operations

7.Rational Numbers

7.1Comparing and ordering rational numbers (free lessons)

7.2Solving problems with rational numbers in decimal form

7.3Solving problems with rational numbers in fraction form

7.4Determine square roots of rational numbers

8.Powers, Exponents and Square Roots

8.1Using exponents to describe numbers (free lessons)

8.2Exponent rules

8.3Order of operations with exponents

8.4Using exponents to solve problems

8.5Squares and square roots (free lessons)

8.6Estimating square roots (free lessons)

9.Number System and Radicals

9.1Understanding the number systems (free lessons)

9.2Prime factorization

9.3Greatest Common Factors (GCF)

9.4Least Common Multiple (LCM) (free lessons)

9.5Rational vs. Irrational numbers

9.6Converting repeating decimals to fractions

10.Ratios, Rates, and Proportions

10.1Ratios (free lessons)

10.3Proportions

11.Pythagorean Theorem

11.1Squares and square roots (free lessons)

11.2Pythagorean theorem

11.3Estimating square roots (free lessons)

11.4Using the pythagorean relationship

11.5Applications of pythagorean theorem

12.Proportional Relationships

12.1Understanding graphs of proportional relationships (free lessons)

12.2Graphing and writing equations of proportional relationships

12.3Applications of proportional relationships (free lessons)

13.Fractions, Decimals, and Percents

13.1Percent of a number

14.Measuring Systems

14.1Metric systems (free lessons)

14.2Imperial systems

14.3Conversions between metric and imperial systems

14.4Conversions involve squares and cubic

15.Coordinates, Quadrants, and Transformations

15.1Cartesian plane

15.2Draw on coordinate planes

15.3Introduction to transformations

15.4Horizontal and vertical distances

16.Linear Relations

16.1Understanding graphs of linear relationships (free lessons)

16.2Understanding tables of values of linear relationships

16.3Applications of linear relationships (free lessons)

17.Linear Equations

17.1Model and solve one-step linear equations:

ax = b

\frac{x}{a} = b

(free lessons)

17.2Solving two-step linear equations using addition and subtraction:

ax + b = c

17.3Solving two-step linear equations using multiplication and division:

\frac{x}{a} + b = c

17.4Solving two-step linear equations using distributive property:

\;a\left( {x + b} \right) = c

18.Linear Inequalities

18.1Express linear inequalities graphically and algebraically (free lessons)

18.2Solving one-step linear inequalities

18.3Solving multi-step linear inequalities

19.Linear Functions

19.1Distance formula:

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

(free lessons)

19.2Midpoint formula:

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

19.3Gradient equation:

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

19.4Gradient intercept form: y = mx + b

19.5General form: Ax + By + C = 0 (free lessons)

19.6Gradient-point form:

y - y_1 = m (x - x_1)

19.7Rate of change

19.8Graphing linear functions using table of values

19.9Graphing linear functions using x- and y-intercepts (free lessons)

19.10Graphing from gradient-intercept form y=mx+b

19.11Graphing linear functions using a single point and gradient

19.12Word problems of graphing linear functions

19.13Parallel and perpendicular lines in linear functions (free lessons)

19.14Applications of linear relations

20.Geometry and Measurement

20.1Parallel and perpendicular line segments

20.2Perpendicular bisectors

20.3Angle bisectors

21.Angles, Lines, and Transversals

21.1Pairs of lines and angles

21.2Parallel lines and transversals

21.3Parallel line proofs

21.4Perpendicular line proofs

22.Properties of triangles

22.1Classifying triangles

22.2Isosceles and equilateral triangles

23.Circles

23.1Circles and circumference

23.2Arcs of a circle

23.3Areas and sectors of circles

24.Symmetry and Surface Area

24.1Line symmetry (free lessons)

24.2Rotational symmetry and transformations

24.3Surface area of 3-dimensional shapes

25.Introduction to 3-Dimensional Figures

25.1Introduction to surface area of 3-dimensional shapes (free lessons)

25.2Nets of 3-dimensional shapes

25.3Surface area of prisms

25.4Surface area of cylinders

26.Volume

26.1Introduction to volume

26.2Volume of prisms

26.3Volume of cylinders

26.4Word problems relating volume of prisms and cylinders

27.Data and Graphs

27.1Reading and drawing histograms

27.2Reading and drawing line graphs

27.3Box-and-whisker plots and scatter plots

28.Statistics

28.1Median and mode

28.3Range and outliers

28.4Application of averages

29.Introduction to Probability

29.1Introduction to probability

29.2Organizing outcomes

29.3Probability of independent events

29.4Comparing experimental and theoretical probability

1.Number Theory

1.1Divisibility Rules

1.2Prime factors

1.3Determining Common Factors

1.4Determining Common Multiples

1.5Introduction to exponents

2.Adding and Subtracting Integers

2.1Introduction to integer addition

2.2Adding integers

2.3Introduction to integer subtraction

2.4Subtracting integers

2.5Application of integer operations

3.Multiplying and Dividing Integers

3.1Understanding integer multiplication

3.2Multiplying integers

3.3Understanding integer division

3.4Dividing integers

3.5Applications of integer operations

4.Operations with Decimals

4.1Adding and subtracting decimals

4.2Multiplying decimals

4.3Dividing decimals

4.4Order of operations (PEMDAS)

5.Adding and Subtracting Fractions

5.1Using models to add and subtract fractions

5.2Adding fractions with like denominators

5.3Subtracting fractions with like denominators

5.4Adding and subtracting fractions with unlike denominators

5.5Adding and subtracting mixed numbers

6.Multiplying and Dividing Fractions

6.1Multiplying fractions and whole numbers (free lessons)

6.2Dividing fractions with whole numbers

6.3Multiplying proper fractions

6.4Multiplying improper fractions and mixed numbers

6.5Dividing fractions and mixed numbers

6.6Applications of fraction operations

7.Rational Numbers

7.1Comparing and ordering rational numbers (free lessons)

7.2Solving problems with rational numbers in decimal form

7.3Solving problems with rational numbers in fraction form

7.4Determine square roots of rational numbers

8.Powers, Exponents and Square Roots

8.1Using exponents to describe numbers (free lessons)

8.2Exponent rules

8.3Order of operations with exponents

8.4Using exponents to solve problems

8.5Squares and square roots (free lessons)

8.6Estimating square roots (free lessons)

9.Number System and Radicals

9.1Understanding the number systems (free lessons)

9.2Prime factorization

9.3Greatest Common Factors (GCF)

9.4Least Common Multiple (LCM) (free lessons)

9.5Rational vs. Irrational numbers

9.6Converting repeating decimals to fractions

10.Ratios, Rates, and Proportions

10.1Ratios (free lessons)

10.3Proportions

11.Pythagorean Theorem

11.1Squares and square roots (free lessons)

11.2Pythagorean theorem

11.3Estimating square roots (free lessons)

11.4Using the pythagorean relationship

11.5Applications of pythagorean theorem

12.Proportional Relationships

12.1Understanding graphs of proportional relationships (free lessons)

12.2Graphing and writing equations of proportional relationships

12.3Applications of proportional relationships (free lessons)

13.Fractions, Decimals, and Percents

13.1Percent of a number

14.Measuring Systems

14.1Metric systems (free lessons)

14.2Imperial systems

14.3Conversions between metric and imperial systems

14.4Conversions involve squares and cubic

15.Coordinates, Quadrants, and Transformations

15.1Cartesian plane

15.2Draw on coordinate planes

15.3Introduction to transformations

15.4Horizontal and vertical distances

16.Linear Relations

16.1Understanding graphs of linear relationships (free lessons)

16.2Understanding tables of values of linear relationships

16.3Applications of linear relationships (free lessons)

17.Linear Equations

17.1Model and solve one-step linear equations:

ax = b

\frac{x}{a} = b

(free lessons)

17.2Solving two-step linear equations using addition and subtraction:

ax + b = c

17.3Solving two-step linear equations using multiplication and division:

\frac{x}{a} + b = c

17.4Solving two-step linear equations using distributive property:

\;a\left( {x + b} \right) = c

18.Linear Inequalities

18.1Express linear inequalities graphically and algebraically (free lessons)

18.2Solving one-step linear inequalities

18.3Solving multi-step linear inequalities

19.Linear Functions

19.1Distance formula:

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

(free lessons)

19.2Midpoint formula:

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

19.3Gradient equation:

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

19.4Gradient intercept form: y = mx + b

19.5General form: Ax + By + C = 0 (free lessons)

19.6Gradient-point form:

y - y_1 = m (x - x_1)

19.7Rate of change

19.8Graphing linear functions using table of values

19.9Graphing linear functions using x- and y-intercepts (free lessons)

19.10Graphing from gradient-intercept form y=mx+b

19.11Graphing linear functions using a single point and gradient

19.12Word problems of graphing linear functions

19.13Parallel and perpendicular lines in linear functions (free lessons)

19.14Applications of linear relations

20.Geometry and Measurement

20.1Parallel and perpendicular line segments

20.2Perpendicular bisectors

20.3Angle bisectors

21.Angles, Lines, and Transversals

21.1Pairs of lines and angles

21.2Parallel lines and transversals

21.3Parallel line proofs

21.4Perpendicular line proofs

22.Properties of triangles

22.1Classifying triangles

22.2Isosceles and equilateral triangles

23.Circles

23.1Circles and circumference

23.2Arcs of a circle

23.3Areas and sectors of circles

24.Symmetry and Surface Area

24.1Line symmetry (free lessons)

24.2Rotational symmetry and transformations

24.3Surface area of 3-dimensional shapes

25.Introduction to 3-Dimensional Figures

25.1Introduction to surface area of 3-dimensional shapes (free lessons)

25.2Nets of 3-dimensional shapes

25.3Surface area of prisms

25.4Surface area of cylinders

26.Volume

26.1Introduction to volume

26.2Volume of prisms

26.3Volume of cylinders

26.4Word problems relating volume of prisms and cylinders

27.Data and Graphs

27.1Reading and drawing histograms

27.2Reading and drawing line graphs

27.3Box-and-whisker plots and scatter plots

28.Statistics

28.1Median and mode

28.3Range and outliers

28.4Application of averages

29.Introduction to Probability

29.1Introduction to probability

29.2Organizing outcomes

29.3Probability of independent events

29.4Comparing experimental and theoretical probability

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