Master First Year Maths

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First Year Maths Topics

Number Theory

Divisibility Rules

Determining Common Factors

Determining Common Multiples

Introduction to exponents

Adding and Subtracting Integers

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Application of integer operations

Multiplying and Dividing Integers

Understanding integer multiplication

Multiplying integers

Understanding integer division

Dividing integers

Applications of integer operations

Operations with Decimals

Adding and subtracting decimals

Multiplying decimals

Dividing decimals

Order of operations (BIDMAS)

Adding and Subtracting Fractions

Using models to add and subtract fractions

Adding fractions with like denominators

Subtracting fractions with like denominators

Adding and subtracting fractions with unlike denominators

Adding and subtracting mixed numbers

Multiplying and Dividing Fractions

Multiplying fractions and whole numbers

Dividing fractions with whole numbers

Multiplying proper fractions

Multiplying improper fractions and mixed numbers

Dividing fractions and mixed numbers

Applications of fraction operations

Rational Numbers

Comparing and ordering rational numbers

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Determine square roots of rational numbers

Powers, and Exponents

Using exponents to describe numbers

Order of operations with exponents

Using exponents to solve problems

Number System and Radicals

Understanding the number systems

Prime factorization

Greatest Common Factors (GCF)

Least Common Multiple (LCM)

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Ratios, Rates, and Proportions

Pythagorean Theorem

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Proportional Relationships

Identifying proportional relationships

Understanding graphs of proportional relationships

Graphing and writing equations of proportional relationships

Applications of proportional relationships

Fractions, Decimals, and Percents

Representing percents

Percent of a number

Converting among fractions, decimals, and percents

Applications of percents

Taxes, discounts, tips and more

Simple interest

Measuring Systems

Imperial systems

Conversions between metric and imperial systems

Conversions involve squares and cubic

Coordinates, Quadrants, and Transformations

Cartesian plane

Draw on coordinate planes

Introduction to transformations

Horizontal and vertical distances

Linear Equations

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

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

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

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

Linear Inequalities

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Linear Functions

Distance formula:

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

Midpoint formula:

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

Gradient equation:

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

Gradient intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form:

y - y_1 = m (x - x_1)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from gradient-intercept form y=mx+b

Graphing linear functions using a single point and gradient

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Geometry and Measurement

Parallel and perpendicular line segments

Perpendicular bisectors

Angle bisectors

Angles, Lines, and Transversals

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Properties of triangles

Classifying triangles

Isosceles and equilateral triangles

Circles

Circles and circumference

Arcs of a circle

Areas and sectors of circles

Symmetry and Surface Area

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Introduction to 3-Dimensional Figures

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface area of cylinders

Volume

Introduction to volume

Volume of prisms

Volume of cylinders

Word problems relating volume of prisms and cylinders

Data and Graphs

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Stem-and-leaf plots

Reading and drawing Venn diagrams

Frequency tables and dot plots

Statistics

Median and mode

Range and outliers

Application of averages

Introduction to Probability

Introduction to probability

Organizing outcomes

Probability of independent events

Comparing experimental and theoretical probability

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