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Bar graphs in data analysis | StudyPug

Algebra 1: Master Core Concepts & Problem Solving

Numbers

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Squares and Square Roots

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Cubic and cube roots

Ratios and Proportions

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Ratios

Rates

Proportions

Percents

Percents, fractions, and decimals

Measurement

Conversions between metric and imperial systems

Metric systems

Imperial systems

Scale diagrams

Similar triangles

Pythagorean theorem

Applications of pythagorean theorem

Introduction to volume

Surface area and volume of prisms

Coordinate Graphs

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

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

Solve Equations

Introduction to linear equations

Applications of linear equations

Absolute Value Equations and Inequalities

Solving absolute value equations

Solving absolute value inequalities

Data and Graphs

Bar graphs in data analysis

Reading and drawing bar graphs

Reading and drawing histograms

Reading and drawing line graphs

Box-and-whisker plots and scatter plots

Reading and drawing Venn diagrams

Stem-and-leaf plots

Number Sequences

Arithmetic sequences

Arithmetic series

Geometric sequences

Sigma notation

Relations and Functions

Understand relations between x- and y-intercepts

Identifying functions

Function notations

Set Theory

Set notation

Set builder notation

Intersection and union of 2 sets

Intersection and union of 3 sets

Direct and Inverse Variation

Direct variation

Relationship between two quantities

Understanding graphs of linear relationships

Linear Functions

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope-Y-intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Applications of linear relations

Linear Inequalities

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Systems of Linear Equations

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Using elimination method to solve systems of equations

Using substitution method to solve systems of equations

Exponents

Exponent rules

Multiplication law: \((a^x)(a^y)=a^{(x+y)}\)

Division law: (a^x / a^y) = a^(x-y)

Negative exponent

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Scientific Notation

Scientific notation

Piecewise Functions

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Exponential Functions

Exponents: Power rule <i>(a^x)^y = a^(x * y)</i>

Exponents: Zero exponent: <i>a^0 = 1</i>

Exponents: Rational exponents

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Continuous growth and decay in exponential and logarithmic functions

Monomials

Multiplying monomial by monomial

Polynomials

Using algebra tiles to factor polynomials

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Factoring

Factoring polynomials: \(ax^2 + bx + c\)

Factoring perfect square trinomials: <i>(a + b)^2 = a^2 + 2ab + b^2</i> or <i>(a - b)^2 = a^2 - 2ab + b^2</i>

Find the difference of squares: <i>(a - b)(a + b) = (a^2 - b^2)</i>

Factor theorem

Common factors of polynomials

Factoring polynomials by grouping

Factoring polynomials: <i>x^2 + bx + c</i>

Quadratic Equations

Characteristics of quadratic functions

Transformations of quadratic functions

Converting from general form to vertex form by completing the square

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: the discriminant

System of linear equations

System of linear-quadratic equations

Functions: Linear, Quadratic, Exponential

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Absolute Value Functions

Absolute value functions

Radical Expressions

Evaluating and simplifying radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Radical Functions and Equations

Radical functions and transformations

Square root of a function

Solving radical equations

Rational Functions and Expressions

Partial fraction decomposition

Long division in polynomial functions

Slant asymptote

Solving rational equations

Adding and subtracting rational expressions 

Multiplying rational expressions

Dividing rational expressions

Vertical asymptote

Horizontal asymptote

Simplifying complex fractions

Using sine ratio to calculate angles and sides (Sin = \(\frac{o}{h})\)

Using cosine ratio to calculate angles and sides (Cos = \(\frac{a}{h}\))

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

 Using tangent ratio to calculate angles and side (Tan = \(\frac{o}{a} )\)

Probability

Fundamental counting principle

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Algebra 1

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<p>Algebra is a branch of mathematics that allows you to solve for unknown variables. It allows relationships to be expressed using mathematical equations rather than English words, which makes it easier to interpret. It is applied in various professional fields, including science, engineering, and economics.</p>
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<h2>What Grade is Algebra 1?</h2>
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Bar graphs in data analysis

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