Interactive Algebra 1 Help and Practice

Squares and Square Roots

Cubic and cube roots

Ratios

Rates

Proportions

Percents, fractions, and decimals

Metric systems

Imperial systems

Conversions between metric and imperial systems

Pythagorean theorem

Introduction to volume

Scale diagrams

Similar triangles

Surface area and volume of prisms

Applications of pythagorean theorem

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

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

Introduction to linear equations

Applications of linear equations

Solving absolute value equations

Solving absolute value inequalities

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

Arithmetic sequences

Geometric sequences

Arithmetic series

Sigma notation

Understand relations between x- and y-intercepts

Identifying functions

Function notations

Relationship between two quantities

Understanding graphs of linear relationships

Direct variation

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: \(y - y_1 = m (x - x_1)\)

Applications of linear relations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

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

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

Exponent rules

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

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

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

Negative exponent

Scientific notation

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

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Using algebra tiles to factor polynomials

Common factors of polynomials

Factoring polynomials by grouping

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

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

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

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Absolute value functions

Evaluating and simplifying radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Solving radical equations

Square root of a function

Radical functions and transformations

Long division in polynomial functions

Vertical asymptote

Horizontal asymptote

Slant asymptote

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Simplifying complex fractions

Partial fraction decomposition

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

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

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

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Probability of independent events

Data collection

Fundamental counting principle

Permutations

Combinations

Probability with Venn diagrams

Probability

Influencing factors on data collection

Median and mode

Mean

Range and outliers

Application of averages

Solving multi-step linear inequalities

Compound inequalities

Notation of matrices

Adding and subtracting matrices

Scalar multiplication

Matrix multiplication

The three types of matrix row operations

Set notation

Set builder notation

Intersection and union of 2 sets

Intersection and union of 3 sets

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions