Ace Your ACCUPLACER Test Prep with Proven Practice

Place value

Comparing and ordering numbers

Rounding numbers

Divisibility Rules

Prime factorization

Determining Common Factors

Determining Common Multiples

Introduction to exponents

Introduction to integer addition

Adding integers

Introduction to integer subtraction

Subtracting integers

Application of integer operations

Understanding integer multiplication

Multiplying integers

Understanding integer division

Dividing integers

Applications of integer operations

Adding and subtracting decimals

Multiplying decimals

Dividing decimals

Order of operations (PEMDAS)

Representing percents

Percent of a number

Converting among decimals, fractions, and percents

Adding and multiplying percents

Applications of percents

Taxes, discounts, tips and more

Simple interest

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 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

Evaluating algebraic expressions

Solving one - step equations: <i>x + a = b</i>

Solving linear equations using multiplication and division

Solving two-step linear equations: <i>ax + b = c</i>, <i>x/a + b = c</i>

Solving linear equations using distributive property: <i>a(x + b) = c</i>

Solving linear equations with variables on both sides

Solving literal equations

Ratios

Rates

Proportions

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Circles and circumference

Arcs of a circle

Areas and sectors of circles

Angles in a circle

Chord properties in circles

Tangent properties in circles

Central and inscribed angles in circle

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface area of cylinders

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Squares and square roots

Pythagorean theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

Median and mode

Mean

Range and outliers

Application of averages

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

Frequency tables and dot plots

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

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

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

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

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

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

Rate of change

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Applications of 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

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

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with the unknown "b" from <i>x^2 + bx + c</i>

Solving polynomials with the unknown "c" from <i>x^2 + bx + c</i>

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

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

Solving polynomials with the unknown "b" from \(ax^2 + bx + c\)

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>

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares: <i>x^2 - y^2</i>

Factoring trinomials

Factoring difference of cubes

Factoring sum of cubes

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Solving rational equations

Applications of rational equations

Simplifying complex fractions

Partial fraction decomposition

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Square and square roots

Cubic and cube roots

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Operations with radicals

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Multiplying radicals

Solving radical equations

Introduction to quadratic functions

Transformations of quadratic functions

Quadratic function in general form: <i>y = ax^2 + bx + c</i>

Quadratic function in vertex form: <i>y = a(x-p)^2 + q</i>

Completing the square

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

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

Applications of quadratic equations

Solving quadratic inequalities

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

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

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

Combination of SohCahToa questions

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Law of sines

Law of cosines

Applications of the sine law and cosine law

Introduction to bearings

Bearings and direction word problems

Angle of elevation and depression

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation

Arithmetic mean vs. Geometric mean

Function notation

Operations with functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Composite functions

Inequalities of combined functions

Inverse functions

One to one functions

Difference quotient: applications of functions

Exponents: Product rule <i>(a^x)(a^y) = a^(x+y)</i>

Exponents: Division rule (a^x / a^y) = a^(x-y)

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

Exponents: Negative exponents

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

Exponents: Rational exponents

Solving exponential equations using exponent rules

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

What is a logarithm?

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Solving logarithmic equations

Graphing logarithmic functions

Finding a logarithmic function given its graph

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x