DIY Reviews are a free collection of resources comprised of videos and practice problems to help you review specific math skills that you may have learned but don't remember well. Click on any of the following topics to polish your skills.
- Arithmetic of Numbers
Types of numbers, ordering numbers, arithmetic with integers, order of operations, absolute value, decimal place value, rounding
- Prime Factorization
Finding prime factors, factor trees, exponent notation, least common multiple (LCM), greatest common factor (GCF)
- Fractions (basic)
Introduction to fractions, ordering and comparing fractions, simplifying, arithmetic with fractions
- Fractions (further topics)
Mixed numbers, improper fractions, arithmetic with mixed numbers, percentages, converting fractions to decimals, decimal arithmetic
- Long Division with Numbers
Division basics, long division with 1- and 2-digit divisors, long division with decimals.
- Exponent Basics
Introduction to exponents, exponents in algebra, laws of exponents
- Geometry Review
Points, lines, planes, angles and their measurement, triangles, quadrilaterals, polygons, perimeter and area, circles, circumference and area, volume. Parallel lines, similar triangles, Pythagorean Theorem, 30-60-90 triangles, isosceles right triangles, area of quadrilaterals, solids and nets, equation of a line, transformations on the coordinate plane.
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- Scientific Notation
Introduction to scientific notation, arithmetic using scientific notation
- Significant Digits
Basics of significant digits, arithmetic with correct significant digits, which zeros are significant, why use significant digits, exact numbers vs. measured numbers.
- Unit Conversion
Introduction, dimensional analysis with one unit and with multiple units and conversion factors, converting units of area and volume, drug dosage calculation, tables of common conversion factors
- Vector Basics
Terminology, magnitude and direction, graphical representation, component form, scalar multiples, adding in both graphical and component form, unit vectors, three-dimensional vectors- notation and applications, dot product, cross product, work and torque applications.
- Solving Linear Equations
Introduction, solving using addition/subtraction, solving using multiplication/division, solving with simplification. Applications: distance, mixture, and work problems. Solving literal equations
- Linear Inequalities in One Variable; Absolute Value
Introduction to inequalities, graphing on number line, solving linear inequalities, interval notation, compound inequalities, absolute value equations and inequalities
- Solving Quadratic Equations
Introduction to quadratic equations, solving by factoring, square root property, completing the square, quadratic formula, using the discriminant, applications
- Simplifying Exponential Expressions
Review of exponent properties, applying exponent rules, negative and fractional exponents, simplifying expressions with negative exponents, rational exponents and radical form, simplifying radicals.
- Radicals and Rational Exponents
Introduction to radicals, simplifying radicals, arithmetic with radical expressions, rationalizing denominators, rational exponents
- Logarithms: Solving Logarithmic and Exponential Equations
Logarithm basics, solving logarithmic equations, solving exponential equations, graphing exponential and logarithmic functions
- Lines: Graphing and Equations
Graphing points and lines on a coordinate plane, slope of a line, graphing lines, parallel and perpendicular lines, finding equations of lines, point-slope form, slope-intercept form, standard form, equations of horizontal and vertical lines
- Factoring Polynomials
Greatest Common Factor (GCF), factoring binomials using the GCF, factoring by grouping, factoring trinomials by trial and error, factoring trinomials using grouping, factoring difference of squares, factoring perfect square trinomials, factoring sum or difference of cubes
- Long Division with Polynomials
Review of long division, dividing a polynomial by a monomial, dividing by a binomial, dividing polynomials, synthetic division
- Systems of Linear Equations
Solving systems of linear equations by graphing, by substitution, and by elimination, classifying systems as consistent/inconsistent or dependent/independent, solving systems with three variables by elimination, applications of linear systems.
- Function Basics and Graphs
Introduction to functions, domain and range, even and odd functions, intercepts, increasing/decreasing intervals, nine basic functions and their graphs, transformations.
- Graphs of Basic Functions; Transformations
Graphs of basic functions, piecewise functions, horizontal and vertical translations, greatest integer function, vertical and horizontal stretch/shrink, reflections
- Graphing Functions: Polynomials
Graphing quadratic functions, increasing/decreasing intervals, maxima/minima, graphing higher degree polynomials, finding a function from its graph, finding zeros of polynomials
- Graphing Functions: Rational Functions
Introduction, vertical asymptotes and holes, horizontal asymptotes, slant or oblique asymptotes, introduction to graphing rational functions, graphing using transformations
- Inverse Functions
Basics of inverse functions, finding the inverse function, inverses of rational functions, inverse of radical functions, composition of functions and how it applies to inverses.
- Conic Sections
Introduction to conic sections, parabolas, ellipse, hyperbola, circle, determining conic from general form, eccentricity.
- Matrices: Introduction and Basic Operation
Introduction to matrices, matrix addition, scalar multiples, equality of matrices, matrix multiplication, identity matrix, transpose of a matrix, determinant, inverse, solving systems of equation using matrix inverse and Cramer's rule methods
- Gauss-Jordan Elimination
Explanation of Gaussian elimination, Gaussian elimination using matrices, Gauss-Jordan elimination method, dependent and inconsistent systems of equations.
- Trigonometry Basics
Radians and degrees, conversion between radians/degrees, arc length, area of a sector, linear and angular velocity, Pythagorean theorem, basic trigonometric ratios, unit circle and circular functions, reciprocal trig functions, special triangles, using a calculator to find trig function values, solving right triangles, application of trig ratios
- Trigonometry - Graphs of Trigonometric Functions
Unit circle, values of sine and cosine for special angles, graphs of sine and cosine functions, graphs of tangent functions, graphs of secant and cosecant functions, finding equations for trigonometric functions from graphs, graph of inverse trig functions.
- Trigonometry - Identities
Co-function identities, Pythagorean identities, sum and difference and double angle identities, half angle identities, power-reducing identities, product-to-sum identities, verifying identities, solving trigonometric equations, summary list of trig identities
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