Week 1: Day 1: Review the basics of arithmetic, including operations with integers, fractions, and decimals. Day 2: Study the properties of real numbers, including commutative, associative, and distributive properties. Day 3: Study the order of operations and how to evaluate expressions. Day 4: Practice simplifying expressions using the order of operations. Day 5: Study equations and inequalities, including how to solve them and their properties.
Day 1: Spend 2 hours reviewing the basics of arithmetic, including operations with integers, fractions, and decimals. Start by refreshing your memory on addition, subtraction, multiplication, and division of integers, fractions, and decimals. Practice some sample problems and ensure that you are comfortable with performing basic arithmetic operations.
0:00 - 0:05: Set up your study space and gather all necessary materials, including a notebook, pen, and calculator (if desired). 0:05 - 0:10: Review the definition and properties of integers, including how to add, subtract, multiply, and divide them. 0:10 - 0:15: Practice solving sample problems involving addition and subtraction of integers, focusing on carrying and borrowing as necessary. 0:15 - 0:20: Practice solving sample problems involving multiplication of integers, focusing on keeping track of negative signs and the order of operations. 0:20 - 0:25: Practice solving sample problems involving division of integers, focusing on understanding how to deal with remainders and fractions. 0:25 - 0:30: Take a quick break to stretch, drink water, or do some light exercise. 0:30 - 0:35: Review the definition and properties of fractions, including how to add, subtract, multiply, and divide them. 0:35 - 0:40: Practice solving sample problems involving addition and subtraction of fractions, focusing on finding common denominators and simplifying fractions as necessary. 0:40 - 0:45: Practice solving sample problems involving multiplication of fractions, focusing on simplifying fractions and canceling common factors. 0:45 - 0:50: Practice solving sample problems involving division of fractions, focusing on understanding how to invert and multiply fractions to simplify the problem. 0:50 - 0:55: Review the definition and properties of decimals, including how to add, subtract, multiply, and divide them. 0:55 - 1:00: Practice solving sample problems involving addition and subtraction of decimals, focusing on lining up the decimal points and carrying as necessary. 1:00 - 1:05: Practice solving sample problems involving multiplication of decimals, focusing on counting the number of decimal places and lining up the digits correctly.
Multiply 3.4 and 0.25. Multiply 1.8 and 0.9. Multiply 0.15 and 2.5. ...
1:05 - 1:10: Practice solving sample problems involving division of decimals, focusing on shifting the decimal point and adding zeros as necessary. 1:10 - 1:15: Take another quick break to rest your eyes, stretch, or move around. 1:15 - 1:20: Review any concepts or problems that you found particularly challenging, using your textbook or online resources if necessary. 1:20 - 1:25: Review any notes or summaries that you've written down during your study session, to reinforce your learning and retention. 1:25 - 1:30: Reflect on your progress and identify any areas where you need more practice or reinforcement, and plan your next study session accordingly.
Day 2: Spend 2 hours studying the properties of real numbers, including commutative, associative, and distributive properties. Familiarize yourself with the definitions of these properties and work through some examples to better understand how they are applied in arithmetic operations.
Day 3: Spend 2 hours studying the order of operations and how to evaluate expressions. Learn the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to help you remember the order of operations. Practice evaluating expressions using this order of operations.
Day 4: Spend 2 hours practicing simplifying expressions using the order of operations. Work through sample problems that require you to apply the order of operations and simplify expressions.
Day 5: Spend 2 hours studying equations and inequalities, including how to solve them and their properties. Learn how to solve linear equations and inequalities, including those with fractions and decimals. Familiarize yourself with the different types of solutions, such as no solution, one solution, and infinite solutions.
Week 2: Day 6: Study linear equations, including how to graph them and their properties. Day 7: Practice solving linear equations in one and two variables. Day 8: Study systems of linear equations, including how to solve them using substitution and elimination. Day 9: Practice solving systems of linear equations. Day 10: Study quadratic equations, including how to solve them using factoring, completing the square, and the quadratic formula.
Week 3: Day 11: Study functions, including how to evaluate them and their properties. Day 12: Study exponential and logarithmic functions, including how to evaluate them and their properties. Day 13: Practice graphing functions and finding their domains and ranges. Day 14: Study polynomials, including how to add, subtract, multiply, and divide them. Day 15: Practice factoring polynomials using various methods.
Week 4: Day 16: Study rational expressions, including how to simplify, multiply, divide, and add them. Day 17: Practice simplifying and solving equations with rational expressions. Day 18: Study radicals and how to simplify expressions with them. Day 19: Practice simplifying and solving equations with radicals. Day 20: Study complex numbers, including how to add, subtract, multiply, divide, and graph them.
Days 21-30: Spend the remaining days reviewing and practicing all the concepts studied in the previous weeks. Solve as many algebra problems as possible, including those found in textbooks and online resources. Additionally, take practice tests to evaluate your understanding and identify areas that require further review.
Week 1: Day 1: Review the basics of angles, including measuring angles in degrees and radians. Day 2: Study the trigonometric functions of sine, cosine, and tangent and their properties. Day 3: Study the unit circle and its relationship to trigonometry. Day 4: Practice evaluating trigonometric functions using the unit circle. Day 5: Study the reciprocal trigonometric functions of cosecant, secant, and cotangent.
Week 2: Day 6: Study the properties of trigonometric functions, including even and odd functions, periodicity, and amplitude. Day 7: Practice graphing trigonometric functions. Day 8: Study the inverse trigonometric functions of arcsine, arccosine, and arctangent. Day 9: Practice finding the inverse trigonometric functions of given values. Day 10: Study the trigonometric identities, including Pythagorean, reciprocal, quotient, and co-function identities.
Week 3: Day 11: Study solving right triangles using trigonometry. Day 12: Practice solving right triangles using trigonometry. Day 13: Study solving oblique triangles using the Law of Sines. Day 14: Practice solving oblique triangles using the Law of Sines. Day 15: Study solving oblique triangles using the Law of Cosines.
Week 4: Day 16: Study the applications of trigonometry in real-world problems, including distance and height measurements, navigation, and engineering. Day 17: Practice solving real-world problems using trigonometry. Day 18: Study the complex numbers and how they relate to trigonometry. Day 19: Practice solving problems involving complex numbers and trigonometry. Day 20: Study the polar coordinate system and its relationship to trigonometry.
Days 21-30: Spend the remaining days reviewing and practicing all the concepts studied in the previous weeks. Solve as many trigonometry problems as possible, including those found in textbooks and online resources. Additionally, take practice tests to evaluate your understanding and identify areas that require further review.
Week 1: Day 1: Review the basics of algebra, including solving linear equations and graphing linear equations. Day 2: Study the definition of a function and the notation used to represent functions. Day 3: Study the domain and range of functions. Day 4: Study the concepts of one-to-one and onto functions. Day 5: Practice identifying functions and determining their domains and ranges.
Week 2: Day 6: Study linear functions and their properties, including slope and intercepts. Day 7: Practice graphing linear functions and determining their equations given a graph. Day 8: Study quadratic functions and their properties, including vertex and intercepts. Day 9: Practice graphing quadratic functions and determining their equations given a graph. Day 10: Study exponential and logarithmic functions and their properties.
Week 3: Day 11: Study trigonometric functions and their properties, including amplitude and period. Day 12: Practice graphing trigonometric functions and determining their properties. Day 13: Study inverse functions and their properties. Day 14: Practice finding inverse functions and verifying them. Day 15: Study composition of functions and their properties.
Week 4: Day 16: Study polynomial functions and their properties, including degree and end behavior. Day 17: Practice graphing polynomial functions and determining their properties. Day 18: Study rational functions and their properties, including asymptotes and holes. Day 19: Practice graphing rational functions and determining their properties. Day 20: Study piecewise functions and their properties.
Days 21-30: Spend the remaining days reviewing and practicing all the concepts studied in the previous weeks. Solve as many function problems as possible, including those found in textbooks and online resources. Additionally, take practice tests to evaluate your understanding and identify areas that require further review.
Week 1: Day 1: Review the basics of points, lines, and planes, and study the concept of collinearity. Day 2: Study the properties of angles, including angle measures and classification of angles. Day 3: Study the properties of triangles, including types of triangles and the Triangle Inequality Theorem. Day 4: Study the properties of quadrilaterals, including types of quadrilaterals and their properties. Day 5: Study the properties of circles, including arc length and sector area.
Week 2: Day 6: Study the properties of polygons, including regular polygons and their properties. Day 7: Practice finding the area and perimeter of polygons. Day 8: Study the properties of congruent and similar figures. Day 9: Practice proving figures are congruent or similar. Day 10: Study the properties of transformations, including reflections, translations, rotations, and dilations.
Week 3: Day 11: Study the properties of three-dimensional figures, including types of polyhedra and their properties. Day 12: Practice finding the surface area and volume of polyhedra. Day 13: Study the properties of cylinders, cones, and spheres. Day 14: Practice finding the surface area and volume of cylinders, cones, and spheres. Day 15: Study the properties of vectors and their application to geometry.
Week 4: Day 16: Study the properties of geometric proofs, including types of proofs and their structure. Day 17: Practice constructing geometric proofs. Day 18: Study the properties of similar triangles, including the ratio of corresponding side lengths. Day 19: Practice using similar triangles to solve geometric problems. Day 20: Study the properties of the Pythagorean Theorem and its application to geometric problems.
Days 21-30: Spend the remaining days reviewing and practicing all the concepts studied in the previous weeks. Solve as many geometry problems as possible, including those found in textbooks and online resources. Additionally, take practice tests to evaluate your understanding and identify areas that require further review.
Week 1: Day 1: Review the basics of algebra, including solving linear equations, graphing linear equations, and manipulating equations. Day 2: Study the Cartesian coordinate system and its properties, including plotting points, graphing lines, and identifying intercepts. Day 3: Study the slope-intercept form of a linear equation and its properties. Day 4: Study the point-slope form of a linear equation and its properties. Day 5: Practice graphing linear equations in various forms.
Week 2: Day 6: Study the properties of circles and their equations in standard and general form. Day 7: Practice graphing circles and determining their properties. Day 8: Study the properties of parabolas and their equations in standard and general form. Day 9: Practice graphing parabolas and determining their properties. Day 10: Study the properties of ellipses and their equations in standard and general form.
Week 3: Day 11: Practice graphing ellipses and determining their properties. Day 12: Study the properties of hyperbolas and their equations in standard and general form. Day 13: Practice graphing hyperbolas and determining their properties. Day 14: Study the properties of polar coordinates and their conversion to Cartesian coordinates. Day 15: Practice plotting points and graphing polar equations.
Week 4: Day 16: Study the properties of conic sections, including their foci, directrices, and eccentricity. Day 17: Practice graphing and determining properties of conic sections. Day 18: Study the properties of vectors and their application to analytical geometry. Day 19: Practice finding vector equations of lines and planes. Day 20: Study the properties of matrices and their application to transformations in analytical geometry.
Days 21-30: Spend the remaining days reviewing and practicing all the concepts studied in the previous weeks. Solve as many analytical geometry problems as possible, including those found in textbooks and online resources. Additionally, take practice tests to evaluate your understanding and identify areas that require further review.
Week 1: Day 1: Review the properties of functions, including domain, range, and function composition. Day 2: Study the properties of linear functions, including slope, intercepts, and transformations. Day 3: Study the properties of quadratic functions, including vertex form, standard form, and solving quadratic equations. Day 4: Study the properties of polynomial functions, including degree and end behavior. Day 5: Study the properties of rational functions, including vertical and horizontal asymptotes and holes.
Week 2: Day 6: Study the properties of exponential functions, including the properties of exponents and logarithms. Day 7: Study the properties of logarithmic functions, including properties of logarithms and solving logarithmic equations. Day 8: Study the properties of trigonometric functions, including the unit circle, trigonometric identities, and solving trigonometric equations. Day 9: Practice graphing trigonometric functions and finding their properties. Day 10: Study the properties of inverse trigonometric functions and their graphs.
Week 3: Day 11: Study the properties of sequences and series, including arithmetic and geometric sequences and series. Day 12: Study the Binomial Theorem and its application to combinatorics and probability. Day 13: Study the properties of polar coordinates and their conversion to Cartesian coordinates. Day 14: Practice plotting points and graphing polar equations. Day 15: Study the properties of complex numbers, including their arithmetic and geometric properties.
Week 4: Day 16: Study the properties of vectors and their application to precalculus. Day 17: Practice finding vector equations of lines and planes. Day 18: Study the properties of matrices and their application to transformations in precalculus. Day 19: Practice using matrices to solve systems of linear equations. Day 20: Study the properties of limits and continuity, including evaluating limits and determining continuity.
Days 21-30: Spend the remaining days reviewing and practicing all the concepts studied in the previous weeks. Solve as many precalculus problems as possible, including those found in textbooks and online resources. Additionally, take practice tests to evaluate your understanding and identify areas that require further review.
Week 1: Day 1: Review the basics of algebra, including factoring, solving equations, and simplifying expressions. Day 2: Study limits, including how to evaluate them and their properties. Day 3: Study the definition of the derivative and how to compute it using the limit definition. Day 4: Practice finding derivatives of various functions, including polynomial, trigonometric, exponential, and logarithmic functions. Day 5: Study the rules of differentiation, including the product rule, quotient rule, and chain rule.
Week 2: Day 6: Study applications of derivatives, including optimization, related rates, and curve sketching. Day 7: Study the definition of the definite integral and how to compute it using Riemann sums. Day 8: Practice finding integrals of various functions, including polynomial, trigonometric, exponential, and logarithmic functions. Day 9: Study the rules of integration, including substitution, integration by parts, and partial fractions. Day 10: Study applications of integration, including areas, volumes, and work.
Week 3: Day 11: Study techniques of integration, including trigonometric substitutions, integration by partial fractions, and integration by parts. Day 12: Practice finding integrals using the techniques studied in Day 11. Day 13: Study improper integrals and how to evaluate them. Day 14: Study sequences and series, including convergence and divergence tests. Day 15: Practice finding sums of sequences and series.
Week 4: Day 16: Study power series and their convergence. Day 17: Study Taylor series and their applications. Day 18: Practice finding Taylor series of various functions. Day 19: Study differential equations, including first-order differential equations and separable differential equations. Day 20: Practice solving differential equations using the techniques studied in Day 19.
Days 21-30: Spend the remaining days reviewing and practicing all the concepts studied in the previous weeks. Solve as many calculus problems as possible, including those found in textbooks and online resources. Additionally, take practice tests to evaluate your understanding and identify areas that require further review.