3 Course 3 of 10
Algebra 1 practice
One problem set for every lesson in the course. Problems go from easy to challenging, and each one has a worked solution.
Unit 1 Monomials
- 1 Algebraic expressions: why we use letters What an algebraic expression is, how to write one properly, how to turn words into algebra and how to evaluate an expression by substituting numbers. 9 problems
- 2 Monomials: coefficient, variable part and degree What a monomial is, how to write it in standard form, how to find its degree, and how to tell when two monomials are like terms. 9 problems
- 3 Combining like terms How to add and subtract monomials, why only like terms can be combined, and a reliable method for simplifying long expressions and removing parentheses. 9 problems
- 4 Multiplying, dividing and raising monomials to powers The exponent rules you need for monomials, and how to multiply, divide and raise monomials to a power, with worked examples and common mistakes. 9 problems
- 5 GCF and LCM of monomials How to find the greatest common factor and the least common multiple of two or more monomials, with the rule for coefficients and variables and worked examples. 9 problems
Unit 2 Polynomials
- 6 Polynomials: terms, degree and standard form What a polynomial is, how to name it by its number of terms, how to find its degree and leading coefficient, and what standard form, complete and homogeneous mean. 9 problems
- 7 Adding, subtracting and multiplying polynomials How to add and subtract polynomials, distribute a monomial over a polynomial and multiply any two polynomials, including the box method and a quick way to check your answer. 9 problems
- 8 Special products: perfect squares and the difference of squares The square of a binomial and the product of a sum and a difference, where the patterns come from, how to use them quickly and the mistakes to avoid. 9 problems
- 9 Cubing a binomial and squaring a trinomial The patterns for the cube of a binomial and the square of a trinomial, how the signs work, Pascal's triangle and fully worked examples. 9 problems
- 10 Polynomial long division How to divide one polynomial by another step by step, find the quotient and remainder, handle missing terms and check your answer. 9 problems
- 11 Synthetic division, the Remainder Theorem and the Factor Theorem A fast shortcut for dividing a polynomial by x − c, how to find a remainder without dividing at all, and how to tell whether x − c is a factor. 9 problems
Unit 3 Factoring
- 12 Factoring out the GCF and factoring by grouping What factoring a polynomial means, how to factor out the greatest common factor, and how to factor four-term polynomials by grouping, with worked examples. 9 problems
- 13 Factoring special products How to recognize and factor a difference of squares, a perfect square trinomial, a perfect cube and a sum or difference of cubes, plus a step-by-step factoring strategy. 9 problems
- 14 Factoring trinomials and using the Factor Theorem How to factor x² + bx + c by finding two numbers with a given sum and product, how to factor ax² + bx + c with the AC method, and how to factor cubics with synthetic division. 9 problems
Unit 4 Rational expressions
- 15 Rational expressions: excluded values and simplifying What a rational expression is, how to find the values that must be excluded from its domain, and how to simplify it correctly by factoring the numerator and the denominator. 9 problems
- 16 Adding, subtracting, multiplying and dividing rational expressions How to find the least common denominator, add and subtract rational expressions, multiply and divide them, raise them to powers and keep track of excluded values. 9 problems
Unit 5 Linear equations
- 17 Solving linear equations What an equation is, the properties of equality, and a step-by-step method for solving linear equations, including fractions, no-solution equations and identities. 9 problems
- 18 Rational equations that lead to linear equations How to solve equations with the variable in a denominator: excluded values, clearing denominators with the LCD, and checking for extraneous solutions. 9 problems
Work each problem out on paper before you open the solution. If your answer is off, compare the steps and find where you went wrong. If a problem stops you cold, go back to the lesson: every set links to it.