Algebra
A1  Solving Linear Equations and Inequalities
A1  Solving Linear Equations and Inequalities
Solving equations differs from evaluating expressions or functions, in that the output is already known. What we seek is the input, or “solution” that lead to that given output. For example, in the equation x + 2 = 8, we know that some number plus two gives us 8. But, what input will make this true? Throughout this unit students will work to solve linear equations, the most common type of equation found on the TASC exam. Students will also work on finding the solution to systems of linear equations, as well as linear inequalities and systems of linear inequalities. Higher order equations will be solved in subsequent units.
Core skills of this unit:

Solve linear equations in one variable

Solve linear inequalities in one variable

Solve systems of linear equations in two variables

Graphically solve linear inequalities in two variables

Graphically solve systems of linear inequalities in two variables
A2  Polynomials and Rational Expressions
The focus of this unit is to use addition, subtraction, multiplication, and division (factoring) to represent algebraic expressions in equivalent forms. For example, the expression 3x2 + 4x2 can be rewritten as 7x2 since the terms are like terms. Students will make use of the distributive property to multiply polynomials and then work to perform the inverse, factoring common factors from polynomials. Students will also discover that a binomial x a binomial can result in a trinomial, as well as a binomial in special circumstances. Students will only be asked to factor quadratic expressions with a lead coefficient of 1. This unit provides the foundation for solving quadratic equations in unit A3 – Solving Quadratic Equations and Simple Radical Equations.
Core skills of this unit:

Add and subtract monomials (combine like terms)

Add and subtract polynomials

Multiply and divide monomials

Multiply monomials and polynomials

Factor monomials from polynomials

Multiply polynomials

Factor quadratics with a lead coefficient of 1

Simplify rational expressions
A3  Solving Quadratics and Radical Equations
In addition to linear equations, the TASC exam requires students to solve equations where the independent variable term is to the power of 2, typically written as x2. These types of equations are called quadratic equations, and can generally fit the form y = ax2 + bx + c, as in 0 = 2x2 + 5x – 12. Students will solve quadratic equations by factoring, by using the quadratic formula, and by completing the square. Graphical methods of solving quadratic equations will also be visited, however this topic is more completely explored in unit F2  Quadratic and Exponential Functions.
Core skills of this unit:

Solve quadratic equations using the zero product property

Solve quadratic equations by factoring

Solve quadratic equations using the quadratic formula

Solve quadratic equations by completing the square

Solve quadratic equations graphically

Solve simple radical equations (square root)
A4  Use and Rearrange Formulas
Students will need to use formulas that are found on the TASC Reference Sheet, as well as given formulas that they may have never seen before. A focus of this unit is on evaluating formulas given values to substitute. Students will also need to have a working knowledge of geometry formulas not found on the TASC Reference Sheet or the exam itself. Some of these formulas include finding the area and circumference of a circle. In addition to using formulas in their given form, students will also need to produce equivalent forms of formulas in terms of a stated variable. For example, if A = p + prt, then what does t equal in terms of p, r and t?
Core skills of this unit:

Use formulas on the TASC Reference Sheet

Using formulas not on the TASC Reference Sheet

Rearrange formulas in terms of a given variable