Math 115—College Algebra
Measurable Outcomes
Mathematics Department, UMass Boston
Reference text: Numbers in brackets refer to sections of Miller, O’Neill, and
Hyde, Intermediate Algebra, fourth edition.
Note: Outcomes marked (Optional) may appear on the final exam with the
unanimous consent of all instructors.
1. Linear equations in one variable
1(a) Distinguish linear from non-linear equations. [1.1]
1(b) Solve linear equations in one variable. [1.1]
1(c) (Optional) Model word problems with linear equations. [1.2]
1(d) Solve for one variable in a linear equation involving several
variables. [1.3]
2. Linear inequalities in one variable
2(a) Solve linear inequalities in one variable. [1.4]
2(b) Describe unions and intersections of sets of real numbers. [1.5]
2(c) Solve systems of linear inequalities connected by “and” or “or.”
[1.5]
3. Equations and inequalities with absolute values
3(a) Solve equations involving one or two absolute value expressions.
[1.6]
3(b) Solve inequalities with one absolute value expression. [1.7]
4. Linear equations in two variables
4(a) Write a linear equation in standard form. [2.1]
4(b) Find the intercepts of a linear equation. [2.1]
4(c) Generate additional solutions of a linear equation. [2.1]
4(d) Recognize horizontal and vertical lines. [2.1]
1
4(e) Interpret slope as rise over run. [2.2]
4(f) Compute the slope of a line from two of its points. [2.2]
4(g) Recognize parallel and perpendicular lines by comparing their
slopes. [2.2]
4(h) Write a linear equation in slope-intercept form. [2.3]
4(i) Graph a linear equation in slope-intercept form. [2.3]
4(j) Find the equation of a line, given its slope and y-intercept.
[2.3]
4(k) Use the point-slope form to find the equation of a line, given
its slope and one point. [2.3]
4(l) Find the equation of a line, given two points. [2.3]
4(m) Write the equation of a line parallel or perpendicular to a given
line, through a given point. [2.3]
4(n) (Optional) Model word problems using linear equations in two
variables. [2.4]
5. Relations and functions
5(a) Write a relation as a set of ordered pairs. [2.5]
5(b) Describe the domain and range of a relation. [2.5]
5(c) Distinguish functions from more general relations. [2.6]
5(d) Recognize the graph of a function using the Vertical Line Test.
[2.6]
5(e) Use function notation. [2.6]
5(f) Read function values from a graph. [2.6]
5(g) Find the largest possible domain of a function, given a formula
for the function. [2.6]
5(h) Recognize constant, linear, and quadratic functions. [2.7]
5(i) Reproduce the graphs of the identity, squaring, cubing, abso-
lute value, square root, and reciprocal functions. [2.7]
5(j) Find the x- and y-intercepts of a function, given a formula for
the function. [2.7]
6. Systems of linear equations
6(a) Determine whether a point is a solution of a system of equa-
tions. [3.1]
6(b) Solve a linear system by graphing. [3.1]
6(c) Solve a linear system using the Substitution Method. [3.2]
2
6(d) Solve a linear system using the Addition Method (i.e. the Elim-
ination Method). [3.3]
6(e) Recognize inconsistent and dependent systems. [3.2, 3.3]
6(f) (Optional) Model word problems with linear systems. [3.4]
7. Polynomials
7(a) Simplify expressions using the laws of exponents. [4.1]
7(b) Use scientific notation. [4.1]
7(c) Recognize monomial, binomial, trinomial, and polynomial ex-
pressions [4.2]
7(d) Add and subtract polynomial expressions. [4.2]
7(e) Recognize the degree of a polynomial expression. [4.2]
7(f) (Optional) Model word problems with polynomial functions.
[4.2]
7(g) Multiply polynomials. [4.3]
7(h) Square a binomial. [4.3]
7(i) (Optional) Cube a binomial. [4.3]
7(j) (Optional) Divide a polynomial by a monomial. [4.4]
7(k) (Optional) Compute quotient and remainder using polyno-
mial long division. [4.4]
7(l) Find the greatest common factor of several monomials. [4.5]
7(m) Factor the greatest common factor out of a polynomial. [4.5]
7(n) Factor a polynomial by grouping. [4.5]
7(o) Factor trinomials. [4.6]
7(p) Recognize and factor perfect square trinomials. [4.7]
7(q) Factor a difference of squares. [4.7]
7(r) (Optional) Factor a sum or difference of cubes. [4.7]
7(s) Write and explain the zero-product rule [4.8]
7(t) Solve polynomial equations by factoring. [4.8]
8. Rational expressions
8(a) Distinguish rational expressions from more general expressions.
[5.1]
8(b) Reduce a rational expression to lowest terms. [5.1]
8(c) Multiply and divide rational expressions. [5.2]
8(d) Find the least common denominator of two rational expressions.
[5.3]
3
8(e) Add and subtract rational expressions. [5.3]
8(f) Reduce compound fractions. [5.4]
8(g) Solve a rational equation in one variable. [5.5]
8(h) Solve for one variable in a rational equation with several vari-
ables. [5.5]
8(i) (Optional) Solve proportions and similar triangles. [5.6]
8(j) (Optional) Recognize direct and inverse variation. [5.7]
9. Radicals
9(a) Correctly interpret and evaluate
√
a (the principal or non-
negative square root of a non-negative real number a). [6.1]
9(b) Find all real solutions of equations of the form x
2
= a. [6.1]
9(c) Correctly interpret and evaluate
n
√
a, where n is any positive
integer and a is a non-negative real number. [6.1]
9(d) Find all real solutions of equations of the form x
n
= a. [6.1]
9(e) Simplify expressions of the form
n
√
a
n
. [6.1]
9(f) Find the third side of a right triangle, given any two sides.
[6.1]
9(g) Find the largest possible domain of a function involving radi-
cals. [6.1]
9(h) Evaluate expressions of the form a
n/m
. [6.2]
9(i) Convert between radical notation and rational exponents. [6.2]
9(j) Simplify expressions involving rational exponents by using the
laws of exponents. [6.3]
9(k) Simplify radical expressions using the fact that
n
√
ab =
n
√
a
n
√
b
when a, b > 0. [6.3]
9(l) Add and subtract radical expressions. [6.4]
9(m) Multiply radical expressions. [6.5]
9(n) Multiply radicals with different indices. [6.5]
9(o) Simplify radical expressions using the fact that
n
p
a/b =
n
√
a/
n
√
b
when a, b > 0. [6.6]
9(p) Rationalize the denominator of a radical expression. [6.6]
9(q) Solve equations involving one or two radical expressions. [6.7]
10. Quadratic equations and quadratic functions
10(a) Solve quadratic equations by completing the square. [7.1]
4
10(b) Solve quadratic equations by using the Quadratic Formula.
[7.2]
10(c) Calculate the discriminant of a quadratic expression. [7.2]
10(d) Use the discriminant to predict the number of real solutions of
a quadratic equation. [7.2]
10(e) (Optional) Solve equations in quadratic form. [7.3]
10(f) Sketch the graph of a quadratic function. [7.4]
10(g) Find the vertex of a parabola. [7.5]
10(h) Solve quadratic optimization problems. [7.5]
11. Polynomial and rational inequalities (Optional)
11(a) (Optional) Solve polynomial inequalities. [7.6]
11(b) (Optional) Solve rational inequalities. [7.6]
5
