Math Skill Check
COLLEGE.MADE
WELCOME to The QCC Math Skill Check Website
During this time of social and physical distancing, we are unable to provide you with the typical on-site placement test needed to determine your current math skills. However, the QCC Math Department cares about your success and wants to provide you with an opportunity to review your current math skills to help us properly place you into the correct course. Your skills may vary depending on a number of factors such as:
β’ the last time you took a math course.
β’ the math courses you took in high school or at your previous college.
β’ the frequency that you use math in your current job or your day-to-day activities.
Keep these things in mind as you work through this website to check your current math skills. An honest review of your skills will better ensure that you succeed in your QCC math course.
Next steps:
1. Each skill check contains a description, sample problems, and directions for level placement.
2. Review each of the skill checks carefully in sequence (starting with Level 1) and take your time: a. Read each description and decide if you are completely comfortable with the
content of that math level and that it completely matches your current math skills.
b. Work on the sample problems for each level. Did you answer all of the questions correctly? If so, you can continue to the next math level skill check.
c. If at any time you feel that the material is beyond your current math skills, then you want to stop and place yourself into that math level (i.e. Level 1, Level 2, etc.).
3. Make a note of the math level where you stopped. You will share this level with an Academic Advisor to help you register for the appropriate math course based on your honest skill check, math history on file, goals, and program of study requirements.
4. Contact QCC Advising at [email protected] or 508-854-4308 for further review and course registration assistance.
Good luck and the QCC Math Department looks forward to working with you as you progress
through your math courses.
LEVEL 1 SKILL CHECK
Description: Level 1 covers all basic operations of real numbers, linear and literal equations, graphing lines
(using tables, x and y-intercepts), the arithmetic of polynomial expressions including properties of
exponents, solving and graphing linear inequalities, perimeters and areas of basic figures, scientific notation
and intrasystem metric conversion.
Sample Problems: Complete the following sample problems.
Solve the inequality
4π₯ + 1 β€ 2π₯ β 5 Answer: π₯ β€ β3
Perform the indicated operation
28π₯8 + 24π₯7 β 24π₯5 + 16π₯3
4π₯5
Answer: 7π₯3 + 6π₯2 β 6 +4
π₯2
Solve the equation
1
4π₯ β
3
8π₯ = 10
Answer: x=-80
Simplify
(π₯5π¦β5)2
π₯β3π¦3
Answer: π₯13
π¦13
Find the product
(π₯ β 8π¦)(π₯ + 3π¦) Answer: π₯2 β 5π₯π¦ β 24π¦2
Add or subtract as indicated.
(6π₯ + 10π₯π¦ β 21π¦) β (12π₯ β 25π₯π¦ β 19π¦) Answer: β6π₯ + 35π₯π¦ β 2π¦
If you are not familiar with items in the above description and you are not able to correctly answer all of
the above questions, then you can stop here and you will need to place yourself into LEVEL 1.
If you are very familiar with the items in the description and you were able to correctly answer all of these
questions, then you can move to LEVEL 2 SKILL CHECK.
LEVEL 2 SKILL CHECK
Description: Level 2 covers major topics in the study of algebra. Students learn to factor polynomials
(common factor, grouping, difference of squares, and trinomials), perform arithmetic operations on
rational expressions and complex fractions, and solve rational, quadratic, (by factoring and formula) and
literal equations. The course also covers applications including the use of the Pythagorean Theorem,
understanding the definition of radical expressions, simplifying radical expressions containing numerical
and variable radicands, graphing linear equations using slope-intercept concepts, and solving 2x2 systems
of linear equations by graphing and elimination.
Sample Problems: Complete the following sample problems.
Factor as completely as possible.
6π₯2 + π₯ β 35 Answer: (3π₯ β 7)(2π₯ + 5)
Solve the equation. Use the quadratic formula.
3π₯2 β 7π₯ β 2 = 0
Answer: 7+β73
6,
7ββ73
6
Find the slope of the straight line through the pair of points.
(2, -2) and (6, -7)
Answer: β5
4
Solve for the unknown side of the following right triangle. Be sure your radical answer is in simplest form.
27
?
22 Answer: 7β5
Multiply and simplify. Assume that all variables represent positive numbers.
β18π₯π¦ β β2π₯π¦2
Answer: 6π₯π¦βπ¦
Divide
π₯2 + π₯ β 30
π₯2 + 15π₯ + 54Γ·
5π₯ β π₯2
π₯2 + 16π₯ + 63
Answer: - π₯+7
π₯
If you are not familiar with items in the description and you were not able to correctly answer all of the
above questions, then you can stop here and you will need to place yourself into LEVEL 2.
If you are very familiar with the items in the description and you were able to correctly answer all of these
questions, then you can move to LEVEL 3 SKILL CHECK.
LEVEL 3 SKILL CHECK
Description: Level 3 covers arithmetic operations on rational expressions; solve equations with fractions;
factor expressions; simplify complex fractions; simplify exponential expressions, roots, radicals, and rational
exponents; solve linear systems using several techniques; use the midpoint and distance formulas;
recognize and graph the equation of a circle; solve linear and absolute value inequalities; solve quadratic
equations by completing the square and by using the quadratic formula; solve equations containing radicals
or absolute values; and perform arithmetic operations on radical expressions and complex numbers.
Sample Problems: Complete the following sample problems.
Solve the equation.
βπ₯ + 3 β π₯ = β3
Answer: x = 6
Solve the equation.
6
π₯ β 2+
4
π₯ β 3=
β6
π₯2 β 5π₯ + 6
Answer: No Solution
Solve
|π₯ β 7| < 9
Answer: β2 < π₯ < 16
Simplify completely.
9
π₯3 β4
π₯π¦2
3π₯3π¦
+2
π₯2π¦2
Answer: 3π¦ β 2π₯
Perform the indicated operation and
completely simplify the result.
βπ₯11π¦π§3
β β40π₯2π¦3
Answer: 2π₯4 β5π₯π¦2π§3
Evaluate:
(8
5)
β 23
Answer: β253
4
If you are not familiar with items in the description and you are not able to correctly answer all the above
questions, then you can stop here and you will need to place yourself into LEVEL 3.
If you are very familiar with the items in the description and were able to correctly answer all of these
questions, then you can move to LEVEL 4 SKILL CHECK.
LEVEL 4 SKILL CHECK
Description: Level 4 covers expanding binomial expressions using the binomial theorem; solve non-linear,
and rational inequalities and write their solutions using interval notation; determine and write linear
equations in several forms; explain the concept of function; graph functions using symmetry test; recognize
and graph functions, including constant, linear, quadratic, polynomial, rational, exponential, and
logarithmic functions; use function transformation techniques; perform composition and arithmetic
operations on functions; find and graph inverses of functions; use properties of logarithms; and solve
logarithmic and exponential equations.
Sample Problems: Complete the following sample problems.
Without a graphing calculator, be able to state the
domain and range and graph the following functions:
π(π₯) = π₯ π(π₯) = |π₯|
π(π₯) = π₯2 π(π₯) = βπ₯
π(π₯) = π₯3 π(π₯) = βπ₯3
π(π₯) =1
π₯
Answer: Unavailable
Solve.
πππ4(π₯ β 1) = 2
Answer: x = 17
Find the equation of the asymptotes
for the graph of:
π(π₯) =4
π₯2 + 8π₯ + 15
Answer: Horizontal: y=0; Vertical: x= -3, x= -5
Find πβ1(π₯) given:
π(π₯) =π₯ β 1
9
Answer: π¦ = 9π₯ + 1
Given: π(π₯) = βπ₯ + 53
and π(π₯) = π₯3 β 1
Find: π(π(π₯))
Answer: βπ₯3 + 43
Solve and graph
the solution set:
βπ₯ + 2
π₯ β 4β₯ 0
Answer: {π₯|2 β€ π₯ < 4}
If you are not familiar with items in the description and you are not able to correctly answer all the above
questions, then you can stop here and you will need to place yourself into LEVEL 4.
If you are very familiar with the items in the description and you were able to correctly answer all of these
questions, then you can move to LEVEL 5 SKILL CHECK.
LEVEL 5 SKILL CHECK
Description: Level 5 covers solving right and oblique triangles and related applications; perform vector
computations and use vector concepts to solve applications; determine the values of trigonometric ratios
of angles and the values of inverse trigonometric ratios of real numbers; work with angles measured in
degrees-minutes-seconds or radians; solve uniform circular motion problems; learn the traditional
trigonometric identities and use them to prove other identities; perform transformations of basic
trigonometric graphs; write equations to describe specific instances of harmonic motion; and solve
trigonometric equations.
Sample Problems: Complete the following sample problems.
Find the exact value:
sinβ1 (ββ3
2)
Answer: βπ
3
Find the reference angle for:
11π
4
Answer: 3π
4
State the domain, range, and period and
be able to graph the following functions:
π¦ = sin π₯ π¦ = cos π₯ π¦ = tan π₯ π¦ = cot π₯ π¦ = sec π₯ π¦ = csc π₯
Answer: Unavailable
Solve:
2 sin π₯ β 1 = 0
on the interval [0, 2π]
Answer: π
6,
5π
6
Indicate an equivalent function:
cot π₯ β sin π₯ = _____________
Answer: cos π₯
Given the point (β5
13,
12
13) on the unit circle that
corresponds to a real number t. Find the value of csc t Answer:
13
12
If you are not familiar with items in the description and you are not able to correctly answer all the above
questions, then you can stop here and you will need to place yourself into LEVEL 5.
If you are very familiar with the items in the description and you were able to correctly answer all of these
questions, then you can stop here and you will need to place yourself into LEVEL 6.
COLLEGE.MADE
This is the end of the Math Skill Check