math skill check

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:

• the last time you took a math course.

• the math courses you took in high school or at your previous college.

• 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.

https://mail.qcc.mass.edu/owa/redir.aspx?C=PjgFYwGuoxkiEGkboad022mt9_xBIXK31rP53wEBmwQkFk0kAebXCA..&URL=mailto%3aadvising%40qcc.mass.edu

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

4𝑥 + 1 ≤ 2𝑥 − 5 Answer: 𝑥 ≤ −3

Perform the indicated operation

28𝑥8 + 24𝑥7 − 24𝑥5 + 16𝑥3

4𝑥5

Answer: 7𝑥3 + 6𝑥2 − 6 +4

𝑥2

Solve the equation

1

4𝑥 −

3

8𝑥 = 10

Answer: x=-80

Simplify

(𝑥5𝑦−5)2

𝑥−3𝑦3

Answer: 𝑥13

𝑦13

Find the product

(𝑥 − 8𝑦)(𝑥 + 3𝑦) Answer: 𝑥2 − 5𝑥𝑦 − 24𝑦2

Add or subtract as indicated.

(6𝑥 + 10𝑥𝑦 − 21𝑦) − (12𝑥 − 25𝑥𝑦 − 19𝑦) Answer: −6𝑥 + 35𝑥𝑦 − 2𝑦

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.


Factor as completely as possible.

6𝑥2 + 𝑥 − 35 Answer: (3𝑥 − 7)(2𝑥 + 5)

Solve the equation. Use the quadratic formula.

3𝑥2 − 7𝑥 − 2 = 0

Answer: 7+√73

6,

7−√73

6

Find the slope of the straight line through the pair of points.

(2, -2) and (6, -7)

Answer: −5

4

Solve for the unknown side of the following right triangle. Be sure your radical answer is in simplest form.

27

?

22 Answer: 7√5

Multiply and simplify. Assume that all variables represent positive numbers.

√18𝑥𝑦 ∙ √2𝑥𝑦2

Answer: 6𝑥𝑦√𝑦

Divide

𝑥2 + 𝑥 − 30

𝑥2 + 15𝑥 + 54÷

5𝑥 − 𝑥2

𝑥2 + 16𝑥 + 63

Answer: - 𝑥+7

𝑥

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.



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.


Solve the equation.

√𝑥 + 3 − 𝑥 = −3

Answer: x = 6

Solve the equation.

6

𝑥 − 2+

4

𝑥 − 3=

−6

𝑥2 − 5𝑥 + 6

Answer: No Solution

Solve

|𝑥 − 7| < 9

Answer: −2 < 𝑥 < 16

Simplify completely.

9

𝑥3 −4

𝑥𝑦2

3𝑥3𝑦

+2

𝑥2𝑦2

Answer: 3𝑦 − 2𝑥

Perform the indicated operation and

completely simplify the result.

√𝑥11𝑦𝑧3

∙ √40𝑥2𝑦3

Answer: 2𝑥4 √5𝑥𝑦2𝑧3

Evaluate:

(8

5)

− 23

Answer: √253

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


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.


Without a graphing calculator, be able to state the

domain and range and graph the following functions:

𝑓(𝑥) = 𝑥 𝑓(𝑥) = |𝑥|

𝑓(𝑥) = 𝑥2 𝑓(𝑥) = √𝑥

𝑓(𝑥) = 𝑥3 𝑓(𝑥) = √𝑥3

𝑓(𝑥) =1

𝑥

Answer: Unavailable

Solve.

𝑙𝑜𝑔4(𝑥 − 1) = 2

Answer: x = 17

Find the equation of the asymptotes

for the graph of:

𝑓(𝑥) =4

𝑥2 + 8𝑥 + 15

Answer: Horizontal: y=0; Vertical: x= -3, x= -5

Find 𝑓−1(𝑥) given:

𝑓(𝑥) =𝑥 − 1

9

Answer: 𝑦 = 9𝑥 + 1

Given: 𝑓(𝑥) = √𝑥 + 53

and 𝑔(𝑥) = 𝑥3 − 1

Find: 𝑓(𝑔(𝑥))

Answer: √𝑥3 + 43

Solve and graph

the solution set:

−𝑥 + 2

𝑥 − 4≥ 0

Answer: {𝑥|2 ≤ 𝑥 < 4}





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.


Find the exact value:

sin−1 (−√3

2)

Answer: −𝜋

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:

𝑦 = sin 𝑥 𝑦 = cos 𝑥 𝑦 = tan 𝑥 𝑦 = cot 𝑥 𝑦 = sec 𝑥 𝑦 = csc 𝑥

Answer: Unavailable

Solve:

2 sin 𝑥 − 1 = 0

on the interval [0, 2𝜋]

Answer: 𝜋

6,

5𝜋

6

Indicate an equivalent function:

cot 𝑥 ∙ sin 𝑥 = _____________

Answer: cos 𝑥

Given the point (−5

13,

12

13) on the unit circle that

corresponds to a real number t. Find the value of csc t Answer:

13

12





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