Name: ______
Practice Test #2
Created for Math 105 – Sp. 10
Instructions: Please show all pertinent work for each problem and box the final answer. Remember that a correct answer does not assure full credit; credit will be assigned for correct work as well as for the correct answer, with emphasis on work. You use a calculator for this exam. Please attach your note card to the back of the test. Good luck!!
1.Give the equation for each line described by the scenario below. The line must be
given in slope-intercept form where possible for full credit.
a)Through the points (0, -5) and (2, -3).
b)Through the points (3, 7) and (3, -1).
c)Through the point (4, -1) and with slope of -3/4. You must use point-slope form
to arrive at slope-intercept form for full credit.
d)Perpendicular to the line x = -1 and through the point (-2, 9).
e)Of the line shown in the graph, using to two points shown.
2. For the equation:-12 – 4y = 3x
a)Put the equation in slope-intercept form. Remember that is solving for one of the variables.
b)On the line provided, give the y-intercept as an ordered pair. ______
c)On the line provided, give the x-intercept as an ordered pair. ______
Show the work in getting the x-intercept in the space provided. Hint: Go back original eq.
d)On the line provided, give a third, integer, ordered pair solution. ______
Show the work in obtaining this solution in the space provided. It may not be done using
the graph, substitution and solving of an equation must be used.
e)On the line provided, give the slope. m = ______
Indicate how you arrived at this answer here.
f)Using 3 points, graph the line on the coordinate system below. Don’t
forget to label your 3 points, put arrows on the line and label the line.
3.Which of the following is a vertical line? (Circle the best answer. Circle only one.)
a)2x = 3y – 5b)y = 3c)2x = 5d) 5y = 9x
4.Which ordered pair lies on the horizontal line 2y = 4?
(Circle the best answer. Circle only one.)
a)(2, 4)b)(2, 0)c)(0, 4)d)(9, 2)
5.Which is the slope of a vertical line? (Circle the best answer. Circle only one.)
a)No slopeb)Zeroc)Undefinedd)Null Set
6.Lines that are parallel have slopes that are:
(Circle the best answer to fill in the blank. Circle only one.)
a)differentb)negative reciprocalc)the same
6.Which line is perpendicular to the line 2x – 3y = 9?
(Circle the best answer. Circle only one.)
a)3x – 2y = -9b)y = 3/2x
c)y = -3/2x – 4.5d)y = 2/3x + 1
7.Which is the equation of a line with zero slope?
(Circle the best answer. Circle only one.)
a)3x = 5yb)y = 3c)2x = 3y – 5 d) 5x = 9
8. Solve the linear inequalities in 1 variable and graph them on a number line. Give
each solution set in interval notation.
a)4(x + 2) 8 > 15 3(x 2)b)-1 < -3x + 5 ≤ 11
9.Circle all the non-linear functions given below.
a)2x + y = x2b)2x + y = 9c)y = 0x + 3
d)| x + 2 | + 5 = y e)x = 9f)y = 7 – √x
10.______On the line provided, write the letter of the function in problem 9 that
can be graphed as a V-Shape.
11. Solve the linear inequalities in two variables: 5x 2y > -10
a)Show 2 labeled points (for each line) that you used to graph
boundary line. (label each line with its equation)
b)Show work for one check point supporting the region shaded (label the
work with the inequality).
12.Factor the following completely:
a)6xy 2x 9y + 3b)10xy 20x2y3 + 30x3y
c)81x2 36x + 4d)x2 17xy + 72y2
e)(x + 1)2 + 5(x + 1) – 6f)x2 + 4x – 3
13.Write in exponential form. (Don't simplify)( 7x2y4 )2
14.Find the root as a real number. Assume the variable represents a positive number.
a)-4x4y2b) x16y32
c)-343 x9y12z21d)√64x8y16
15.Find the root of each (don’t assume that the variable is positive)
c)3√(-27)3d)7√(3 + 5x)7
e)√9x4f)√4x2 + 2x + 1
16.Write each expression in radical form
a)(5x2)b)(2x y2)
17.Evaluate if possible. If the expression isn’t , so state.
a)(-32)b)(-64)
c)(-8)d)9 + 64
18.Rewrite the following radical expression into a single radical expression using
your knowledge of rational exponents and exponent rules.
a) 4 x b)12y 8x
3 x
19.Graph the following using 5 labeled points. Make sure the correct shape is form!
You should be thinking in terms of translations (2.7 form 2.1).
y = (-√x) + 5