Math 150 Test #5B Print this test. When you have completed this test submit your
answers in Test #5B Answers. Remember that work must be shown on questions that are
not multiple choice (Part II).
Part I: Select the letter of the correct answer.
1.) Solve the following system of equations simultaneously for x.
2x + 3y = 6 and 4x – 5y = 2
x=
A) 4
11 B) 11
10 C) 10
11 D) 18
11 2.) Solve the following system of equations simultaneously for y.
x = 5y – 2 and 3x + 2y = 7
y=
13
17
31
B)
C)
17
13
17
2
3.) Solve for x: 3x – 4x = 3x + 6 ;
x=
A) D) 1
17 7 ± i 23
1± 73
2
2
B) − & 3
C)
D)
&3
2
3
6
3
Solve the following quadratic equation using the quadratic formula.
Express your answer in simplest radical form. 2x2 – 4x + 1 = 0; A) 4.) A) 2 2 B) 2 C) 2± 6
2 D) 2± 2
2 For questions #5 – 8 use the following: y = x2 + 4x – 5
5.) Where does the graph of this function cross the x-axis? x =
A) -5 B) -5 & -1 C) -5 & 1 D) 5 & -1 6.) Find the equation for the axis of symmetry. (Use y = x2 + 4x – 5)
A) x = -2 B) x = 2 C) x = -5/2 D) x = 4 7.) Find the coordinates of the vertex. (Use y = x2 + 4x – 5)
A) (2, 7) B) (-2, -9) C) (4, -5) D) (4, 27) x= y = x2 + 4x – 5
8.) Is the extreme point (vertex) a maximum or a minimum point? Explain.
Pick the ONE answer below that is completely correct. (Read these carefully.)
The vertex is ____
A)
B)
C)
D)
9.) a maximum point since the curve is concave-upward.
a maximum point since the curve is concave-downward.
a minimum point since the curve is concave-downward.
a minimum point since the curve is concave-upward. Simplify i18 where i = - 1
A) -i B) i C) 1 D) -1 10.) Combine: (8 – 4i) – (2 – 3i) – (-5 + i)
A) 11 – 2i B) 9i C) 12 D) 11 – 8i 11.) Multiply (4 + 3i) by its conjugate and simplify.
A) -4 – 3i B) 7 + 24i C) 7 D) 25 12.) Solve the following quadratic equation. Simplify your answer.
x2 – 4x + 5 = 0;
x=
A) 2 ± 2i 2 B) 2 ± 15 C) 2 ± i D) − 2 ± 2i Part II: Show all of your work using the methods used in the lectures. To receive
credit you must type out your work.
13.) Solve by completing the square. Show all steps. Leave your answer in simplest
radical form. 2x2 - 12x + 2 = 0 14.) Divide and simplify:
Keep the fractions.) 3
2 − 3i (Do not write your answer in decimal form. 15.) Solve the following radical equation for x. Remember to show the check.
16 − 4 x + 1 = x 16.) Reduce the following system of three equations to a system of two equations in two
unknowns by eliminating y. Show all of your work. Your answer will be two
equations, neither of which contains a y. Type out your work using the methods
used in class (in the lectures). You are not solving for x, y and z.
a) 2x + y - 3z = -4
b) 3x - 2y + z = 19
c) x + 3y + 2z = -5 17.) Solve the following word problem using two variables and a system of two
equations.. You must use an algebraic solution and show your equations to receive
credit. The cost of 3 hamburgers and 2 sodas is $14.90. The cost of one
hamburger is 30 cents more than the cost of two sodas. Find the cost of one
hamburger. (Let x = the cost of one hamburger and y = cost of one soda.)

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