1.
Percentage =
413
*100% = 737.5%
56
Answer: D) 737.5%
2.
Let x represent the unknown angle.
The complementary angle is 90 – x.
The supplementary angle is 180 – x.
180 – x = 3(90 – x) – 20
180 – x = 270 – 3x – 20
3x – x = 270 – 20 – 180
2x = 70
x = 35
Answer: C) 35º
3.
-7(x – 4) – 16x < 3(-7x – 7) – 3x
-7x+ 28 – 16x < -21x – 21 – 3x
-23x + 28 < -24x – 21
24x – 23x < -21 – 28
x < -49
In interval notation, the solution is (-∞, -49).
Answer: D
4.
Perimeter = 2 * length + 2 * width
Width = 11
Perimeter ≤ 72
2L + 2*11 ≤ 72
2L + 22 ≤ 72
2L ≤ 72 – 22
2L ≤ 50
L ≤ 25
Answer: C) 25 meters
5.
The graph shown includes all values that are less than 5. The right parenthesis
at x = 5 shows that 5 is not included in the interval, so the solution is x < 5.
Answer: D) x < 5
6.
Let x represent the first of the three numbers. The next consecutive number is
then x + 1, and the second consecutive number is x + 2.
The sum of all three numbers is x + (x + 1) + (x + 2), and is equal to 486.
x + (x + 1) + (x + 2) = 486
3x + 3 = 486
3x = 486 – 3
3x = 483
x = 161.
The first number is 161.
The second number is 162.
The third number is 163.
Answer: D) 161, 162, 163
7.
37%(x) = 183
0.37x = 183
x = 183/0.37
x = 494.59
Round this up to 495
Answer: D) 495
8.
-7b + 1 + 5b = -3b + 6
-2b + 1 = -3b + 6
3b – 2b = 6 – 1
b=5
Answer: A) {5}
9.
14x < 28
x < 28/14
x<2
In interval notation, the solution is (-∞, 2)
Answer: D
10.
120 30 * 4 4
=
=
30 30 *1 1
Answer: B)
4
1
11.
1
8
− +z=
9
9
−1+ 9z = 8
9z = 8 +1
9z = 9
z =1
Answer: B) {1}
12.
Let x represent the unknown number of defective widgets.
8
x
=
72 216
72x = 8 ( 216 )
x=
8 ( 216 )
72
x = 24
Answer: C) 24 widgets
13.
In fencing a garden, you are interested in knowing how much fencing material is
needed to go around the outside edge of the garden. This involves the perimeter of
the garden, not the area.
Answer: B) Perimeter
14.
60%(x) = 61
0.6x = 61
x = 61 / 0.6
x = 101.6667
Round this up to 102
Answer: A) 102
15.
-x = 0.92
To obtain just x on the left side, we need to eliminate the negative sign. To
achieve this, multiply both sides by -1.
Answer: D) -1
16.
y = -3x + 6
Determine the intercepts.
The x-intercept is found by setting y = 0:
0 = -3x + 6
3x = 6
x=2
The x-intercept is (2, 0).
The y-intercept is found by setting x = 0:
y = -3(0) + 6
y=6
The y-intercept is (0, 6).
The only graph with a line through these two points is graph C.
Answer: C
17.
The x-coordinate of point A is -3.
The y-coordinate of point A is 0.
As an ordered pair, the coordinates of point A are (-3, 0)
The x-coordinate of point B is 6.
The y-coordinate of point B is -4
As an ordered pair, the coordinates of point B are (6, -4)
Answer: D) A(-3, 0); B(6, -4)
18.
The point A(0, -2) will have an x-coordinate of 0, and a y-coordinate of -2.
The point B(-5, 0) will have an x-coordinate of -5, and a y-coordinate of 0.
The only graph that has these two points plotted is graph B.
Answer: B
19.
To check to see if (2, 4) is a solution to -17x – 12y = -82, substitute 2 in place of x
and 4 in place of y and test the equality:
-17(2) – 12(4) = -82
-34 – 48 = -82
-82 = -82
Since the last equation is a true statement, the ordered pair (2, 4) is a solution.
Answer: A) Yes
20.
The total price, y, is equal to 2.10x:
y = 2.10x
For x = 11 gallons, the total price is:
y = 2.1(11)
y = 23.10
Answer: A) $23.10
21.
The mapping shown is given as a function g, so f(7) cannot be determined from
the mapping shown.
Answer: C) Cannot be determined
22.
Answer: C) the value of the dependent variable when the independent
variable is 8
23.
2(x + 5) – (2x + 10) = 0
2x + 10 – 2x – 10 = 0
0=0
Since this last statement is true, and not dependent on the value of x, x can
be any real number.
Answer: C) {all real numbers}
24.
Let M represent the number of magazines.
Let L represent the number of letters.
Let B represent the number of bills.
Let A represent the number of ads.
Since the total number of mail items is 19:
M + L + B + A = 19
Since they received the same number of letters as magazines, L = M.
Since they received three more bills than letters, B = L + 3.
Since they received five more adds than bills, A = B + 5.
Substitute for L, B, and A to get:
M + M + (L + 3) + (B + 5) = 19
Substitute again for L and B to get:
M + M + (M + 3) + (L + 3 + 5) = 19
Finally, substitute again for L to get:
M + M + (M + 3) + (M + 3 + 5) = 19
M + M + M + 3 + M + 8 = 19
4M + 11 = 19
4M = 19 – 11
4M = 8
M = 8/4
M=2
They received 2 magazines.
Answer: A) 2 magazines
25.
12
1
8
t− t=t−
7
21
3
Multiply through by 21 to get:
(21)
12
1
8
t − ( 21) t = ( 21) t − ( 21)
7
21
3
36t − t = 21t − 56
Then solve for t:
36t − t − 21t = −56
14t = −56
t=
−56
14
t = −4
Answer: C) {-4}
26.
The volume of water in the reservoir is equal to the area of the base, multiplied by
the depth of the water:
Area of base = 7 meters * 8 meters = 56 meters2
Volume = 56 meters2 * 6 meters = 336 meters3
Answer: C) 336 m3
27.
x – 2y = 6
The x-intercept is found by setting y = 0:
x – 2(0) = 6
x = 6.
The x-intercept is (6, 0)
The y-intercept is found by setting x – 0:
0 – 2y = 6
y = -3
The y-intercept is (0, -3)
The only table of values that includes these two points is choice D
Answer: D
28.
2x – 3y = -16
Rearrange this equation to be in y = mx + b form:
3y = 2x + 16
y = (2/3)x + 16/3
The slope is equal to the coefficient of the x term: 2/3
Answer: A) 2/3
29.
17
*100% = 0.787%
2159
Round this off to 0.8%
Answer: B) 0.8%
30.
3x – 4y = 17
Rearrange this into y = mx + b form:
4y = 3x – 17
y = (3/4)x – 17/4
The slope is equal to the coefficient of the x term, ¾
Answer: D) 3/4