1) Simplify. 125 – 2^2 x 5 / (13 x 3 – 7 x 5)
= 125 – 4 x 5 / (39 – 35)
= 125 – 20/4
= 125 – 5
= 120
2) Simplify. (13 + 2)^2 – (7-6)^2
= (15)^2 – (1)^2
= 225 – 1
= 224
3) Simplify. (77 – 17) x [(10 + 12 / 2) – (3 x 3 – 2 x 2)]
= 60 x [(10 + 6) – (9 – 4)]
= 60 x [16 – 5]
= 60 x 11
= 660
4) Simplify the expression by collecting like terms. 7x – 19 + 3x + 46
= 7x + 3x – 19 + 46
= 10x + 27
5) Find the perimeter of a 13ft by 11ft rectangular bedroom.
Perimeter = 13 + 13 + 11 + 11 = 48 ft
6) Solve using integer or simplified fraction. 9x – 3 = 78
9x – 3 + 3 = 78 + 3
9x = 81
x = 81/9
x=9
7) Solve using the multiplication principle. 5/6m = 10
Assuming that “m” is in the denominator of the fraction:
5
= 10
6m
⎛ 5 ⎞
⎜⎝
⎟ ( 6m ) = 10 ( 6m )
6m ⎠
5 = 60m
m=
5
60
m=
1
12
However, if the problem is actually:
5
m = 10
6
then the solution is:
⎛ 5 ⎞ ⎛ 6⎞
⎛ 6⎞
⎜⎝ m ⎟⎠ ⎜⎝ ⎟⎠ = 10 ⎜⎝ ⎟⎠
6
5
5
m = 12
8) A family has an annual income of $34,200. Of this, ¼ is spent for food, 1/5 for
housing, 1/10 for clothing, 1/9 for savings, ¼ for taxes, and the rest for other expenses.
How much is spent on each?
Food = (34,200)(1/4) = 8,550.00
Housing = (34,200)(1/5) = 6,840.00
Clothing = (34,200)(1/10) = 3,420.00
Savings = (34,200)(1/9) = 3,800.00
Taxes = (34,200)(1/4) = 8,550.00
Other expenses = 34,200 – (8550 + 6840 + 3420 + 3800 + 8550) = 3,040.00
9) Solve using the addition and multiplication principles. Simplify as a fraction. 11/3a +
7/2 = 33/4
Assuming that “a” is in the denominator of the first term, the solution is:
11 7 33
+ =
3a 2 4
⎛ 11 ⎞
⎛ 7⎞
⎛ 33 ⎞
⎜⎝ ⎟⎠ (12a ) + ⎜⎝ ⎟⎠ (12a ) = ⎜⎝ ⎟⎠ (12a )
3a
2
4
44 + 42a = 99a
44 + 42a − 42a = 99a − 42a
44 = 57a
a=
44
57
If “a” is not in the denominator of the first term, then the solution is:
a=
57
44
10) Divide. Write a mixed numeral for the answer. -4 5/6 / 1 7/8
5
4 *6 + 5
29
−
−
116
⎛ 29 ⎞ ⎛ 8 ⎞
6=
6
= 6 = ⎜− ⎟⎜ ⎟ = −
7
1* 8 + 7
15
⎝ 6 ⎠ ⎝ 15 ⎠
45
1
8
8
8
−4
11) Answer should be a mixed numeral. A carpenter used boards of length 5 2/9ft and 5
26/27ft in the construction of shelves. How many feet of board were used?
2
26 ⎛ 5 * 9 + 2 ⎞ ⎛ 5 * 27 + 26 ⎞ 47 161
5 +5
=⎜
+
⎟ +⎜
⎟⎠ =
9
27 ⎝
9 ⎠ ⎝
27
9
27
⎛ 47 ⎞ ⎛ 3 ⎞ 161
=⎜ ⎟⎜ ⎟ +
⎝ 9 ⎠ ⎝ 3 ⎠ 27
=
141 161
+
27 27
=
302
27
= 11
5
27
12) Combine like terms. 2.9a + 9.6d – 9.5a + 8.6d
= (2.9 – 9.5)a + (9.6 + 8.6)d
= -6.6a + 18.2d
13) Simplify. (5 – 0.02)^2 / 4 + 8.6 x 0.3
= (4.98)^2 / 4 + 8.6 x 0.3
= (24.8004) / 4 + 8.6 x 0.3
= 6.2001 + 8.6 x 0.3
= 6.2001 + 2.58
= 8.7801
14) Solve. 3.2a + 1.57 = -7.71
a = -2.9
15) For the following set of numbers find the average, the median, and the mode. Round
to the nearest tenth. 23, 17, 24, 18, 26, 26
Average = 22.3
Median = 23.5
Mode = 26
16) Suppose you draw a card from a well-shuffled deck of 52 cards. Find the probability
of drawing a red picture card (jack, queen, or king)
P(red picture card) = 3/26
17) Solve for x. 6.53/8.5 = 9.17/x (Round to four decimal places)
x = 11.9364
18) It takes 40oz of grass seed to seed 2000ft^2 of lawn. At this rate, how much would be
needed for 5500ft^2 of lawn.
110 oz
19) Translate to an equation and solve. 50% of what is $25
The equation is 0.5x = 25
The solution is x = 50
20) Find the circumference of a circle. Use 22/7 for pi. Radius is 18cm
Circumference = 2(pi)(r) = 2(22/7)(18) = 792/7 cm ≈ 113.14 cm
21) Subtract the polynomials. (8bp – 9b^2p + 17bp^2) – (11bp^2 – 2bp -17b^2p)
6bp^2 + 10bp + 8b^2p
22) Multiply. 5a^4b^3(6a^4b^5 – 5a^3b)
= 30a 8b 8 − 25a 7b 4
23) Multiply. (3 – x)(5 – 3x)
= 3x2 – 14x + 15
24) Factor. X^7 + 9x^6
x6(x + 9)
25) Multiply and Simplify. Give answers using positive exponents. (9m^-9y^18) x (9m^-16y^-7)
81y11
− 25
m
26) Convert to scientific notation. 240,000,000,000
2.4 x 1011
27) Multiply. Write the result using scientific notation. (5.8 x 10^9)(6.8 x 10^-3)
3.944 x 107