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MATD 0330 BASIC MATH SKILLS
REVIEW FOR TEST 3
(Basic 4-Function, 10-Key Calculator Allowed – No Scientific or Graphing Calculators)
New material covered: 1.1-1.3, 2.1-2.3, and handouts Exercise Sets 2.2 and 2.3
1.
Find the absolute values:
a.
b.
c.
d.
e.
|–8|
|6|
|0|
|7.9|
|–11 3 |
8
2.
Find: 63
3.
Rewrite using exponents: 4 • 4 • 4 • 4 • 4 • 4
4.
Find: |23| – |32|
5.
Find: 25 • 72
6.
On the number line, A = 51 and B = –17. Write an expression that represents the
distance between A and B. Then evaluate the expression to find the distance.
7.
Find the GCF and LCM of 14 and 63.
8.
Find the GCF and LCM of 28 and 42.
9.
Find the GCF and LCM of 6, 8, and 9.
10.
Find the GCF and LCM of 12, 36, and 60.
11.
Simplify to lowest terms:
12.
Find: 21 • 18
13.
Find: 49 ÷ 196
14.
Find: 11 – 9
15.
Find: 7 + 7
16.
Find:
17.
Find: – 84 – 29
35
40
60
135
15
15
15
11
16
20
–
9
20
252
300
MATD 0330 BASIC MATH SKILLS
REVIEW FOR TEST 3
18.
Find: –11 – (–41)
19.
Find: (–9) • 12
20.
Find: (–23) • (–12)
21.
Find: (–96) ÷ 6
22.
Find: (–143) ÷ (–13)
23.
Find: 4 + 3 • 7
24.
Find: 30 ÷ [3 – (4 • 2)]
25.
Find: 28 ÷ (5 – 3)2 + 6
26.
Find: (14 – 5) ÷ 32 + 4 • 2
27.
Evaluate each of the following:
a.
(–8)2
b.
–82
c.
(–5)3
d.
–53
28.
Evaluate each of the following:
a.
x3 for x = –4
b.
–x3 for x = –4
c.
x4 for x = –3
d.
–x4 for x = 3
29.
What are the terms and coefficients in the expression 6a3 – 7ab + b2 – 9?
30.
Simplify: 5 – (w + 8 – 6w)
31.
Simplify: 9 – 4(y – 2)
32.
Simplify: 7a – 12 – 4a – 16
33.
Simplify: 8(x + 3) – 7(x + 2)
34.
Evaluate 4x + 6y – 7 when x = 4 and y = –2.
35.
Evaluate 7x2 – 3x – 9y when x = – 3 and y = 11.
36.
Evaluate 2x3 – 4xy – 5xz + 8z – 11 when x = 4, y = – 6, and z = 3.
37.
Solve: x + 8 = 13
38.
Solve: k – 22 = 8
39.
Solve: 7 – s = 2
MATD 0330 BASIC MATH SKILLS
REVIEW FOR TEST 3
40.
Solve: m + 33 = 2m – 9
41.
Solve: 5 + 4w = –27 + 2w
42.
Solve: –8 – 3y = 1
43.
Solve: –3(p – 4) = 6
44.
Solve: 4s – 7 = –2(1 – s)
45.
Solve:
6
y
7
= 12
46.
Solve:
4
(r
5
– 10) = r + 2
47.
Solve:
1
a
4
=
48.
The formula for the area of a rectangle is A = L • W, where A is the area of the
rectangle, L is its length, and W is its width. Solve this formula for W.
49.
The formula for the circumference of a circle is C = 2πr, where C is the
circumference and r is the radius of the circle. Solve this formula for r.
50.
If triple a number is decreased by four, the result is thirty–five. (a) Write an
equation. (b) Solve the equation.
51.
If the sum of a number and nine is multiplied by three, the result is 102. (a) Write
an equation. (b) Solve the equation.
52.
The perimeter of a rectangle is 42 feet. The width is 3 feet less than the length.
(a) Define the variable expressions. (b) Write an equation. (c) Solve the equation
and find the dimensions of the rectangle.
53.
The perimeter of a rectangle is 88 centimeters. The length is 7 centimeters
shorter than double the width. (a) Define the variable expressions. (b) Write an
equation. (c) Solve the equation and find the dimensions of the rectangle.
54.
A triangle has a perimeter of 87 inches. The second side of the triangle is five
inches less than the first side. The third side is 8 inches longer than twice the first
side. (a) Define the variable expressions. (b) Write an equation. (c) Solve the
equation and find the length of each side of the triangle.
55.
The sum of three consecutive odd integers is 63. (a) Define the variable
expressions. (b) Write an equation. (c) Solve the equation and find the integers.
56.
The sum of two numbers is 20. Three times the smaller plus twice the larger is
47. (a) Define the variable expressions. (b) Write an equation. (c) Solve the
equation and find the numbers.
2
(a
3
+ 10)
MATD 0330 BASIC MATH SKILLS
REVIEW FOR TEST 3
ANSWERS
1.
a.
b.
c.
d.
8
6
0
7.9
e.
11
3
8
2.
216
3.
46
4.
–1
5.
1,568
6.
|51 – (–17)|
7.
GCF: 7, LCM: 126
8.
GCF: 14, LCM: 84
9.
GCF: 1, LCM: 72
10.
GCF: 12, LCM: 180
11.
21
25
12.
27
100
13.
9
16
14.
2
15
15.
49
60
16.
19
80
17.
–113
or
|–17 – 51|
or 51 + 17
Distance = 68 units
MATD 0330 BASIC MATH SKILLS
REVIEW FOR TEST 3
ANSWERS
18.
30
19.
–108
20.
276
21.
–16
22.
11
23.
25
24.
–6
25.
13
26.
9
27.
a.
b.
c.
d.
28.
Don't forget the parentheses when substituting in values.
a. (–4)3 = (–4)(–4)(–4) = –64
b. –(–4)3 = –(–4)(–4)(–4) = –(–64) = 64
c. (–3)4 = (–3)(–3)(–3)(–3) = 81
d. –(3)4 = –(3)(3)(3)(3) = –81
29.
Terms: 6a3, –7ab, b2, –9
Coefficients: 6, –7, 1, –9 (–9 is also called a constant because it has no variable part)
30.
5w – 3
31.
–4y + 17
32.
3a – 28
33.
x + 10
34.
–3
35.
–27
36.
177
64
–64
–125
–125
MATD 0330 BASIC MATH SKILLS
ANSWERS
37.
x=5
38.
k = 30
39.
s=5
40.
m = 42
41.
w = –16
42.
y = –3
43.
p=2
44.
s=
45.
y = 14
46.
r = –50
47.
a = –16
48.
A
W=L
49.
r= C
50.
a.
3n – 4 = 35
b.
The number is 13.
a.
3(n + 9) = 102
b.
The number is 25.
a.
Let x = the length of the rectangle in ft
Then x – 3 = the width of the rectangle in ft
b.
2(x) + 2(x – 3) = 42, or
x + (x – 3) + x + (x – 3) = 42, or
4x – 6 = 42
c.
The length is 12 ft.
The width is 9 ft.
51.
52.
5
2
2π
REVIEW FOR TEST 3
MATD 0330 BASIC MATH SKILLS
REVIEW FOR TEST 3
ANSWERS
53.
54.
55.
56.
a.
Let x = the width of the rectangle in cm
Then 2x – 7 = the length of the rectangle in cm
b.
2(2x – 7) + 2(x) = 88, or
x + (2x – 7) + x + (2x – 7) = 88, or
6x – 14 = 88
c.
The width is 17 cm.
The length is 27 cm.
a.
Let x = the length of the first side in inches
Then x – 5 = the length of the second side in inches
Then 2x + 8 = the length of the third side in inches
b.
x + (x – 5) + (2x + 8) = 87, or
4x + 3 = 87
c.
The sides are 21 inches, 16 inches, and 50 inches.
a.
Let x = the first odd integer
Then x + 2 = the next consecutive odd integer
Then x + 4 = the third consecutive odd integer
b.
x + (x + 2) + (x + 4) = 63, or
3x + 6 = 63
c.
The odd integers are 19, 21, and 23.
a.
Let x = the smaller number
Then 20 – x = the larger number
b.
3x + 2(20 – x) = 47, or
x + 40 = 47
c.
The smaller number is 7, and the larger number is 13.