Download CM: Review for SLO Name: Tell which set or sets the number

CM: Review for SLO
Name:
Tell which set or sets the number belongs to: natural numbers, whole numbers, integers, rational numbers,
irrational numbers, and real numbers.
1) 97
Tell whether the statement is true or false.
2) Some real numbers are integers.
Write the fraction in lowest terms.
91
3)
117
4)
2
7
Multiply or divide as indicated. Write the answer in lowest terms.
2 11
5) 
8 24
Evaluate.
6)  0.56 
3
Simplify the expression. (Remember the order of operations.)
7) 8  42   9  6 
Solve.
8) The temperature at 5:00 was -4° C. Four hours later, it was -11° C. What was the change in temperature?
Use the distributive property to write the expression without parentheses. Then simplify, if necessary.
1
9)  9 x  6 
3
The bar graph shows the number of tickets sold each week by the garden
club for their annual flower show. Use the graph to answer the question.
10) During which week were 11 tickets sold?
Simplify the expression. First use the distributive property to remove any
parentheses.
11)  8z  2   3z  1
Write the following phrase(s) as an algebraic expression and simplify if possible. Let x represent the
unknown number.
12) The difference of nineteen and a number, divided by four
Solve the problem by combining like terms.
13) Given the following quadrilateral, express the perimeter as an algebraic
expression containing the variable x.
(3x+3) inches
(x-4) inches
4 inches
5x inches
Solve the equation.
14) -0.6 + x = 24.7
15) (y - 3) - (y + 7) = 8y
16) 6(x + 5) - ( 6x + 30) = 0
Solve.
17) The sum of four times a number and three is the same as the difference of twice the number and eleven.
Find the number.
Solve the formula for the specified variable.
1
18) A  bh for b
2
Solve the inequality. Graph the solution set and write it in interval notation.
19) 4 
x
7
Solve.
20) David has $13,000 to invest. He invests $8000 in a mutual fund that pays 12% annual simple interest. If he
wants to make at least $2200 in yearly interest, at what minimum rate does the remainder of the money need
to be invested?
Complete the ordered pair so that it is a solution of the given linear equation.
21) 7x + y = -26
( -4, ), (0, ), (1, )
Complete the table of ordered pairs for the given linear equation; then plot the solution.





22) 5x + 2y = 10

Identify the intercepts.
Find the slope of the line if it exists.
23)
24)
Determine the slope and the y-intercept of the graph.
Determine whether the lines through the
are parallel, perpendicular, or neither.
26)
6x + 2y = 8
15x + 5y = 21
25) -x + 10y = 40
Use the slope-intercept form of the linear equation to write an equation of the line with given slope and yintercept.
7
27) Slope ; y-intercept (0, -4)
3
Find the domain and the range of the relation.
28) {( 7, 4), ( 7, -6), ( 7, -4)}
Use the vertical line test to determine whether the graph is the graph of a function.
29)
Decide whether or not the ordered pair satisfies the system of linear equations.
2 x  14  y
30) ( -5, 4); 
3x  23  2y
The double line graph below shows the number of Acme Superstores vs. the number of General
Superstores.
31) Approximately how many more stores did General have than Acme in 2002?
Solve the system of equations by the substitution method.
5y  x  39
32) 
3x  6y  36
Solve the system of equations by the addition method.
4 x  y  25
33) 
4 x  y  7
x y
 5  5  1
34) 
 x  y   13
 3 3
3
Graph the inequality.
35) y ≥ -5x
36) x + 5y ≤ 7
37) Graph the solution of the system of
linear inequalities.
  4x  y

 x  4y  2
Evaluate the expression.
38) 33
Find the value of the polynomial at the given replacement values.
39) 3x 2  7x  x 4 when x = 2
40) x + 7 when x = 4
Perform the indicated operations.
41) Subtract x from x 3  6 x  14
Find the following product.
42) ( 5z + 3)2
Simplify the expression
45)
10pq 
43)  6y  1  7y 2  4y  9 
44)  8a  5
3
Write the number in scientific notation.
3
25p3q 3
46) 0.000090413
Evaluate the expression using exponential rules. Write the result in standard notation.
47)  5.6  103    5.7  102 
48)  6  103  7  102 
Perform the division.
48 x 7  64 x 5  40 x 3
49)
8x 5
50)
x 4  81
x 3
Factor out the GCF from the polynomial.
51) 21x 3  9 x 2  15x
Factor the polynomial completely. If the polynomial cannot be factored, write prime.
52) 3x 3  3x 2y  18 xy 2
53) x 2  30 x  225
55) 20x 3  15x2  24 x  18
54) 27p3  1
Solve the equation.
56) x 2  3x  40  0
57) x 2  x  42
58) 10 x 2  23x  4  8
Match the equation with its graph.
59) y  x  x  6 
A.
B.
C.
D.
Solve the problem.
60) The width of a rectangle is 6 kilometers less than twice its length. If its area is 108 square kilometers, find
the dimensions of the rectangle.
61) Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6
more than twice the shorter leg.
Find the value of the expression for the given
replacement value.
a2
62)
; a= 9
1  a2
Find all values that make the expression
undefined.
9
63)
z5
Multiply. Simplify if possible.
9 x 4  72x
x2  x  2
64)

3x 2  12 4 x 3  8 x 2  16 x
Divide. Simplify if possible.
15r 2  38rt  24t 2 35r 2  32rt  12t 2
65)

21r 2  34rt  8t 2 42r 2  61rt  14t 2
Perform the indicated operation. Simplify if possible.
x 2  5x
6
x4 9
66)
67)


x 2
x 2
14 14
Solve the equation.
x 6 x 7

70)
3
6
68)
4
14

2
25x  1 1  25x 2
71)
5a 3 7
 
a
4 a
69)
4
9
x
Write a direct variation equation, y = kx, that describes the graph.
72)
Solve.
73) The amount of water used to take a shower varies directly as the amount of time that the shower is in
use. A shower lasting 21 minutes requires 10.5 gallons of water. Find the amount of water used in a shower
lasting 7 minutes.
Simplify the complex fraction.
7
y
74)
6
y 8
Find the square root if it is a real number.
75)  64
Approximate the square root to 3 decimal places.
76) 5
Simplify the expression by combining like radicals where possible.
77) 8 3 2  3 2  11
Simplify the expression.
78) 36  605  81  720
79)
2a  5 32a  7 8a
Solve the equation.
80) 2x  1  3  10
81)
24 x  48  x  4
Find the length of the unknown side of the right triangle with sides a, b, and c, where c is the hypotenuse.
82) a  16, c  2 145