Download Keystone Review – Real Number System Name: Date: 1. The value

Keystone Review { Real Number System
Name:
1.
The value of 5
A.
2.
Date:
1
25
Evaluate:
2
B.
7.
is
1
25
C.
10
D.
25
Which expression represents the number 0.00017
written in scienti c notation?
A.
1:7
10
4
B.
1:7
104
C.
1:7
10
3
D. 1:7
103
10x0
8.
A.
3.
Which expression is equivalent to x
A.
4.
9x5
B.
The expression
A.
6.
B.
y2
x
C.
x
y2
45
B.
33
C.
63
D. 192
y2 ?
D. xy
2
9.
Debbie solved the linear equation 3(x + 4)
as follows:
2 = 16
Which expression is equivalent to (3x2 )3 ?
A.
5.
xy2
1
3 [2 + 6 ( 3)] simpli es to
The expression 15
2w5
B.
9x6
10w3
5w
2w8
C.
2
27x5
D. 27x6
She made an error between lines
is equivalent to
C.
20w5
D. 20w8
If 0.000023 is expressed in the form 2:3
what is the value of n ?
10.
10n ,
A.
1 and 2
B.
C.
3 and 4
D. 4 and 5
Which represents an irrational number?
A.
page 1
2 and 3
0
B.
3
4
C.
p
3
D.
p
4
Keystone Review { Real Number System
11.
Which does not represent a rational number?
A.
12.
3
2
B.
p
7
p
C.
If x = 13, then the value of
A.
a rational number
B.
an irrational number
C.
unde ned
p
x
16
17.
D. 0:29
A.
5 is
18.
D. an integer
13.
14.
The expression
p
50 10
B.
C.
p
10 5
p
D. 10 50
p
The expression 3 27
A.
15.
p
500 is equivalent to
A.
p
7 3
B.
If the sum of
of x.
p
23 3
19.
p
5 10
20.
p
15 3
p
D. 4 3
The sum of
A.
p
7 20
p
B.
6
C.
3
D. 4
A.
p
a2 + b2 = a + b
B.
C.
a+b a b
= +
c
c c
D. (a + b)2 = a2 + b2
ab = b
The statement \n is even and a perfect square" is
true when n equals
1
B.
18
C.
25
D. 4
Under which operation is the set of positive
rational numbers not closed?
A.
addition
B.
subtraction
C.
multiplication
D. division
p
p
p
50 and x 2 is 8 2, nd the value
21.
16.
5
Which statement is always true if the domain of
the variables is the set of positive integers?
A.
p
12 is equivalent to
C.
The statement \x is divisible by 3 and x is greater
than 3" is true for which whole number?
p
18 and 6 2 is
B.
p
9 2
C.
p
15 2
D. 18
page 2
If a and b are any two whole numbers, which
statement is always true?
A.
2a + b = 2b + a
B.
a+b=b+a
C.
ab = ba
D. a
b=b
a
Keystone Review { Real Number System
22.
Which set is not closed under addition?
A.
natural numbers
B.
even integer
C.
whole numbers
D. odd integers
page 3
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Licensed for use by Problem-Attic
Keystone Review { Real Number System
1.
Answer:
B
2.
Answer:
10
3.
Answer:
B
4.
Answer:
D
5.
Answer:
C
6.
Answer:
5
7.
Answer:
A
8.
Answer:
C
9.
Answer:
B
10.
Answer:
C
11.
Answer:
B
12.
Answer:
B
13.
Answer:
C
14.
Answer:
A
15.
Answer:
3
16.
Answer:
B
17.
Answer:
B
18.
Answer:
C
19.
Answer:
D
20.
Answer:
B
11/01/2012
21.
Answer:
B
22.
Answer:
D
Keystone Review { Properties of Real Numbers
Name:
1.
2.
Date:
Which sentence is an example of the distributive
property?
A.
ab = ba
B.
C.
a(b + c) = ab + ac
D. a 1 = a
5.
a(bc) = (ab)c
The sentence 3 + (5 + 2) = (5 + 2) + 3 illustrates
A.
the commutative property of addition
B.
the associative property of addition
C.
the distributive property of multiplication over
addition
6.
Which is an illustration of the associative
property?
A.
x
y=y
B.
x
(y
z) = (x
y)
(x
C.
x
(y
z) = (y
z)
x
D. x
(y
z) = (x
y)
z
3(1 + x)
3(x + 1)
3 x+3 1
3x + 3
Which sentence illustrates the commutative
property for addition?
A.
(a + b) + c = a + (b + c)
B.
a(b + c) = ab + ac
C.
a+0=a
7.
D. a + b = b + a
A.
associative
B.
C.
distributive
D. identity
Which property is illustrated by the equation
8 + 0 = 8?
A.
additive inverse
B.
additive identity
C.
commutative property
1. Given
2. Multiplication axiom
4. 1 x = 2
4. Multiplicative inverse
5. x = 2
page 1
Reasons
1. 3x = 6
2. 13 (3x) = 13 (6)
3. ( 13 3)x = 2
D. distributive property
commutative
In the solution of this problem, which property of
real numbers justi es statement 5?
Statements
4.
z)
In the step-by-step simpli cation of the expression
below, which property is not used?
D. the additive identity element
3.
x
3. Associative property
5.
A.
Closure
B.
Identity
C.
Commutative
D. Inverse
Keystone Review { Properties of Real Numbers
8.
The additive inverse of a
A.
a+b
C.
9.
13.
B.
D.
b
a+b
1
a
b
a
3
B.
3
a
C.
Which equation illustrates the multiplicative
inverse property?
A.
b 0=0
B.
b + ( b) = 0
C.
b+0=b
D. b
1
b
=1
a
?
3
Which is the additive inverse of
A.
10.
a
b is
3
a
D. 0
14.
Which propertypof real
p numbers is illustrated by
3 + 3 = 0?
the equation
A.
additive identity
B.
commutative property of addition
C.
associative property of addition
The reciprocal of the expression
2 3
+ is
x 1
A.
2 + 3x
x
B.
C.
2x + 3
D. 2 + 3x
x
2 + 3x
D. additive inverse
15.
11.
12.
What is the multiplicative inverse of
The product of
A.
1
B.
1
5
?
C.
1
a2
A.
commutative property of addition
B.
distributive property
C.
additive inverse property
D. additive identity property
1
, a6=0, and its reciprocal is
a
1
Which property is illustrated by the equation
3
3
2x + 0 = 2x
D. 0
page 2
Acces format version 4.4.146
c 1997{2011 EducAide Software
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Licensed for use by Problem-Attic
Keystone Review { Properties of Real Numbers
1.
Answer:
C
2.
Answer:
A
3.
Answer:
D
4.
Answer:
B
5.
Answer:
D
6.
Answer:
A
7.
Answer:
B
8.
Answer:
B
9.
Answer:
A
10.
Answer:
D
11.
Answer:
5
12.
Answer:
A
13.
Answer:
D
14.
Answer:
B
15.
Answer:
D
11/01/2012
Keystone Review { Algebraic Expressions
Name:
1.
If x represents an even number, which expression
represents an odd number?
A.
2.
3.
4.
5.
Date:
x2
B.
x+3
C.
3x
D.
6.
x
3
Which expression represents the number of cents
in d dimes and n nickels?
A.
d+n
B.
15(d + n)
C.
10d + 5n
D.
d
n
+
10 5
n+8
B.
C.
10n + 7
D. 2n + 7
A.
90
C.
180
3x
3x
B.
3x
90
D. 3x
180
7.
Find the value of (x2
8.
When x = 2 and y = 3, which expression has the
smallest value?
If n + 7 represents an even number, the next larger
even number is represented by
A.
What is the supplement of an angle that
measures 3x ?
A.
(x
C.
x+y
5x + 4) if x = 7.
B.
y)
x y
D. x
y
n+9
x
, y6=0?
y
9.
If x = 4y, what is the value of
10.
If a = 2 and b = 3, what is the value of
11.
Find the sum of 5x3
12.
From 6x2
Maria is twice as old as Sue. If x represents Sue's
age, which expression represents how old Maria
will be in three years?
A.
2x
C.
1
2x
B.
3
x+3
D. 2x + 3
3x2 + 5 and
2x3 + 6x2
If x represents the smallest of three consecutive
odd integers, then the largest would be represented
by
A.
x+2
3a2 b ?
B.
x+3
C.
x+4
D. x + 5
page 1
3x + 9 subtract 2x2
5x + 8.
5.
Keystone Review { Algebraic Expressions
13.
The expression y3 + y3 is equivalent to
A.
14.
16.
17.
18.
B.
The quotient of
A.
15.
2y6
3x3
2y3
C.
y9
19.
D. y6
18x6
is equal to
6x3
3x2
B.
The product of 3x2 y3 and
C.
12x2
20.
D.
4x3 y4 is
A.
7x5 y7
B.
x5 y7
C.
12x5 y7
D.
12x6 y12
The quotient
A.
4x2 y3
C.
12x2 y3
16x3 y5
4xy2
The product of
3x2 y3
12x3
21.
is equivalent to
and
B.
4xy7
D.
12x3 y3
4xy2
is equivalent to
7x2 y5
A.
x2
16
B.
C.
x2
8x + 16
D. x2 + 8x + 16
A.
2x2
C.
2x2 + x
6
B.
2x2
x
6
D. 2x2 + 7x
6
Which expression is equal to (x + 3)2 ?
A.
x2 + 6
B.
C.
x2 + 6x + 9
D. x2 + 3x + 9
22.
Express (4x
23.
Factor: x2 + 5x
7x2 y6
B.
C.
12x2 y6
D. 12x3 y5
24.
Factor: 25x2
3)(x + 5) as a trinomial.
25.
Factor: x2
page 2
x2 + 16
The binomials (x 2) and (2x + 3) are the factors
of which polynomial?
A.
Express the product (2x
4)2 is equivalent to
The expression (x
x2 + 9
5)(6x + 5) as a trinomial.
24
9
5x + 6
6
Keystone Review { Algebraic Expressions
26.
Factor: b2
27.
If x 3 is a factor of x2 + x
factor is
12, then the other
A.
x
4x
3
4
B.
3x
4
C.
4
33.
What value of k makes the trinomial x2
a perfect square?
34.
If (x 3) and (x + 7) are the factors of the
trinomial x2 + ax 21, what is the value of a ?
D. x + 4
A.
28.
29.
Written in factored form, the binomial a2 b
is equivalent to
A.
ab(a
b)
B.
C.
a2 (b
b2 )
D. a2 b2 (b
32.
35.
b)(a + b)
a)
B.
12x2
C.
8x3
6xy
B.
24xy2
If a + b = 5 and a
a2 b2 .
C.
b = 3,
12xy2
4
C.
7
D. 4
Which expression is the simplest form of
25x4 y2 15x2 y
if x6=0 and y6=0?
5xy
A.
5x2 y 3
5xy
B.
C.
5x2 y
D. 5x3 y
3
5x3 y 3x
5xy
3x
D. 4x2
36.
The greatest common factor of 12x2 y3 and 24xy2
is
A.
31.
96x5
B.
ab2
The greatest common monomial factor of 12x2
and 8x3 is
A.
30.
(a
3
10x + k
D. 2xy
nd the value of
37.
x2
If x6=2, then
2x
equivalent to
4
, in simplest form, is
4
A.
x
2
page 3
B.
C.
x
2
2
1
B.
2
C.
2
x+2
2
D.
For which value of x is the expression
x
unde ned?
A.
If (2x + 3)(x 2) is written in the form ax2 + bx + c,
what is the value of c ?
x
x
2
D. 0
Keystone Review { Algebraic Expressions
38.
The expression
x is equal to
A.
C.
39.
40.
2 or
(x
5
is meaningless when
2)(x + 3)
3
2 or 3
B.
41.
p
p
If 84 is simpli ed to a b such that a and b are
integers, what is the value of a ?
42.
p p
If x > 0, the expression ( x)( 2x) is equivalent to
2
D. 0
A.
Express as a single fraction in simplest form:
a 2a
+
3
5
Express in simplest form:
2+
x
4
x
2
43.
2
page 4
2x
B.
If a > 0, then
A.
2
p
p
7a
p
B.
2x
C.
p
x2 2
p
D. x 2
9a2 + 16a2 equals
p
5 a
C.
5a
D. 7a
Acces format version 4.4.146
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_
Licensed for use by Problem-Attic
Keystone Review { Algebraic Expressions
11/01/2012
1.
Answer:
B
21.
Answer:
C
2.
Answer:
C
22.
Answer:
24x2
3.
Answer:
B
23.
Answer:
(x + 8)(x
4.
Answer:
D
5.
Answer:
24.
Answer:
(5x
C
6.
Answer:
25.
Answer:
(x
3)(x
C
7.
Answer:
26.
Answer:
(b
2)(b + 2)
18
8.
Answer:
27.
Answer:
D
A
9.
Answer:
28.
Answer:
A
4
29.
Answer:
D
30.
Answer:
C
10.
Answer:
36
11.
Answer:
3x3 + 3x2
12.
Answer:
31.
Answer:
15
4x2
13.
Answer:
32.
Answer:
6
B
14.
Answer:
33.
Answer:
25
A
15.
Answer:
34.
Answer:
D
C
16.
Answer:
35.
Answer:
D
A
17.
Answer:
36.
Answer:
D
D
18.
Answer:
2x2
37.
Answer:
B
19.
Answer:
C
38.
Answer:
A
20.
Answer:
B
39.
Answer:
11a
15
+ 2x + 1
+ 7x
15
10x
25
3)
3)(5x + 3)
2)
Teacher's Key
40.
Answer:
x
41.
Answer:
2
42.
Answer:
D
43.
Answer:
C
Page 2
Keystone Review { Equations
Name:
Date:
1.
Solve for x: 0:6x + 1:5 = 3:9
2.
Solve for x:
3.
Solve for x: 5x
4.
5.
6.
2
5x
Solve for x: 3(2
7= 3
2(x + 1) = 10.
x) = 8(x
x
1
Solve for x:
8.
Solve for x:
9.
Solve for a in terms of b and c: 3a + 4b = c
10.
Solve for r in terms of C and : C = 2 r
11.
If dx
4
=
1
2
7.
1
3
= , x6=0, x6=
x+2
x
2
2)
The solution set of the equation x2
A.
f0; 4g
B.
C.
f 4g
D. f4g
A.
4x = 0 is
2 = h, then x is equal to
h+
2
d
B.
2
h
h+2
d
D.
80
D. 100
C.
d
h
+2
d
f4; 4g
What is the solution set of the equation
x2 3x 10 = 0?
A.
(5; 2)
B.
( 5; 2)
C.
(5; 2)
D. ( 5; 2)
3x
5=5
Solve for x:
13.
p
Solve for x: 3 2x + 5
14.
p
p
If 4 5 = n, the value of n is
A.
page 1
p
12.
10
B.
20
15 = 0
C.
Acces format version 4.4.146
c 1997{2011 EducAide Software
_
Licensed for use by Problem-Attic
Keystone Review { Equations
1.
Answer:
4
2.
Answer:
10
3.
Answer:
4
4.
Answer:
2
5.
Answer:
A
6.
Answer:
A
7.
Answer:
3
8.
Answer:
1
9.
Answer:
c 4b
3
10.
Answer:
C
2
11.
Answer:
C
12.
Answer:
10
13.
Answer:
10
14.
Answer:
C
11/01/2012
Keystone Review { Relations & Functions
Name:
1.
2.
Date:
During a 45-minute lunch period, Albert (A)
went running and Bill (B) walked for exercise.
Their times and distances are shown in the
accompanying graph. How much faster was Albert
running than Bill was walking, in miles per hour?
3.
If x and y are de ned as indicated by the
accompanying table, which equation correctly
represents the relationship between x and y?
x
y
2
1
5
7
3
7
3
11
A.
y=x+2
B.
y = 2x + 2
C.
y = 2x + 3
D. y = 2x
3
page 1
Which graph represents a function?
A.
B.
C.
D.
Keystone Review { Relations & Functions
4.
Which graph does not represent a function of x?
6.
A.
7.
B.
Which relation is not a function?
y = 2x + 4
B.
C.
x = 3y
D. x = y2 + 2x
8.
3
1
B.
2
C.
0
D. 4
Which set of ordered pairs is not a function?
A.
f(3; 1); (2; 1); (1; 2); (3; 2)g
B.
f(4; 1); (5; 1); (6; 1); (7; 1)g
C.
f(1; 2); (3; 4); (4; 5); (5; 6)g
D. f(0; 0); (1; 1); (2; 2); (3; 3)g
D.
5.
2
4x + 3
Given the relation
R = f( 2; 3); (a; 4); (1; 9); (0; 7)g. Which
placement for a makes this relation a function
A.
C.
y = x2
A.
9.
If f (x) = 3
10.
If f (x) = x3
A.
Which relation is also a function?
A.
x2 + y2 = 64
B.
C.
x2
D. xy = 64
4y2 = 64
0
x2 , nd f ( 2).
3 , then f ( 1) is equivalent to
B.
2
C.
2
D. 4
x4 + 4y2 = 64
11.
page 2
If f (x) =
p
25
x2 , nd the value of f (3).
Keystone Review { Relations & Functions
12.
13.
14.
4
What is the domain of the function f (x) = p
x+1
over the set of real numbers?
A.
fx j x = 1g
B.
C.
fx j x < 1g
D. fx j x > 1g
fx j x
16.
1g
Which graph illustrates the relationship x varies
directly as y ?
A.
B.
C.
D.
In which function is the range equal to the
domain?
y = x2
A.
y = 2x
B.
C.
y = log x
D. y = x
17.
Which graph illustrates a quadratic relation whose
domain is all real numbers?
A.
Which table is an example of y varying directly
with x.
A.
B.
B.
C.
D.
C.
D.
3
5
4
5
y
x
3
4
5
x
y
5
x
3
If y varies directly as x and y = 32 when x = 4,
nd the value of y when x = 5.
page 3
4
4
7
3
6
y
9
16
25
x
3
4
5
y
15.
6
6
8
10
Acces format version 4.4.146
c 1997{2011 EducAide Software
_
Licensed for use by Problem-Attic
Keystone Review { Relations & Functions
1.
Answer:
4
2.
Answer:
D
3.
Answer:
D
4.
Answer:
A
5.
Answer:
D
6.
Answer:
D
7.
Answer:
D
8.
Answer:
A
9.
Answer:
1
10.
Answer:
D
11.
Answer:
4
12.
Answer:
D
13.
Answer:
D
14.
Answer:
C
15.
Answer:
40
16.
Answer:
B
17.
Answer:
D
11/01/2012
Keystone Review { Graphing I: Points & Lines
Name:
1.
2.
3.
Date:
Which point satis es the equation 2x + 3y = 8?
A.
(1; 4)
B.
C.
( 1; 3)
D. ( 2; 4)
(2; 2)
Which point lies on the graph of the equation
3x + y = 9?
A.
( 1; 9)
B.
C.
(1; 1)
D. (0; 9)
8.
(9; 0)
9.
If (k; 3) is a point on the graph of the equation
x + 2y = 8, what is the value of k ?
5.
If (a; 3) is a point on the graph of the equation
2x + 3y = 5, then the value of a is
1
B.
2
C.
2
10.
D. 7
What is the y-intercept of the graph of the
equation y = 14 x 23 ?
A.
2
3
B.
2
3
C.
1
4
D.
11.
1
4
page 1
(0; 8)
B.
(8; 0)
C.
(0; 4)
D. (4; 0)
The graph of the equation x + 3y = 6 intersects the
y-axis at the point whose coordinates are
A.
The equation of a line is y = mx 1. Find the
value of m if the line passes through the point
(2; 3).
A.
What are the coordinates of the point where the
graph of the equation x + 2y = 8 crosses the y-axis?
A.
4.
6.
7.
(0; 2)
B.
(0; 6)
C.
(0; 18)
D. (6; 0)
The graphs of the equations 4x y = 6 and
x + y = 4 intersect at the point whose coordinates
are
A.
(2; 2)
B.
(5; 1)
C.
(1; 3)
D. (2; 2)
At which point will the graphs of the equations
2x + y = 8 and x y = 4 intersect?
A.
(0; 4)
B.
(4; 0)
C.
( 4; 0)
D. (5; 2)
What is the slope of the line that passes through
the points (4; 5) and (7; 3)?
Keystone Review { Graphing I: Points & Lines
12.
13.
A.
1
B.
C.
zero
D. unde ned
15.
1
What is the slope of the line whose equation is
5y = 2x + 10?
A.
14.
18.
The slope of the line determined by the points
( 3; 2) and (2; 3) is
5
2
B.
2
C.
2
5
In which graph does the slope of line ` equal
zero?
A.
B.
C.
D.
D. 5
Which equation represents a line with a slope
of 2?
A.
y = 2x
C.
y=x
1
2
B.
y = 2x + 1
D. y = x + 2
19.
The slope of the graph of the equation x = 3 is
A.
1
B.
C.
3
D. unde ned
Which graph represents a line that has a negative
slope?
A.
B.
C.
D.
0
16.
Two points whose coordinates are (4; 17) and (2; a)
determine a line whose slope is 6. Find the value
of a.
17.
The line that passes through point ( 1; 4) and
point (6; y) has a slope of 75 . Find y.
page 2
Keystone Review { Graphing I: Points & Lines
20.
23.
Which is an equation for line ` in the
accompanying diagram?
The graph of which equation passes through points
(0; 6) and (4; 1) ?
A.
y = 2x + 2
A.
y = 74 x + 6
B.
y = 2x
C.
y=
C.
y = 2x
4
7
4x
B.
+6
y = 47 x + 6
D. y =
4
7x
+6
4
D. y = 2x + 2
24.
21.
The diagram shows the graph of the line m
Which phrase describes the graph of y = 1 on
the coordinate plane?
A.
a line parallel to the y-axis and 1 unit to the
right of it
B.
a line parallel to the y-axis and 1 unit to the
left of it
C.
a line parallel to the x-axis and 1 unit below
it
D. a line parallel to the x-axis and 1 unit above
it
25.
Which equation represents this line?
y = 21 x + 2
A.
y = 2x + 1
B.
C.
y = 2x + 1
D. y =
1
2x
+2
26.
22.
Which is an equation of the line that passes
through the point (5; 2) and has a slope of 3?
A.
y = 3x
13
C.
y = 3x + 13
B.
y = 3x
13
D. y = 3x + 13
Which equation is equivalent to x + 2y = 6?
A.
y= x+6
B.
y=
1
2x
6
C.
y= x+3
D. y =
1
2x
+3
A line is represented by the equation y = 3x
Which statement about the line is true?
1
3.
A.
The slope of the line is
B.
The y-intercept is
C.
Point (1; 4) lies on the line.
7.
D. This line is parallel to the line whose
equation is y = 2x 7.
page 3
7.
Keystone Review { Graphing I: Points & Lines
27.
28.
32.
The graph of which equation does not pass
through the origin?
A.
y=x
B.
y= x
C.
y=0
D. y = 1
Which statement is false about the line whose
equation is y = 2x 5?
A.
Its slope is
B.
It is parallel to the line whose equation is
y = 2x + 5.
C.
Its y-intercept is
D. It is perpendicular to the line whose equation
is y = 21 x 5.
29.
3
5
B.
1
5
C.
5
3
What is the slope of a line parallel to the line
whose equation is y = 52 x 3?
31.
Which equation represents a line parallel to the
line whose equation is y = 2x 7?
C.
y = 2x
y= 7
B.
y = 21 x
D. y =
C.
y = 3x
B.
5
y=
1
3x
5
D. y = 3x + 5
34.
Which is an equation of the line that has a
y-intercept of 2 and is parallel to the line whose
equation is 4y = 3x + 7?
A.
y = 34 x
2
B.
C.
y = 43 x
2
D. y =
y = 34 x + 2
4
3x
2
D. 5
30.
A.
y = 13 x + 5
Write an equation of the line that passes through
the point (1; 6) and is parallel to the line whose
equation is y = 3x 5.
What is the slope of a line perpendicular to the
graph of the equation 5x 3y = 2?
A.
A.
33.
2.
5.
Which is an equation of a line perpendicular to
the line whose equation is y = 13 x 5?
1
2x
7
35.
!
!
The slope of AB is 32 and the slope of CD is
x 2
!
!
. If AB k CD, nd the value of x.
6
36.
Two lines are represented by the equations
1
2 y = 6x + 10 and y = mx. For which value of m
will the lines be parallel?
A.
+7
page 4
12
B.
3
C.
3
D. 12
Acces format version 4.4.146
c 1997{2011 EducAide Software
_
Licensed for use by Problem-Attic
Keystone Review { Graphing I: Points & Lines
11/01/2012
1.
Answer:
D
20.
Answer:
B
2.
Answer:
D
21.
Answer:
A
3.
Answer:
2
22.
Answer:
C
4.
Answer:
2
23.
Answer:
C
5.
Answer:
C
24.
Answer:
C
6.
Answer:
A
25.
Answer:
D
7.
Answer:
C
26.
Answer:
B
8.
Answer:
A
27.
Answer:
D
9.
Answer:
D
28.
Answer:
B
10.
Answer:
B
29.
Answer:
A
30.
Answer:
2
5
11.
Answer:
2
3
12.
Answer:
B
31.
Answer:
A
13.
Answer:
C
32.
Answer:
C
14.
Answer:
B
33.
Answer:
y = 3x + 3
15.
Answer:
D
34.
Answer:
A
16.
Answer:
5
35.
Answer:
6
17.
Answer:
9
36.
Answer:
A
18.
Answer:
D
19.
Answer:
D
Keystone Review { Graphing II: AV & Inequalities
Name:
1.
Which point satis es the inequality 2x + y > 10?
A.
2.
3.
(2; 3)
B.
(3; 4)
C.
(3; 2)
5.
Which equation is represented by the
accompanying graph?
D. (4; 3)
The accompanying diagram shows a graph of
which inequality?
A.
y<x+1
A.
y = jxj
B.
y>x+1
C.
y = jx + 3j
C.
y
x+1
D. y
x+1
Which ordered pair is in the solution set of
y 2x + 3?
A.
4.
Date:
(1; 4)
B.
(3; 2)
C.
(0; 5)
6.
3
B.
1
y = (x
3)2 + 1
D. y = jx
3j + 1
Which equation represents the function shown in
the accompanying graph?
D. (0; 0)
The graph of which inequality is shown in the
accompanying diagram?
A.
y>2
C.
y
2
B.
x>2
D. x
2
page 1
A.
f (x) = jxj + 1
B.
f (x) = jxj
C.
f (x) = jx + 1j
D. f (x) = jx
1
1j
Keystone Review { Graphing II: AV & Inequalities
7.
The graph of y = jx + 2j is shown below.
Which graph represents y =
jx + 2j?
A.
B.
C.
page 2
Acces format version 4.4.146
c 1997{2011 EducAide Software
_
Licensed for use by Problem-Attic
Keystone Review { Graphing II: AV & Inequalities
1.
Answer:
D
2.
Answer:
B
3.
Answer:
C
4.
Answer:
A
5.
Answer:
D
6.
Answer:
A
7.
Answer:
D
11/01/2012
Keystone Review { Absolute Value & Inequalities
Name:
1.
Date:
What is the solution set of the equation
j3 2xj = 5?
A.
f 1; 4g
B.
C.
f 1g
D. f4g
4g
f1;
2.
Solve for the negative value of x: j2x
3.
Which is a graph of the solution set of
j3x + 1j = 5?
A.
B.
C.
D. 
6.
2
1
0
1
2
2
1
0
1
2
2
1
0
1
2
2
1
0
1
2
8j = 18
7.
If x is an integer, which is the solution set of
1 x < 2?
A.
f0; 1g
B.
f 1; 0; 1; 2g
C.
f0; 1; 2g
D. f 1; 0; 1g
When x is an integer, what is the solution set of
5 x < 8?
A.
f5; 6; 7; 8g
B.
f5; 6; 7g
C.
f6; 7; 8g
D. f6; 7g
!
!
8.
!
!
…
The solution set of jx
A.
fx j x > 5g
B.
fx j x < 1g
C.
fx j 1 < x < 5g
2j < 3 is
D. fx j x < 1 or x > 5g
4.
5.
The inequality 3x + 2 > x + 8 is equivalent to
A.
x>
C.
x>3
3
2
B.
x>
3
2
9.
D. x < 3
Which is the greatest integer that makes the
inequality 3 2x > 9 a true statement?
A.
2
B.
2
C.
5
D.
The solution set of j2x
A.
fx j 5
B.
fx j x
C.
fx j 3
D. fx j x
4
page 1
x
22g
8g
x
8g
3_x
8g
5j
11 is
Keystone Review { Absolute Value & Inequalities
10.
13.
What is the solution set of j4x + 8j > 16 ?
A.
fx j 6 < x < 2g
4
3
B.
fx j 2 < x < 6g
C.
fx j x < 6 or x > 2g
A.
2<x
D. fx j x < 2 or x > 6g
C.
2
14.
11.
Which inequality is represented by the
accompanying graph?
Which equation states that the temperature, t, in a
room is less than 3 from 68 ?
A.
C.
j3
t j < 68
B.
tj < 3
j68

B.
D. j68 + t j < 3
C.

D.
12.
Which graph represent the solution of the
inequality 2x + 3 > 9?
A.

B.
C.
D. 
1
1
1
1
0
0
0
0
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
15.
!

B.
!
…
C.
!
D. 
page 2
0
1
2
3
x
4
3
B.
2
x<3
D.
2<x<3
!
3
5
3
1
1
3
5
5
3
1
1
3
5
5
3
1
1
3
5
5
3
1
1
3
5
!
…
!
!
…
!
Which is the graph of the solution set of
j2x 1j < 9?
A.
!
…
1
Which graph represents the open sentence
5 x < 0?
A.
j3 + t j < 68
2
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
!
!
!
!
…
Keystone Review { Absolute Value & Inequalities
16.
Which graph represents the solution set of
j2x + 1j > 7?
A.

B.
C.
D.

5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
!
…
!
!
…
!
page 3
Acces format version 4.4.146
c 1997{2011 EducAide Software
_
Licensed for use by Problem-Attic
Keystone Review { Absolute Value & Inequalities
1.
Answer:
A
2.
Answer:
5
3.
Answer:
C
4.
Answer:
C
5.
Answer:
D
6.
Answer:
D
7.
Answer:
B
8.
Answer:
C
9.
Answer:
C
10.
Answer:
C
11.
Answer:
C
12.
Answer:
C
13.
Answer:
A
14.
Answer:
D
15.
Answer:
B
16.
Answer:
A
11/01/2012
Keystone Review { Systems of Equations
Name:
1.
Date:
Solve the following system of equations
algebraically and check:
5.
x 4y = 16
y=1 x
Which ordered pair is in the solution set of the
system of inequalities shown in the accompanying
graph?
A.
(2; 5)
B.
(2; 2)
C.
(4; 3)
D. ( 4; 3)
2.
Solve the following system of equations for x:
3x + y = 9
2x y = 6
6.
3.
The accompanying diagram represents the graphs
of the inequalities y 3 and x < 2.
Which ordered pair names a point in the solution
set of this system of inequalities?
Solve the following system of equations for x:
3x + 3y = 21
6x 3y = 6
A.
(3; 5)
B.
(3; 5)
C.
( 3; 5)
D. ( 3; 5)
4.
Which ordered pair is in the solution set of the
system of inequalities shown in the graph?
A.
(0; 0)
B.
(1; 5)
C.
( 3; 3)
7.
Which is a solution for the following system of
equations?
y = x2
y = 4x + 12
D. (3; 3)
page 1
A.
( 2; 4)
B.
(6; 36)
C.
(2; 4)
D. ( 6; 24)
Acces format version 4.4.146
c 1997{2011 EducAide Software
_
Licensed for use by Problem-Attic
Keystone Review { Systems of Equations
1.
Answer:
x = 4, y = 3
2.
Answer:
3
3.
Answer:
3
4.
Answer:
A
5.
Answer:
B
6.
Answer:
C
7.
Answer:
C
11/01/2012
Keystone Review { Word Problems & Applications
Name:
1.
2.
3.
4.
Three bags of potatoes and four cases of corn cost
$40. Five bags of potatoes and two cases of corn
cost $34. Find the cost of one bag of potatoes and
the cost of one case of corn. [Show or explain the
procedure used to obtain your answer.]
6.
If y + 1 is an even integer, what is the next
consecutive even integer?
7.
Find three consecutive even integers such that the
sum of the smallest integer and twice the second
is 12 more than the third. [Only an algebraic
solution will be accepted.]
8.
Three numbers are in the ratio 2 : 3 : 5. If the
smallest number is multiplied by 8, the result is
32 more than the sum of the second and third
numbers. Find the numbers. [Only an algebraic
solution will be accepted.]
9.
Lois is four times as old as her son Dan. The
sum of their ages is 40. How old is Dan?
10.
If 4 more than twice a number is 18,
number.
11.
Three numbers are represented by 2x, 3x, and 4x.
Find the value of x if the mean of the three
numbers is 15.
12.
The mean of three numbers is 25. The second
number is four less than twice the rst. The third
number is two more than four times the rst. Find
the smallest number.
Lois rented a car for $74.00 a week plus $0.14
for each mile the car is driven. What is the
greatest number of miles Lois can drive the car if
she wishes to spend at most $130.00? [Only an
algebraic solution will be accepted.]
A truck traveling at a constant rate of 45 miles
per hour leaves Albany. One hour later a car
traveling at a constant rate of 60 miles per hour
also leaves Albany traveling in the same direction
on the same highway. How long will it take for
the car to catch up to the truck, if both vehicles
continue in the same direction on the highway?
A girl can ski down a hill ve times as fast as
she can climb up the same hill. If she can climb
up the hill and ski down in a total of 9 minutes,
how many minutes does it take her to climb up
the hill?
A.
5.
Date:
1.8
B.
4.5
C.
7.2
D. 7.5
The sophomore class at South High School raised
$800 from the sale of tickets to a dance. Tickets
sold for $1.50 in advance and $2.00 at the door.
If a total of 475 tickets were sold, what was the
number of tickets sold at the door? [Show or
explain the procedure used to obtain your answer.]
page 1
nd the
Keystone Review { Word Problems & Applications
13.
At a school costume party, seven girls wore masks
and nine boys did not. If there were 15 boys at
the party and 20 students did not wear masks,
what was the total number of students at the
party?
A.
30
B.
33
C.
35
17.
D. 42
Larry has 7 more dimes than nickels, for a total
value of $1.45. If n represents the number of
nickels, which equation could be used to nd the
number of nickels Larry has?
A.
n + (n + 7) = 145
B.
5n + 5(n + 7) = 145
C.
5n + 10(n + 7) = 145
D. 15(n + n + 7) = 145
14.
Stan was trying to guess Melanie's age. She told
him her age was an even number and a multiple
of three. What could be Melanie's age?
A.
15.
16.
10
B.
12
C.
15
18.
Which equation could be used to solve the
problem below?
If three times a number is increased by 24,
the result is 4 less than seven times the
number.
D. 16
A.
3(x + 24) = 7x
C.
3x + 24 = 7x
4
4
B.
3x + 24 = 4
D. 27x = 7x
7x
4
Sara's telephone service costs $21 per month plus
$0.25 for each local call, and long-distance calls
are extra. Last month, Sara's bill was $36.64, and
it included $6.14 in long-distance charges. How
many local calls did she make?
19.
A painting that regularly sells for a price of $55 is
on sale for 20% o . The sales tax on the painting
is 7%. Will the nal total cost of the painting
di er depending on whether the salesperson
deducts the discount before adding the sales tax or
takes the discount after computing the sum of the
original price and the sales tax on $55?
The formula C = 95 (F 32) can be used to nd
the Celsius temperature (C) for a given Fahrenheit
temperature (F). What Celsius temperature is equal
to a Fahrenheit temperature of 77 ?
20.
On February 18, from 9 a.m. until 2 p.m., the
temperature rose from 14 F to 36 F. What was
the total increase in temperature during this time
period?
A.
8
B.
25
C.
45
D. 171
A.
page 2
50
B.
36
C.
32
D. 22
Acces format version 4.4.146
c 1997{2011 EducAide Software
_
Licensed for use by Problem-Attic
Keystone Review { Word Problems & Applications
1.
Answer:
$4/bag of potatoes; $7/case of corn
2.
Answer:
400
3.
Answer:
3 hours
4.
Answer:
D
5.
Answer:
175
6.
Answer:
y+3
7.
Answer:
6, 8, 10
8.
Answer:
8, 12, 20
9.
Answer:
8
10.
Answer:
7
11.
Answer:
5
12.
Answer:
11
13.
Answer:
B
14.
Answer:
B
15.
Answer:
38
16.
Answer:
B
17.
Answer:
C
18.
Answer:
C
19.
Answer:
No, it will not di er
20.
Answer:
A
11/01/2012
Algebra 1 Practice Keystone Exam 1. Which of the following inequalities is true for ALL real values of x? a. x 3 ! x 2 b. 3x 2 ! 2x 3 c. (2x)2 ! 3x 2 d. 3(x ! 2)2 " 3x 2 ! 2 2. An expression is shown to the right: 2 51x Which value of x makes the expression equivalent to 10 51 a. 5 b. 25 c. 50 d. 100 3. Two monomials are shown below. 450x 2 y 5
3,000x 4 y 3 What is the least common multiple (LCM) of these monomials? a. 2xy b. 30xy c. 150x 2 y 3 d. 9,000x 4 y 5 4. Simplify: 2(2 4 )!2 1
a.
8
1
b.
4
c. 16 d. 32 5. A theme park charges $52 for a day pass and $110 for a week pass. Last month, 4,432 day passes were sold and 979 week passes were sold. Which is the closest estimate of the total amount of money paid for the day and week passes for last month? a. $300,000 b. $400,000 c. $500,000 d. $600,000 6. (x + 3)(2x 2 + 5x + 2) The above expression simplifies to a. 2x 3 + 11x 2 + 17x + 6 b. 2x 2 + 6x + 5 c. 9x 2 + 21x + 6 d. 2x 3 + 5x 2 + 6 7. When the expression x 2 ! 3x ! 18 is factored completely, which is one of its factors? a. (x-­‐2) b. (x-­‐3) c. (x-­‐6) d. (x-­‐9) !3x 3 + 9x 2 + 30x
; x " !4,!2,0 8. Simplify: !3x 3 ! 18x 2 ! 24x
!1 2 5
a.
x ! x
2
4
1
5
b.
x 3 ! x 2 ! x 2
4
x+5
c.
x!4
x!5
d.
x+4
9. Jenny has a job that pays her $8 per hour plus tips (t). Jenny worked for 4 hours on Monday and made $65 in all. Which equation could be used to find t, the amount Jenny made in tips? a. 65 = 4t + 8 b. 65 = 8t ÷ 4 c. 65 = 8t + 4 d. 65 = 8(4) + t 10. One of the steps Jamie used to solve an equation shown below.
!5(3x + 7) = 10
!15x + !35 = 10
Which statements describe the procedure Jamie used in this step and identify the property that justifies the procedure? a. Jamie add -­‐5 and 3x to eliminate the parentheses. This procedure is justified by the associative property. b. Jamie added -­‐5 and 3x to eliminate the parentheses. The procedure is justified by the distributive property. c. Jamie multiplied 3x and 7 by -­‐5 to eliminate the parentheses. The procedure is justified by the associative property. d. Jamie multiplied 3x and 7 by -­‐5 to eliminate the parentheses. The procedure is justified by the distributive property. 11. Francisco purchased x hot dogs and y hamburgers at a baseball game. He spent a total of $10. The equation below describes the relationship between the number of hot dogs and the number of hamburgers purchased. 3x + 4y = 10 The ordered pair (2,1) is the solution to the equation. What does the solution represent? a. Hamburgers cost 2 times as much as hot dogs b. Francisco purchased 2 hot dogs and 1 hamburger c. Hot dogs cost $2 each and hamburgers cost $1 each d. Francisco spent $2 on a hot dogs and $1 on a hamburgers 12. Anna burned 15 calories per minute running for x minutes and 10 calories per minute hiking for y minutes. She spent a total of 60 minutes running and hiking and burned 700 calories. The system of equations shown below can be used to determine how much time Anna spent on each exercise. 15x + 10y = 700
x + y = 60
What is the value of x, in minutes Anna spent running? a. 10 b. 20 c. 30 d. 40 13. Samantha and Maria purchased flowers. Samantha purchased 5 roses for x dollars each and 4 daisies for y dollars each and spent $32 on the flowers. Maria purchased 1 rose for x dollars and 6 daisies for y dollars each and spent $22. The system of equations below represents this situation. 5x + 4y = 32
x + 6y = 22
Which statement is true? a. A rose costs $1 more than a daisy. b. Samantha spent $4 on each daisy. c. Samantha spent more on daisies than she did on roses. d. Samantha spent over 4 times as much on daisies as she did on roses. 14. A compound inequality is shown to the right. 5 < 2 ! 3y < 14 What is the solution set of the compound inequality? a. -­‐4 > y > -­‐1 b. -­‐4 < y < -­‐1 c. 1 > y > 4 d. 1 < y < 4 15. The solution set of an inequality is graphed on the number line below. "$$$$$$$$$
# !5 -4 -3 -2 -1 0 1 2
The graph shows the solution set of which inequality? a. 2x + 5 < -­‐1 b. 2x + 5 ! "1 c. 2x + 5 > -­‐1 d. 2x + 5 ! "1 16. A baseball team had $1,000 to spend on supplies. The team spent $185 on a new bat. New baseballs cost $4 each. The inequality 185 + 4b ! 1,000 can be used to determine the number of new baseballs (b) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true? a. The team can purchase 204 new baseballs. b. The minimum number of new baseballs that can be purchased is 185. c. The maximum number of new baseballs that can be purchased is 185. d. The team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum. 17. Mike always leaves a tip of between 8% and 20% for the server when he pays for his dinner. This can be represented by the system of inequalities shown below, where y is the amount of tip and x is the cost of the dinner. y > 0.08x y < 0.2x Which of the following is a true statement? a. When the cost of the dinner (x) is $10, the amount of the tip (y) must be between $2 and $8. b. When the cost of the dinner (x) is $15, the amount of the tip (y) must be between $1.20 and $3.00. c. When the cost of the tip (y) is $3, the amount of the dinner (x) must be between $11 and $23. d. When the cost of the tip (y) is $2.40, the amount of the dinner (x) must be between $3 and $6. 18. Tim’s scores for the first 5 times he played a video game are listed below. 4,526 4,599 4,672 4,745 4,818 Tim’s scores follow a pattern. Which expression can be used to determine his score after he played the video game n times? a. 73n + 4,453 b. 73(n + 4,453) c. 4,453n + 73 d. 4,526n 19. A pizza restaurant charges for pizzas and adds a delivery fee. The cost (c), in dollars, to have any number of pizzas (p) delivered to a home is described by the function c = 8p + 3. Which statement is true? a. The cost of 8 pizzas is $11 b. The cost of 3 pizzas is $14 c. Each pizza costs $8 and the delivery fee is $3 d. Each pizza costs $3 and the delivery fee is $8. 20. The table below shows values of y as a function of x. X Y 2 10 6 25 14 55 26 100 34 130 Which linear equation best describes the relationship between x and y? a. y = 2.5x + 5 b. y = 3.75x + 2.5 c. y = 4x + 1 d. y = 5x 21. Jeff’s restaurant sells hamburgers. The amount charged for a hamburger (h) is based on the cost for a plain hamburger plus an additional charge for each topping (t) as shown in the equation below. H = 0.06t + 5 What does the number 0.06 represent in the equation? a. the number of toppings b. the cost of a plain hamburger c. the additional cost of each topping d. the cost of a hamburger with 1 topping 2
22. A ball rolls down a ramp with a slope of . At one point the ball is 10 feet 3
high, and at another point the ball is 4 feet high, as shown in the diagram below. What is the horizontal distance (x), in feet, the ball traveled as it rolled down the ramp from 10 feet high to 4 feet high? a. 6 b. 9 c. 14 d. 15 23. A juice machine dispenses the same amount of juice into a cup each time the machine is used. The equation below describes the relationship between the number of cups (x) into which juice is dispensed and the gallons of juice (y) remaining in the machine. x + 12y = 180 How many gallons of juice are in the machine when it is full? a. 12 b. 15 c. 168 d. 180 24) 25) 26) 27) 28) 29) 30) 31) 32)