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WorksheetsExam Review - Foundations of Math 1
Total questions: 175
Worksheet time: 10hrs 53mins
4( x + 2) = 16
What is the solution to the equation?
-2
0
1
2
The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?
15x + 2.5 = 10x + 3
15 + 2.5x = 10 + 3x
15 - 2.5x = 10
15 - 10 = 2.5x + 3x
Given ax−b=c, solve for x.
x = ac+b
x = ac−b
x = ca+b
x = bc+a
Given V=lwh, solve for l.
l=hVw
l=whV
l=wVh
l=Vwh
V=πr2h solve for π
π=Vr2h
π=Vr2h
π=Vhr2
π=r2hV
Solve for x.
4x−5=3
x = -2
x = 8
x = 32
x = 24
Solve for x
4x+6=30
(a)
Solve for g
7g+4=10+5g
g = 1
g = 6
g = 2
g = 3
Solve for m.
4(m+5)=2(m+12)
m = 2
m = 8
m = 14
m = -10
Solve for m.
6(m−2)=18
m = 6
m = 5
m = 14
m = -10
Solve for v.
6v+8v+20=118
v = 7
v = 98
v = 20
v = 0
Solve for y
4y+3(4−y)=17
y = 5
y = 10
y = 15
y = 20
Solve the proportion.
q=2
q=9
q=9/2
q=2/9
x= 28/3
x = 3/28
x = 7/3
None of the above
What is the solution to this equation?
None of These
No Solution
All Real Numbers
Solve:
3x + 15 = 3(x + 5)
No Solution
x = 15
All Real Numbers
4(1-x)+3x=-2(x+1)
4(3r+4)=−8(2r+5)
r=−6
r=−2
Infinitely Many Solutions
No Solution
Solve for w:
52w+6=8w=17
w=40
w=27
w=−23
(solve for x)
5a + 2b - 3a + 4
-9(14p - 8) - 4p
Solve . |-12| + 8 - 20
-24
1
24
0
1
4
144
288
36 - [1 + (7 x 2)] - (3 + 1)
4
12
17
21
5x0=0
Mult. Prop. of 0
Multiplicative inverse
Multiplicative Identity
Substitution
5x1=5
Multiplicative identity
Multiplicative inverse
Mult. Prop. of 0
Substitution
2+0=2
Additive identity
additive inverse
substitution
distributative
a+(-a)=0
Additive inverse
additive identity
substitution
distributive
5+7=5+7
Reflexive
symmetric
transitive
substitution
if a=b, then b=a
symmetric
reflexive
transitive
substitution
if a(b+c)=ab+ac, then ab+ac=a(b+c)
distributive
substitution
Associative
communitive
Commutative Property
Associative Property
Choose the property: 3 • (4 • 5) = (3 • 4) • 5
Associative
Commutative
Distributive
Identify this property.
If j = k, then k = j.
Addition Property of Equality
9(−3)=−3(9)
Associative Property of Addition
Commutative Property of Addition
Associative Property of Multiplication
Commutative Property of Multiplication
74⋅47=1
Multiplicative Inverse Property
Additive Inverse Property
Multiplicative Identity Property
Additive Identity Property
11+(−11)=0
Additive Identity Property
Additive Inverse Property
Associative Property of Addition
Multiplication Property of Zero
8⋅1=8
Multiplicative Identity Property
Multiplicative Property of Zero
Multiplicative Inverse Property
Additive Identity Property
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.
2 times the difference of t and 11
Which expression represents this situation after x number of months?
Turn x+5 into words
the difference of x and 5.
the sum of x and 5.
the quotient of 5 and x.
the product of x and 5.
Turn x/2 into words.
the product of x and 2.
the difference of x and 2.
2 less than x.
the quotient of x and 2.
Turn m-10 into words.
the product of m and 10.
the sum of m and 10.
the difference of m and 10.
10 more than m.
Turn the 3(x+2) into words.
the product of 3 and the sum of x and 2.
the sum of x and 2.
the product of 3 and 2x.
the quotient of 3 and the sum of x and 2.
Turn 6/x into words.
the quotient of 6 and x.
the quotient of x and 6.
the sum of 6 and x.
the difference of 6 and x.
Turn 12x-4 into words.
4 less than the product of 12 and x.
4 more than product of 12 and x.
the quotient of 12x and 4.
the difference of 4.
Which matches the equation below?
3x −11 = 17
Eleven less than the product of a number and three equals seventeen.
Three times a number, increased by seventeen is eleven.
Seventeen less than the product of three and a number is eleven.
half a number x plus 4
The sum of three times a number and ten is equal to eight times the number.
Solve for a.
a = pw
a = wp
a = pw
a = w+p
b=h2A
b=h2
b=2Ah
b=2Ah
a - b - c = 9 , for a
p = 2l + 2w
solve for w
w=2lp−2
w=2p−2l
w=2p+2l
w=2p−l
Function
Not a Function
List the ordered pairs
(1,3), (2,6), (3,9), (4,12)
(3,1), (6,2), (9,3), (12,4)
Input and Output
Output and Input
Is the relation a function?
Yes, each input has one output
No, each input has more than one output
No, the cost of the movies is different
Yes, each output has one input
Evaluate r(3)
r(3) = 16
r(3) = 12
r(3) = 13
r(3) = 0
f(-2) = -1
f(-2) = -9
f(-2) = 9
f(-2) = 0
If I know that f(2) = 4, what is another way I can write my answer?
2,4
(2, 4)
That is the only way to write it.
4x - 7, find g(-9).
Given g(x) = 4x - 7 and g(x) = 13, find x.
x = 5
g(-9) = -43
x = 5/4
The set of all x-values used to graph a function are called the ____.
Domain
Range
Relation
Function
what is f(-1)?
What is the value of f(-5)?
-2
2
4
0
Suppose f(x) = x2 - 8. Evaluate f(2) - f(3).
-7
5
-1
-5
If f(x)=21(x+5)−3 , find f(−9) .
4
−5
−10
8
Given:
h(x)=4−2x2Find:
h(−3)
-14
14
-16
16
Given:
h(x)=−x2+3xFind:
h(5)
-10
40
10
-40
Given:
Find:
f(−1)
20
-20
-25
-1
R: {0, 1, 2, -4}
R:{-4, -3, 1}
R:{1, -3, -4}
R: {1, -3, -4, 1}
Which of these sets is the RANGE of the graph?
{0, 6, 12, 18}
{-2, 0, 2, 4}
{-2, 2, 4}
{6, 12, 18}
Which number is not an element of the domain?
2
1
0
6
What is the domain of this graph?
{-2 ≤ x ≤ 4}
{-5 ≤ x ≤ 4}
{-4, 0, -2}
{-4 ≤ x ≤ 2}
What is the domain of this graph?
All Real Numbers
x ≥ -2
x < 6
-2 < x < 6
x ≤ -2
Parabolas go up forever. What is the range?
y ≥ -2
y ≥ 0
y < 5
y < 2
y > 0
What is the range of this graph?
y < 3
y > -3
y ≥ 0
All Real Numbers
The (a) of this graph is {1,3,4,5,6}
R: {0, 1, 2, -4}
R:{1, -3, -4}
R:{1, -3, -4}
What is the DOMAIN of this graph?
NOTE* that is an OPEN circle.
x < -3
x ≤ -3
x > -3
x ≥ -3
What is the Domain?
y ≥ 6
All real numbers
-10 ≤ y ≤ 6
-10 ≤ x ≤ 6
What is/are the x-intercept(s)?
(3 , 0)
(0 , 3)
(6 , 0)
(0 , 6)
What is/are the y-intercept(s)?
(3 , 0)
(0 , 3)
(6 , 0)
(0 , 6)
Which value(s) are the x-intercept(s)?
(-3 , 0)
(0 , -15)
(1 , -16)
(5 , 0)
Which intervals represent the positive portions of the graph?
-3 < x < 5
x > 0
x < -3 and x > 5
x < 0
Which intervals represent the negative portion of the graph?
-3 < x < 5
x > 0
x < -3 and x > 5
x < 0
-1<x<4
-1<x<6
Identify the function's x- and y-intercepts.
x-int (-2,0), (1,0), and (3,0) and y-int (3,0)
x-int (-2,0), (1,0), and (3,0) and y-int (0,3)
x-int (0,-2), (0,1), and (0,3) and y-int (0,3)
x-int (0,-2), (0,1), and (0,3) and y-int (3,0)
What are the x-intercepts of this function?
0 and 2
-4 and 0
2 and 3
0 and 4
Where is the function positive?
0<x<4
at the vertex (2,4)
y≤4
−∞<x<∞
Which story matches the graph?
The population size grows somewhat fast at first, and then the rate of growth slows.
The population size grows at a constant linear rate for some time, then decreases at a constant linear rate for a while, and then increases at a constant linear rate slower than the original rate of increase.
The population starts out at 0 and grows at a constant rate.
The population size grows at a constant rate for some time, then doesn’t change for a while, and then grows at a constant rate once again.
Natasha rides her bicycle to school. She rides slowly uphill for 5 minutes when she first leaves her house, then speeds up and rides at a consistent speed on flat road for 15 minutes. The last 7 minutes of her ride, she goes faster and faster, flies downhill until she arrives at school. Which graph shows the relationship between Natasha’s speed on her bicycle and time?
What is the total distance covered by 2 pm?
40 miles
30 miles
60 miles
10 miles
Which of the relations below is a function?
{(2, 3), (3, 4), (5, 1), (2, 4)}
{(2, 3), (3, 4), (6, 2), (7, 3)}
{(2, 3), ( 3, 4), (6, 2), (3, 3)}
Is the relation depicted in the table below a function?
Yes
No
Cannot be determined from a table
The graph of a relation is shown below. Is the relation a function?
Yes
No
Cannot be determined from a graph
Which graph represents a function?
What is the DOMAIN?
(scale goes by 1)
0 ≤ x < 3
0 < x ≤ 3
-2 ≤ x ≤ 1
-2 ≤ y ≤ 1
Joe is losing an average of .5 pounds a week.
Discrete
Continuous
Discrete or continuous data?
Discrete
Continuous
Discrete or continuous data?
Discrete
Continuous
Discrete
Continuous
Discrete
Continuous
Discrete
Continuous
Is this function linear or nonlinear?
Linear function because the rate of change is constant.
Linear function because the rate of change is NOT constant.
Nonlinear function because the rate of change is constant.
Nonlinear function because the rate of change is NOT constant.
Does the table represent a linear or nonlinear function? Explain.
Linear function because the rate of change is constant.
Linear function because the rate of change is NOT constant.
Nonlinear function because the rate of change is constant.
Nonlinear function because the rate of change is NOT constant.
Is this function linear or nonlinear?
Linear function
Nonlinear function
Does the equation represent a linear or nonlinear equation?
Linear
Nonlinear
Is the equation linear or nonlinear?
Linear
Nonlinear
Does the equation represent a linear or nonlinear equation?
Linear
Nonlinear
This is hard...
Does this graph represent a linear or nonlinear relationship?
Linear
Nonlinear
Does this graph represent a linear or nonlinear relationship?
Linear
Nonlinear
Does this graph represent a linear or nonlinear relationship?
Linear
Nonlinear
Which of the following are nonlinear?
Is the function y=x28 linear or nonlinear?
Linear
Nonlinear
Is the function 2x+3y=7 linear or nonlinear?
Linear
Nonlinear
Does this equation represent a LINEAR or NONLINEAR function?
linear
nonlinear
Is this function linear or nonlinear?
Linear function
Nonlinear function
