Download Algebra I Midterm Review 2010-2011

Algebra IA Midterm Review 2016-2017
Real Numbers – Classifying (Natural, Whole, Integer, Rational, Real, Irrational)
N – Natural
W – Whole
Z – Integer Q – Rational
R – Real
I – Irrational
1. Give one example of an Irrational Number:________________
2. Real Numbers can be classified as ________________ or ______________.
3. If a number is a Whole number, it will always be a:
a) N, Z, Q, R
b) Z, Q, R
c) N, Z, Q, R, I d) Z, I, R
Identify all number system(s) to which each of the following numbers belongs.
4. 52
5. 22.3
7. 4
8. 
6.
16
10
2
9. Graph the following numbers in order from least to greatest on the provided real number line.
7
2.5, -2, 4, - , -1.5
2
Simplify the following square roots.
1.
144
2.  289
4.
98
5.
150
3.
100
49
6.
972
7.
24  48
8.
75  128
9.
363  20
10. Identify which value of x will make the following two expressions equivalent.
6 13x  18 13
Operations with Integers
Find each sum or difference.
1. (22)  (9)
2. (13)  8
3. (41)  12
5. (7)  (5)
6. 12  (6)
Find each product or quotient.
4. (20)  (4)
7. The outside temperature was 15 at noon and 4 at midnight. By how much did the
temperature decrease?
8. Fabio rode his scooter 2.5 miles to his friend’s house, then 1 mile to the video store, then 3
miles to the video store. If Fabio rode the same route back home, how far did he travel in all?
9. Donna makes $8 per hour working at her after school job. She typically works 15 hours per
week. Donna pays $25 in taxes each week, and also likes to go to the movies twice a week.
Movie tickets are $10 per movie. How much does Donna still have available to put into her
savings?
Operations with Rational Numbers (Hint: Your calculator is your friend!)
Add, Subtract, Multiply, or Divide the following fractions. Show ALL work. Simplify final
answers when possible. Good luck!
1 5

2 2
10.
5 2

7 3
11.
2 4

3 5
12.
1 2 5
 
2 3 8
13.
2 3

5 8
14.
1 4 3
 
2 3 4
9.
 1 7
 2 3
15.      
Writing Algebraic Expressions
Write an Algebraic Expression for the following verbal expressions.
1. A number w more than twice a number c.
2. Five less than the product of ten and x.
3. One fourth of the area a.
4. Jocelyn makes x dollars per hour working at the grocery store and n dollars per house
babysitting. Write an expression that describes her earnings if she babysat for 20 hours and
works for 32 hours.
Order of Operations (P E M/D A/S)
Evaluate/Simplify the following expressions using your order of operations.
1. (7) 2
2. 10 2
4. 5 10  (5  2)3   3
5.
7. 7
(5)2  2  8
10  32
(
-2
3. 16  (9  5)  32
8. 8 - 4 × 32
)
6 3  5  2 12  4
0
9. Below is an order of operations problem that has been simplified incorrectly. Find and identify
the mistake and correct the problem.
3
43 ¸ 2 × 4 éë5 - 6 ( 2 ) ùû +1
64 ¸ 2 × 4 éë5 - 6 (8)ùû +1
64 ¸ 8 [ 5 - 48] +1
8 [ -43] +1
-344 +1
-333
Evaluating Algebraic Expressions
Evaluate the following expressions given that a  3, b  5, c  2 .
1.
a 2  bc
b  ac
2.
1
(b  c)  4a 2
2
2
 bc 
3. 
 b
ac
4. 3 6a 2 b + c
Properties of Real Numbers
Identify the property being illustrated as commutative, associative, identity, inverse or
distributive.
1. 5+ (3x + 2) +10 = 5+ 3x + (2+10)
3. 7×
2.
1
=1
7
5 2  3 25  3

12
12
4. 12x 2 ×1=12x 2
Identify the additive inverse, multiplicative inverse, additive identity, and multiplicative
identity for each of the following.
4.
1
2
Additive Inverse:________ Multiplicative Inverse:________
Additive Identity:________Multiplicative Identity:_________
Simplify the following Algebraic Expressions by combining like terms.
1. 2x  5  3x
2. 8xy + 2x + 6yx
3. m 2 n  2mn  5n 2 m  7nm  3
The Distributive Property
Simplify the following Algebraic Expressions by using the Distributive Property and
combining like terms.
3. 5( x 2  3x  4)
1. 5(2 x  3)  10
2. ( x  1)(2 x  3)
4. (3m)(m  4)(2m  1)
5. 4 x 2  1 2 x  3


6. (x - 4)(x +1)(5x - 2)
7. Find m if the polynomial expression (mx  1)( 2 x  4) simplifies to 30 x 2  58 x  4 .
a) m  30
b) m  15
c) m  28
d) m  60


 

8. Find m if the polynomial expression 5x 2  m 3x 2  4  24 x 2  32 simplifies to 15 x 4  20 x 2
a) m  8
b) m  5
c) m  2
d) m  32
9.Jillian is creating a painting on a rectangular canvas with a height that is 5 inches longer than
the height.
a) Write a polynomial expression in simplified form that represents the area of the
canvas.
b) Jillian now decides to add a 2 inch wide from around all sides of the rectangular
canvas. Write a polynomial expression in simplified form that represents the area of
the rectangular canvas with the frame.
Simplify the following expressions involving Absolute Value:
1. 6  2
2. 5 2  32

3. 2 4 2

3
Relations and Functions
1. Given the relation: {(3, -6), (2, -2), (-1, 0), (1,-2), (-3,,4), (2,0)}, complete each of the following:
a)
Create a mapping diagram for the relation.
b) Is this relation a function? Explain why or why not.
c)
What is the domain of this relation?
d) What is the range of this relation
2. Graph the relation on the following coordinate plane.
{(3, -6), (2, -2), (-1, 0), (1,-2), (-3,,4), (2,0)},
3. Use the below mapping diagram to answer the following questions.
2
3
0
-3
4
-1
5
a) Is the above relation a function? Explain why or why not.
b) Identify the domain:
c) Identify the range:
d) List the ordered pairs represented in the above mapping diagram
4. In order for the graph of a relation to be a function, it must pass the ____ test.
a) Horizontal Line Test
b) Vertical Line Test
c) Origin Test
d) Slope Test
Directions 5-10. Determine, yes or no, whether the below tables, graphs & mapping
diagrams represent functions.
5.
6.
7.
8.
9.
10.
11. Circle all graphs that represent a function.
Function Notation
Refer to the functions below to answer all questions:
f ( x)  x  3
g ( x)  2 x  4
h( x)  x 2  3x
a) f (4)
b) g(-3)
c) h(5)
d) g(3b)
e) h(m + 2)
f) f (5a)
g) g(10) - 5
h) f (2) - h(4)