Name: ______________________________ Date: _________________________

Algebra I Midterm Review Packet: 2016-2017 Topics

***Remember: This review packet only provides SAMPLE questions for each Unit. You CANNOT study this review packet alone. It will give you an idea of which topics you may need to study more than others. You MUST look over all notes, homeworks, quizzes and tests to be prepared for the Midterm Examination.***

Unit 1: □ Translating Algebraic Expressions □ Properties of Numbers □ Linear Equations □ Literal Equations

Unit 2:

□ Perimeter and Area Word Problems □ Consecutive Integer Word Problems □ Age Word Problems

Unit 3:

□ Interval Notation □ Linear Inequalities □ Compound Inequalities

Unit 4:

□ Adding/Subtracting Monomials □ Multiplying Monomials □ Dividing Monomials □ Adding/Subtracting Polynomials □ Multiplying Polynomials □ Dividing Polynomials □ Zero/Negative Exponents

Unit 5:

□ Factoring - GCF

□ Factoring - DOTS

□ Factoring – Trinomials (a = 1) □ Factoring – Grouping

□ Factoring Completely

Unit 6: □ Relations and Functions □ Domain and Range □ Evaluating Functions □ Composition of Functions

Unit 7:

□ x and y intercepts □ Rate of Change/Slope □ Vertical and Horizontal Lines □ Writing the Equation of a Line

-“Slope-Intercept” -“Point-Slope”

□ Parallel and Perpendicular Lines □ Graphing Linear Functions □ Applications involving Linear Functions □ Piecewise Functions – Evaluate □ Piecewise Functions - Applications

Unit 8:

□ Systems of Equations – Graphically

□ Systems of Equations Applications

UNIT 1:

1) Solve for x:

2 3x 5 4x 18

2) Solve for x:

2

5x 1

5x 8 14

3) Solve for x:

axm 2m10

4) Solve for r:

21

3V r h

5) Translate the following: a) 16 more than a number is three less than twice that number b) The product of 3 and a number is five times that number decreased by 12

6) The following equations are an example of which property?

a) b) xy yx

c) 1

1aa

UNIT 2: (Use a single variable, x…not a system using 2 variables)

UNIT 3:

1) Convert the following from interval notation to inequality notation:

a) ,5

b) [ 3,8)

2) Solve and graph your solution on a number line:

3x5x 7 31

1. The perimeter of a rectangle is 52 feet. The length of the rectangle is 10 feet longer than the width. Find the dimensions of the rectangle.

2. Find four consecutive odd integers such that the sum of the first three exceeds the fourth by 18

3. Carmen is 12 years older than David. Five years

ago the sum of their ages was 28. How old are they

now?

4. The sum of the ages of John and Mary is 32. Four

years ago, John was twice as old as Mary. Find the

present age of each.

3) Solve and graph your solution on a number line:

10 2x 4 16

4) Solve and graph your solution on a number line:

3x 7 8 or 5x 317

Unit 4:

Simplify:

1) 2x 3y 5x10y 2) 3x5y2 2x3y 3) 2x4 5

4) 30x10y4

5x2y4

5) Write the expression with a positive exponent. Then simplify if possible.

a) 31 b) x4 c) 5

2x

d) 2 5 63x y z

6) Evaluate: 3x0 5x 0

Simplify:

7) 2x2 5x 8 3x2 7x 6 8) 5x2 3x 1 2x2 4x 9

9) 2x 4 3x 1 10)

8 5

4

24 6

6

x x

x

11) 2 6 32 5 xx x 12)

4 2 2 2

2

8 1812 3

3

y x yx xy

xy

13) If the area of a rectangle is represented by 4x2 12x 9 and its width by 2x 3, determine its length. What can you then conclude about this specific rectangle?

14) Write in standard form. 2

3 2 2 1x x

Unit 5: Factor Completely:

1) 4x2 12x 2) 3a2bc3 6ab2c2

3) x2 81 4) 64 y2

5) 2 2121

3625x y 6) a4 b4

7) x2 8x12 8) x2 8x15

9) 23 15 42x x 10) 232 12 54x x x

11) 24 6 7x x 12) 24 6 8x x

13) 212 28 3 7x x x

13)

14) 6x2 11x10

Unit 6:

1) If 2 3

,6 5

xf x

x

then evaluate

1

2f

.

2) If function B consists of {(3,7), (5,9), (7, 11), (x, 13)}, which value of x could be added to the set B while keeping it a function?

(1) 9 (3) 3 (2) 7 (4) 5

3) Which of the following represent a function?

4) If 2 3f x x x and 4g x x , evaluate

a) ( 3)f b) 1f g

c) f g x

Unit 7: 1) Find the x and y intercepts of the linear function

3x 4y 12

2) Find the rate of change (slope) of the line that

passes through the points 3,6 and 1,7

3) Write the equation of the line that has a slope of 3

4 and passes through the point 8,2 .

i) Point-Slope Form: ii) Slope-Intercept Form:

4) Graph the linear function 3y 2x 12

5) On the same graph, graph 2

2 43

y x

6) Is 3

4,2

a solution to 3y 2x 12 ? Explain.

5) Evaluate:

f x 3x 4, x 1

5x 2, x 1

a) f 2 b) f 1 c) f 3

6) Given the piecewise functions, evaluate:

7) Sketch the graph of the piecewise function:

f x 2x 1, x 1

3x 2, x 1

7) A garage charges the following rates for parking (with a 6 hour limit):

$4 per hour for the first 4 hours

No additional charge for the next 2 hours Graph the function that represents the scenario above. Include labels to show what the axes represent and scales for the axes.

8) The function f (x) is shown in the table at the right. a) Does f(x) have a constant rate of change? Explain. b) Determine the rate of change from x = 0 to x = 1. c) Determine the rate of change from x = 1 to x = 2. d) Determine the rate of change from x = 2 to x = 3. e) Find the average rate of change over the interval 1 < x < 3.

Unit 8:

1) Solve the following system graphically:

2y 4x 4

y 3x 1

2) Rowan has $50 in a savings jar and is putting in $5 every week. Jonah has $10 in his own jar and is putting in $15 every week. a) Write linear functions representing the amount of money in the jars for each boy as a function of w, number of weeks. b) Algebraically, determine the number of weeks it takes for the boys to have the same amount of money in their jars.

3) The sophomores at Siloam are raising money by selling T-shirts and baseball caps. The total number of items sold was 63. The profit they received for each T-shirt sold was $5.00, and the profit on each cap was $2.50. If the students made a total profit of $210, how many T-shirts and how many caps were sold? (Solve graphically using a calculator.)

4) The cost of a pack of chewing gum in a vending machine is $0.75. The cost of a bottle of juice in the same machine is $1.25. Julia has $22.00 to spend on chewing gum and bottles of juice for her team and she must buy seven packs of chewing gum. If b represents the number of bottles of juice, write an inequality that represents the maximum number of bottles she can buy. Then solve this inequality.