Algebra 1 Midterm Study Guide & Review Packet 2015
ALGEBRA 1 MIDTERM STUDY GUIDE
Chapter 1- Foundations for Algebra
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Evaluating Expressions
Translating expressions ex. “3 times the sum of x and 25.”  3(x+25)
Simplifying square roots and determining which whole numbers a non-perfect square will fall
between
o Example: √11 falls between 32 = 9 and 42 = 16
Distributive Property
Real Number system – classify and compare on a number line
o
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Natural numbers, whole numbers, integers, rational numbers, irrational numbers, real
numbers
Algebraic Properties - Commutative, Associative, Distributive, Inverse, Identity, Reflective,
Transitive, Closure, Zero product
Chapter 2 – Solving Equations
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Solving one-variable equations
o 5(𝑥 − 10) = 2(𝑥 + 3)
o Distribute, combine like terms, balance the equation, solve for the given variable
Solving proportions
o

4
=
𝑥−5
2
Percents
o

𝑥+2
𝑃𝑎𝑟𝑡
𝑊ℎ𝑜𝑙𝑒
𝑥
𝑖𝑠
𝑥
= 100 or 𝑜𝑓 = 100
o Use the previous equation when solving questions like: 45 is 15% of what number?
Percent Change – increase and decrease
Applying equations to model real-world scenarios
o Example: Perimeter problems, Money problems
Chapter 3 – Solving Inequalities
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Solving Inequalities and graphing the solution on a number line
Solving Compound Inequalities and graphing the solution on a number line
Working with Sets – Roster form, Set-Builder Notation
Union and Intersection of Sets
Solving Absolute Value Equations and Inequalities (know the rules!)
Chapter 4 - Functions
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Analyzing a Graph – tell a story
Algebra 1 Midterm Study Guide & Review Packet 2015
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Function Rules – Domain (input) and Range(output)
Functions can be represented in tables, graphs, equations, words, mapping diagrams
Function – only one output for every input
Write and Graph function rules
Chapter 5 – Linear Functions
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Calculate slope (steepness of a line) of a line using rise and run on a graph and the formula
o 𝑚=
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𝑦2−𝑦1
𝑥2−𝑥1
Horizontal and Vertical lines
o Horizontal line: y = # (slope = 0 b/c no rise)
o Vertical line: x = # (slope is undefined b/c no run – can’t divide by 0!)
o Horizontal and Vertical lines are perpendicular, meaning the slopes are OPPOSITE
RECIPROCALS!
Slope-Intercept Form - 𝑦 = 𝑚𝑥 + 𝑏 (10 second graph!)
Standard Form – Ax + By = C Find x- and y-intercepts to graph line
o To solve for the x-intercept, plug in zero to the equation for y, and solve for x
o To solve for the y-intercept, plug in zero to the equation for x, and solve for y
Point-Slope Form – 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1) You need a POINT (x1, y1) and a SLOPE (m) – just
plug in!
Convert between all 3 Forms (Slope-Intercept, Standard, and Point-Slope)
Direct Variations
o 𝑦 = 𝑘𝑥, 𝑤ℎ𝑒𝑟𝑒 𝑘 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒!
o Line passes through the origin, b=0
Parallel and Perpendicular lines
o Parallel Lines have the same slope
o Perpendicular lines have the opposite reciprocal slope (flip & change the sign)
Chapter 6 – Systems of Equations
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Solve a System of Equations by Graphing
Solve a System of Equations using Substitution (algebra)
Solve a System of Equations using Elimination (algebra)
3 types of systems
o Independent – solution is a point (x,y) where they intersect
o Dependent – solution is ALL or INFINITE points – same line!
o Inconsistent – NO solution – lines are parallel so no points in common
Review all notes, tests and quizzes from MP1 & MP2. Complete the study
guide problems that follow…
Happy Studying!
Algebra 1 Midterm Study Guide & Review Packet 2015
Part 1: Multiple Choice
Identify the choice that best complete the statement or answers the question.
q8
1. Which of the following value of q makes the equation
 3 true?
q4
a. 3
b. 8
c. 10
d. -5
2. Evaluate the expression: 7   9  6 2  (5 10)
a. -43
b. -33
c. 52
d. 42
3. Write an equation to model the sentence: “Double the sum of 8 and the number p is 12”
a. 16 p  12
b. 2( p  8)  12
c. 2(8 + p) = 12
d. 2(8  p)  12
4. Which of the following square roots falls between 4 and 5?
a.
2
b. 17
c.
27
d. 15
5. Evaluate the expression:
a.
b.
c.
d.
29−23[(62 +82 )÷100]
9−4×2
3
4
5
6
6. Which of these values for k makes the expression k 3  5k 2 1 the least?
a. -1
b. -5
c. 5
d. 1
Algebra 1 Midterm Study Guide & Review Packet 2015
7. Write an inequality to model the expression: “Half the product of 7 and a number w is at most 15.”
7w
 15
a.
2
7w
 15
b.
2
7w
c.
 15
2
7w
 15
d.
2
8. When r is -6, find the value of
r  2r  3r  4r
r
a. -54
1
b. 5
6
c. -6
d. 10
9. Evaluate:  0
a. No Solution
b. 0
c. All Real numbers
d. -0
10. Which verbal expression models 8  3(x  5)
a. 8 more than triple the difference of a number x and 5.
b. 8 more than triple the quotient of a number x less than 5.
c. 8 more than triple the difference of 5 and a number x.
d. 8 more than triple the product of 5 more than a number x.
11. Which of the following equations represents the Commutative Property of Multiplication?
a. 3x  2   3x  6
b. 3 x  x  3
c. 3x  x(3)
d. 3( x * 2)  (3 x) * 2
12. Which expression is equivalent to 3  x ?
a. x  3
b. x  3
c. x  3
d. x  3
Algebra 1 Midterm Study Guide & Review Packet 2015
1
13. To which subset of the real numbers does
belong?
6
a. Irrational
b. Rational
c. Integer
d. Whole
14. You can tell that . 5 is a rational number because it what?
a. Non-repeating decimal
b. Non-terminating decimal
c. Repeating decimal
d. Non-repeating and a non-terminating decimal
15. Which of the following number sets does 0 NOT belong too?
a. Natural
b. Whole
c. Integers
d. Rational
16. Which of the following numbers is not irrational?
a.  5
b.
63
c.
81
d. 0.1010010001000010...
17. What property is illustrated by the equation 5  (6  (6))  5 ?
a. Additive Inverse Property
b. Associative property of Addition
c. Transitive Property
d. Multiplicative Inverse Property
5
(12x  30)
6
10x  30
10x  25
12x  25
10  25x
18. Simplify
a.
b.
c.
d.
19. When is the statement, “Every integer greater then and equal to zero is a whole number” true?
a. Always
b. Sometimes
c. Never
Algebra 1 Midterm Study Guide & Review Packet 2015
20. Solve the equation: 3x  17  15  6x  2
a. 2
b. 0
c. No Solution
d. All Real Numbers
21. Which of these equations solution is All Real Numbers?
a. 3x  4  7
b. 6x  8  .5(12x  16)
c. 5x  6  6  5x
d. x  12
22. Which of these sequences can you use to solve the equation 5(t  4)  65 ?
a. Distribute the 5 and then subtract 4
b. Subtract 4 and then distribute the 5
c. Add 4 and then divide by 5
d. Divide by 5 and then add 4
23. Solve the equation: 6(8x 12)  x  (3 x)
a. 1.5
b. 75
c. -17
d. -3.5
24. 112% of what is 320?
a. 432
b. 358.4
c. 285.7
d. 35
25. Solve the proportion:
a.
b.
c.
d.
4
2

(x  6) x
-2
3
2
0
26. The temperature at 3 P.M. was 40F and the temperature at 8 P.M. was 12F . What is the percent
of change of the temperature from 3 P.M. to 8 P.M.?
a. 233% Increase
b. 70% Decrease
c. 233% Decrease
d. 70% Increase
Algebra 1 Midterm Study Guide & Review Packet 2015
27. Carl wants to purchase a $127 watch. New Jersey has a 7% sales tax. If Carl has $135, will he be able
to afford the watch?
a. Yes
b. No
28. The perimeter of the rectangle is 68units. What is the value of x?
a.
b.
c.
d.
6.4
13.2
4.9
8
3x  2
2x
29. What is the solution of 4x  y  w when you solve for y?
a. w  4x
b. w  4x
w
c.
4x
d. w  4x
30. Find the slope of the line that contains the points (8, -2) and (-1,7)
a. 1
b. -1
c. 1.2
d. -1.2
31. Identify the range of the function f(x) = 10 – 2x given the domain {-2,5}
a. {6,0}
b. {-2,5}
c. {-14,0}
d. {14,0}
32. Identify the range of the relation: {(0,3), (6,0), (5,-12), (5,0)}
a.
b.
c.
d.
{3,5,-12}
{3,-12,6}
{3,-12,0}
{3,-12}
Algebra 1 Midterm Study Guide & Review Packet 2015
33. What is the slope of the graph to the right?
a.
b.
c.
d.
Undefined
0
-2
4
34. Which of the following is a point on the linear function y 
a.
b.
c.
d.
2
x 7?
3
(3,5)
(3,-5)
(-5,3)
(-5,-3)
35. Write the equation 4x  2y  100 in slope intercept form.
a. y  2x 100
b. y  2x  25
c. y  2x  50
d. 2x  y  50
36. Which of the following is modeled by the direct variation equation y  3x ?
a. As x increases, y decreases
b. As x decreases, y increases
c. As y increases, x decreases
d. As x decreases, y decreases
37. Which form of linear equations is y  3  4(x  3) written in?
a. Slope Intercept Form
b. Point Slope Form
c. Standard Form
d. None of the above
38. Which form of linear equations is 3x  5y  12 written in?
a. Slope Intercept Form
b. Point Slope Form
c. Standard Form
d. None of the above
Algebra 1 Midterm Study Guide & Review Packet 2015
39. Which form of linear equations is x  5y  12 written in?
a. Slope Intercept Form
b. Point Slope Form
c. Standard Form
d. None of the above
40. Which pair of lines is parallel?
a. y = 5x +1 and y = -5x - 2
b. y = 2x + 3 and y = 2x - 7
c. y = 4x + 3 and y = -8x + 3
d. y = -5 and x = 4
41. What is the equation of the line that has a y-intercept of 7 and perpendicular to y  2x ?
1
x7
a. y 
2
b. y  2x  7
1
c. y  x  7
2
d. y  2x  7
42. Write the equation y  3  2(x  4) in slope-intercept form.
a. y  2x 1
b. 2x  y  5
c. y  2x  5
d. No Solution
43. Which equation represents the line shown in the graph to the right?
2
a. y  1  (x  2)
3
2
b. y  1  (x  2)
3
2
c. y  1  x  2
3
2
(x  2)
d. y  1 
3
44. Which of the following reasons DOES NOT explain why the linear equation y  .5x  7 is not written
in standard form.
a. a, b, and c are not all integers.
b. a is negative.
c. y is written before x in the equation.
d. The constant, 7, is isolated on the right side of the equation.
Algebra 1 Midterm Study Guide & Review Packet 2015
45. Write the equation y  2x  5 in standard form?
a. y  5  2x
b. 2x  y  5
1
5
c. x  y 
2
2
d. 2x  y  5
46. Which equation represents the line that passes through the points (1.5, 2) and (2, 0)?
a. y  8(x  2)
b. y  8(x  2)
c. y  2  8(x 1.5)
d. y  2  8(x  1.5)
47. Which inequality is represented by the graph?
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¬¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾
-7
-6
a.
b.
c.
d.
-5
-4
-3
-2
-1
0
r  4
r  4
r  4
r  4
48. Which inequality is equivalent to t  4  15 ?
a. t  11
b. t  11
c. t  11
d. t  11
49. Which inequality is equivalent to 5  3x  5  4 ?
a. 0  x  3
b. 0  x  3
1
1
c. 3  x  6
3
3
d. No Solution
50. Which inequality is equivalent to x > -3 and x < 3?
a. 3x  9
b. 3 x  9
c. 3 x  9
d. x  3  6
1
2
3
4
5
6
7
Algebra 1 Midterm Study Guide & Review Packet 2015
51. Which of the following is a solution to 3 3x  5 12  3 ?
a. 0
b. All Real Numbers
c. 1
d. No solution
52. The ordered pair (3, -4) is a solution to which inequality below?
a. x  2y  7
b. 2x  y  2
c. 2x  y  2
d. 4x  2y  4