Download Pre-AP Algebra 1 Midterm Review Students are expected to

Pre-AP Algebra 1 Midterm Review
Students are expected to demonstrate their mastery of the following objectives on the Algebra 1 midterm, which will be
administered in class on 12/12 and 12/13. Use this list—in conjunction with your warm ups, notes, homework, quizzes, tests,
and other handouts—to prepare for the midterm. Practice problems from the textbook are written in italics.

classify and order numbers (rational, whole, natural, irrational, real, integer) [64 – 68]

simplify expressions using order of operations and integer operations [8 – 12]

use the commutative, associative, and distributive properties to simplify algebraic expressions [96 - 99]

use data sets to write functional equations

use models, tables, graphs, descriptive, and equations to represent relationships

identify and use independent and dependent relationships

identify restrictions to domain and range

justify why data is discrete or continuous

evaluate a pattern in a table or drawing to determine the equation of a function or sequence (using finite differences
and the zero term) and use the equation to predict certain values

translate and evaluate expressions

identify and justify positive/negative/no correlation

determine characteristics of relations/functions (vertical line test), such as domain and range, discrete vs. continuous
[35 – 39; 49 – 50]

use the properties of equality to solve problems involving ratios, proportions, and percents algebraically (part to part
and part to whole) [162 – 180]

determine whether a table, graph, or scenario depicts a proportional relationship/direct variation or not [253 – 258]

combine like terms to simplify expressions

translate and solve the following types of equations: 1-step, 2-step, multi-step, equations with variables on both sides,
equations with fractional coefficients (Be prepared to justify each step with properties). Chapter 3

write equations or inequalities to answer questions arising from situations and solve them

solve and graph simple and compound inequalities (open circle versus closed circle) Chapter 6

Linear equations Chapter 4 and 5
o
determine slopes from graphs, tables, and equations
o
graph a linear equation
o
Write a linear equation using a graph, a slope and a point, or two points
o
write and analyze equations in slope-intercept, point-slope, and simplified standard form and transform
equations from one form to another
o
interpret and predict the effects of changing slope and y-intercept for an equation
o
determine the intercepts of an equation and graph a line
o
write equations of parallel and perpendicular lines

interpret and write piecewise functions

determine the domain and range for a function and write it in set notation

interpret distance versus time graphs

create a scatterplot given a set of data, determine the correlation, and create a line of “good fit” [325 – 330]
Pre-AP Algebra 1 Midterm Practice Problems
***DISCLAIMER***
By giving these practice problems, Ms. Wu DOES NOT mean to imply that completing it alone is sufficient preparation for
the final exam. You should STUDY your notes, LEARN the vocabulary, and REVIEW the mistakes you’ve made in the past by
looking over graded quizzes. (Like Function notation is not on the practice final, but it will be on the final)
The table below shows the number of hours worked and the amount of money each person earned.
Hours Worked
Pay ($)
8
40
10
46
13
52
15
76
16
85
21
102
1) Graph the data on a set of coordinate axes.
2) Is there a correlation between the data sets?
3) If so, describe the correlation that exists.
Classify each of the following as either continuous or discrete. Explain how you know.
4) The number of slices of pizza sold in the cafeteria during A-lunch.
5) The temperature inside Mr. Hook’s room throughout the day
6) Sketch a graph showing Ed’s distance away from work as a function of time.
Ed lives 10 miles from work and is late. He rushes out of bed and into his car. He speeds down the street for 1 minute
(and goes 1/4 mile) and gets stopped by a red light. He waits at the red light for two minutes. Then he enters the
highway and drives the speed limit for 3 minutes before he hits traffic. He drives half of the speed limit for the
remainder of his trip to work.
7) Identify the independent and dependent variable: Distance from lightning, time it takes to hear thunder
In which quadrant or on which axis is each
of the following points located?
8) (-4, 7)
9) (0, 12)
10) (-6, -9)
Simplify the following expressions.
11) 3 (4-5) + 3[5 – 3 (2-2) 2]
12)
14 ( 3 - 1) + 15
96 – (5 * 10 + 3)
13) Ivan earned a 78 on the first six weeks, an 84 in the second six weeks, and an 82 in the third six weeks. What does he have to
get on the final exam to get a course semester average of 85? Can Ivan do well enough on the final to have a final average of
90% or higher? Solve algebraically.
14) Use a = -15, b = 5, c = - ½, and d = ¾ to evaluate the algebraic expression:
-a – 2b – 2c +8d
Solve each of the following equations for x.
15)
2x
 12  14
7
16) 3 x  4  6 x  2(4  x)  11x
19)
3
2
x 5
4
3
20)
17)
2
(4 x  3)  5
3
18)
2x  5
 12
3
x  6 4x  7

2
4
State the number property that is illustrated in each of the following.
21) Line 1: ½ + 1/8
22) Line 1: x ( x * y)
Line 2: ½ * 4/4 + 1/8
Simplify each expression:
23) Line 1: 3x – 2y + 3x
Line 2: (x*x)y
Line 2: 3x + 3x – 2y
24) 3x + 2y – 6x + 8y – 2 + 3y – 12
25) -3(2x- 4) + 3x
26) -4x2 – 2x(x – 3) + 5x
27) Find the range when the domain is {-1, 0, ½} for the function y = 5 x2 + 4.
28) Using the domain {-3, -2, -1, 0, 1, 2, 3} create a table and a graph of the following function: y = x 2 + 3x + 1
Solve the following equalities and then graph the solution set. Plug in a value from the solution set to check that it makes the
inequality true.
29)
30)
31) Define the variable, translate the inequality, solve, and graph: A house and lot together cost more than $89,000. The house
costs $1,000 more than seven times the cost of the lot. How much does the lot cost?
32) How do you determine if a table/graph is a function?
33) How do you determine if a graph/table is a direct variation or linear (non-direct variation)?
34) Tell whether the given set of points lie on a single line: (3,2); (4,5); and (6, 11)
35) Suppose the ordered pairs are for the same direct variation. Find the missing value. (2, 1) and (5, y)
36) The point (6, 8) belongs to a direct variation. What is the equation for that direct variation?
Given the following information, write equations in point-slope, slope-intercept, and simplified standard forms.
37) slope = 4, point: (2,5)
39)
38) two points: (5, 6) and (8, 12)
x
y
3
-5
5
-9
6
-11
8
-15
41)
40)
x
y
-2
5
-1
5
0
5
1
5
2
5
41) Find the slope of the line through the points (-2, 7) and (-5, -7).
42) Find the slope of the line 3x – 5y = 10.
43) Write an equation of the line that intersects the x axis at 4 and is parallel to the graph of y = 3x – 3.
44) State the slope and y-intercept of the line -2x + y = 7.
45) A mass of 25 g stretches a spring 10 cm. If the distance, D, a spring is stretched is directly proportional to the mass (M),
what mass will stretch the spring 22 cm? Write a direct variation equation involving D and M and use it to solve the
question.
46) State the domain and range of the relation. Is the relation a function? {(3, 4), (2, 3), (3, 6), (2, 0)}
47) State the domain and range of the relation. Is the relation a function? {(-1, 1), (1, 1), (2, 4), (-2, 4)}
48)
What are the equations of the vertical and horizontal lines that go through the point (4, 17)?
49) A rectangle has a perimeter of 48 cm. If the width and the length are consecutive odd integers, find the dimensions of the
rectangle. Solve this algebraically.
50) Solve
.
Set up a proportion to solve each of the following.
51)
If Bob spends $18.50 on 2.5 pounds of cheese, how much will 6 pounds of the same cheese cost?
52)
75% of what number is 32?
53)
Ms. Hill gets 12 markers out of her marker bin and finds that 3 of them are dried out. If there are 82 markers in the bin,
how many would you suspect have dried out?
54) Translate and solve the following: Three times a number increased by 44 is the same as the opposite of the number. Find
the number.
55)
Solve:
56) Solve:
. If the equation is an identity or if it has no solution, write identity or no solution.
57) The sum of a mystery number and two times itself is three times the sum of twice the number and 1. Find the mystery
number.
58) The sum of three consecutive odd numbers is 105. Find the numbers.
59) Given the sequence -11, -14, -17, -20 … , determine the equation given that -11 is the value of the first term. Then use the
equation to determine the value of the 523rd term.
60) How prepared do you feel for the midterm exam? If you’ve reached this point, you’re in good shape (unless you’re starting
from the bottom). Don’t forget to review your notes, re-work homework and assessment problems, and ASK
QUESTIONS IF NEEDED! Ask Ms. Wu, ask your friends, ask anyone you think can help. Ms. Wu wants you to do well,
really! 