Download Warm-Up

Name _________________________________________________________
Algebra 1 Semster 1 Final Review Chapters 1 - 5
Chapter 1
Solve the equation.
z
 12
4
3. 5n   20
4. g  5  17
1. 4x + 2 = 3
2.
5. 13  3 p  10  23  3 p
6. 7  4 y  39
8. 4 x  8  6 x  5  33
9. 52c  7  3c  7c  5
10.
3b + 12 + b = 30 + 4b
1
6 x  4  52 x  8
2
13.
3
1
d  12  2d  6
2
2
11. 7n  3  2n  23
12.
14. b  12  15
15.
7. 3  t  11.5  t
2r  5  3r
16.
2k  6  k
Solve the literal equation for y.
21.
5x  y  2
22. 2 x  5 y  3 y  8
23. The formula for the area of triangle is A = 1/2 bh
a. Solve the formula for the height h.
b. A triangle has an area of 50 square inches and base of 5 inches. What is the height of the triangle?
24. The measures of two angles of a triangle are each four times the measure of the third angle. What is the measure of
the third angle? Hint angles of a triangle add up to 180°
25. At a book fair, a tote bag costs $5 and books cost $3.50 each. You spend a total of $19 before taxes. How many
books did you buy in addition to the one tote bag?
26. For a school play, the maximum age for a youth ticket is 18 years old. The minimum age is 10 years old. Write an
absolute value equation for which the two solutions are the minimum and maximum ages for a youth ticket.
27. Your business needs to print brochures. You call two different print shops about prices. Each print shop charges a
set-up fee for preparing the brochure and a price per brochure.
a. The total cost is the same for
each company. How many
brochures is your business
printing?
Brochure
set-up fee
Price per
brochure
Company A
$50
$1.50
Company B
$75
$1.00
b. You decide to increase the
number of brochures. From
which company should you order?
Copyright © Big Ideas Learning, LLC
All rights reserved.
Algebra 1
Assessment Book
15
Chapter 2
Write the sentence as an inequality.
1. The sum of twice a number n and 8 is at most 25.
2. The temperature t is at least 75F.
3. The cost of a ticket t will be no more than $26.
Write an inequality that represents the graph.
4.
5.
Solve the inequality. Graph the solution.
6.  9  m  6
7.
 3z  6  3z
Solve the inequality.
8. 4x + 24 ≥ 4x + 32
9. 4k  3  3k   2
10. 4n  3  6n  8  2n
Solve the inequality. Graph the solution.
11.  3 y  9 or 2 y – 6  2
12.
1  c  2  3
Solve the inequality. Graph the solution (13 and 14 only)
13. |3 − 2𝑥| ≤ 7
14. |𝑥 + 5| ≥ 3
15. 2 x  6  0
16. |5𝑥 − 2| ≥ -3
Write and graph a compound inequality that represents the numbers that
are not solutions of the inequality represented by the graph shown.
17.
18.
19. You need to write an essay that has at least 500 words. You have written
285 words so far. Write and solve an inequality that represents the number
of words w that you have left to write.
20. You need at least 30 cubic feet of sand to fill a sand box. Each bag contains 2.5 cubic feet of sand. Write and solve
an inequality that represents the number of bags b that you need to buy.
21. You are planning a school carnival. The equipment costs $180 to rent. You plan to charge $4.00 per ticket. You
would like to have a profit of at least $500. Write and solve an inequality that represents the number of tickets t that
you need to sell.
16
Algebra 1
Assessment Book
Copyright © Big Ideas Learning, LLC
All rights reserved.
22. You want to purchase a calculator for at most $115. You have saved $30 so far. You earn $7.50 per hour at your
job. Write and solve an inequality that represents the number of hours h that you need to work.
Chapter 3
Determine whether the relation is a function. If the relation is a function, determine whether the function is linear
or nonlinear. Circle the correct answer.
1.
x
1
3
5
3
y
4
2
0
2
2.
y  3
3. 2 x  5 y  10
4.
5
 y  7
x
Find the domain and range of the function represented by the graph. Determine whether the domain is discrete or
continuous. 5.
6.
7- 9 Evaluate the function when x = -1 and x = 0.
7. g  x  3x 2  1
8. b x   2 x  4
9.
h x    x  5
14.
1 x  y  8
2
Find the value of x so that f  x   3. Circle your answer
10.
11. f(x) = 2x - 1
Find the x- and y-intercepts of the graph of the linear equation.
12. 2 x  3 y  6
13.  3x  5 y   30
The points represented by the table lie on a line. Find the slope of the line. Circle your answer.
15.
x
5
3
1
1
y
7
4
1
2
16.
x
2
2
2
2
y
6
3
7
1
Graph the linear equation.
17. x – 3y = 6
18. y = -2/3x + 1
19. 𝒇(𝒙) = 𝟑 − 𝒙
20. f(x) = 3
21. 1/2x + y = -4
22. x = 4
Find the slope, y-intercept, and x-intercept of the graph of the linear equation.
23. 5x  3 y  15
24. y  x  3
Copyright © Big Ideas Learning, LLC
All rights reserved.
25. x   4
Algebra 1
Assessment Book
17
Use the graph of f and g to describe the transformation from the graph
of f to the graph of g.
26.
27.
f(x) = x – 5, g(x) = -f(x)
28.Given 𝑔(𝑥) = |𝑥 − 3|
(a) Describe the transformation from the
graph of f  x  x to the graph of g,
and
(b) Graph g.
What is the domain of g(x)?
What is the range of g(x)?
Chapter 4
Graph the function & State the domain and Range
1
1. 𝑓(𝑥) = { 2
𝑥 − 3, 𝑖𝑓 𝑥 > 1
−2𝑥 + 1, 𝑖𝑓 𝑥 ≤ 1
Choose the correct slope-intercept
3. slope = 3/7; y-intercept = 4
5. passes through (4, 7) (-1, 17)
2. Write the equations of the piecewise.
𝑓(𝑥) = {
, 𝑖𝑓 𝑥 ≤ ___
, 𝑖𝑓 ___ < 𝑥 < ___
, 𝑖𝑓 𝑥 ≥ ____
form of the equation with the given characteristics.
4. Slope = -1/2 passes through ( -6, 10)
6. Parallel to the line y = -5x – 3; passes through (7, -11)
7. Perpendicular to the line y = ½x – 4; passes through (3, -4)
18
Algebra 1
Assessment Book
Copyright © Big Ideas Learning, LLC
All rights reserved.
Write the point-slope form of the equation with the given characteristics.
8. slope = 3; y-intercept = 5
9. Slope = -3; passes through (-4, 7)
10. Parallel to the line =
7
59
𝑥 − 5 ; passes through (0, 7)
11. Perpendicular to the line y = -3x – 7; passes through (6, 7)
Determine if the sequence is arithmetic. If so, find the common difference, write the next 3 terms and write the
equation, then Graph
12. 1, 5, 9, 11…
13. -11, -7, -3, …
14. Given the sequence: -7, -2, 3, 8, …
a. Find a113
Snowfall
Gloves
(inches)
Sold
x
y
Y Model
Residual
15. The table shows the number y of gloves sold for each amount x (in inches) of
snowfall.
y = -1.3x + 1 models the data. Is the model a good fit? Explain.
-8
9
-6
10
-4
5
-2
8
0
-1
2
1
4
-4
6
-12
8
-7
The equation
Show all your work
Determine if the given lines are parallel, perpendicular, or neither. Explain your answer
16. y = x + 4
y - x = 10
17. y – 2x = 4
y = -1/2x + 5
18. Evaluate the function
𝑓(𝑥) = {
5𝑥 − 1, 𝑖𝑓 𝑥 < −2
}
𝑥 + 3, 𝑖𝑓 𝑥 ≥ −2
19. Graph the step function
Copyright © Big Ideas Learning, LLC
All rights reserved.
a. f( -7) =
b. f(5) =
c. f(-2) =
3 𝑖𝑓 − 3 < 𝑥 ≤ −1
5 𝑖𝑓 − 1 < 𝑥 ≤ 1
𝑓(𝑥) = {
}
7 𝑖𝑓 1 < 𝑥 ≤ 3
9 𝑖𝑓 3 < 𝑥 ≤ 5
Algebra 1
Assessment Book
19
Chapter 5
Solve the system of linear equations using any method.
1. x  5 y   30
2. x  2 y   3
3x  5 y  10
4.
y   2x  3
3. 5 x  4 y  15
10 x  8 y  30
 5 x  2 y  51
5.
y  5x  6
6. x   y  1
2x  y  6
 4x  2 y  8
 5 x  2 y   65
Graph the inequality in a coordinate plane.
7.
y  0
8. 2 x  5 y  10
Graph the system of linear inequalities.
9. 3x  2 y   2
10. 2 x  3 y  6
 4 x  6 y  18
x  2y  2
11.You have $8.80 in pennies and nickels. You have twice as many nickels as pennies. Write a system of linear equations
that models the situation. How many of each type of coin do you have?
Compare the slopes and y-intercepts of the graphs of the equations in the linear system to determine whether
the system has one solution, no
solution, or infinitely many solutions. Explain.
12. x   3 y  28
13. 2 x  3 y  11
x  4 y  36
14. x  2 y  3
 4 x  6 y   22
 2 x  4 y   20
15. You make $5 an hour in tips working at a video store and $7 an hour in tips working at a landscaping company.
You must work at least 4 hours per week at the video store, and the total number of hours you work at both jobs in a
week cannot be greater than 15.
a. Write a system of linear inequalities to model the number of hours that you could work at each location in a
week.
b. Graph the system of linear inequalities.
c. Write an equation that models the total tips you receive from the two jobs.
d. Identify and interpret a solution of the system.
Write a system of linear inequalities represented by the graph.
17.
18.
Solve the equation by graphing. Check your solutions.
19. 2 x  3  x  2
20
Algebra 1
Assessment Book
20.
x  1  2x  5
21.
 x  2x  3
Copyright © Big Ideas Learning, LLC
All rights reserved.