Download Write an algebraic express

Name___________________________________Per________ 1st SEMESTER ALGEBRA 1 FINAL REVIEW (Revised 1/17)
Write an algebraic expression for each verbal expression.
1.
the product of 41 and a
2.
the sum of 35 and m
Write a verbal expression for the algebraic expression.
3.
7𝑥 3 + 5𝑥
4.
5𝑥 4
6
5. Simplify: 62 + 3(10 – 3)
6. Evaluate the following expression if a = 10, b = 7, and c = 6:
3c + bc – 2a
Simplify the expression.
7.
10.
11.
4 + 47 − 9 + 𝑦
3(16−2)
8(5)+2
8.
9𝑏 − 5(−2 − 8𝑏)
9.
2(5𝑥 + 13𝑎 − 8𝑎)
+7
Stephanie spends $16 each month to belong to a photography club. As a member of the club she can develop
rolls of film for $3.50 each. Write and solve an equation to find the total amount Stephanie will spend this month
if she develops 4 rolls of film.
12.
If 𝑔(𝑥) = 𝑥 2 + 3𝑥 − 5, 𝑓𝑖𝑛𝑑 𝑔(−3)
13.
If 𝑔(𝑥) = 8𝑥 − 5, 𝑓𝑖𝑛𝑑 𝑔(−3)
Translate the sentence into an equation.
14. Seven times the difference of a and b is equal to nine times c.
15. The number x divided by the number y is the same as six more than three times the difference of x and y.
Solve the equation. Then check your solution.
16.
19.
3
2
5
7
− +𝑧 =−
3
5
𝑘=6
17.
90 = n – 24
18.
20.
5𝑥 + 9 = 14
21.
3
2
5
5
𝑚
72
𝑎
−3
=
8
12
+ 7 = −15
22.
5𝑥 + 75 = −8𝑥 − 55
23.
− 𝑥−6=7+ 𝑥
24.
3m – 4 = –5m + 52
25.
4(−3𝑧 + 7) = 2(−6𝑧 + 5)
26.
–16(1x – 4) = –2(8x – 32)
27.
|2𝑥 − 5| = 29
28.
Evaluate 17 – |6 – 6z| if z = 4.
29.
Solve the proportion:
=
State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change.
Round to the nearest whole percent.
30.
original amount:
40
new amount:
20
Solve the equation or formula for the variable specified.
31.
𝑑𝑓 + 7ℎ = 5 𝑓𝑜𝑟 𝒅
32.
5𝑥 − 4𝑦 = 20 𝑓𝑜𝑟 𝒚
33. Find the x and y intercepts:
Use the diagram below to answer questions 34 and 35.
Source: U.S. Bureau of Census
34. For which 10-year period was the rate of change of the population of Green Bay the greatest?
35. Find the rate of change from 1980 to 1990.
36. Find the slope: (–3, –2), (1, –5)
37. Find the slope: (–5, –1), (–5, 4)
Determine whether the sequence is an arithmetic sequence. If it is, state the common difference.
38. –4, –13, –22, –31, . . .
39. 9, 0, –6, –18, …
Find the next three terms of the arithmetic sequence.
40.
, 9,
, 10, . . .
41. 7, 4 , 1, -2, . . .
Write an equation of the line with the given slope and y-intercept.
42. slope:
, y-intercept: –9
43. Graph the equation 3𝑥 + 𝑦 = 5
Write an equation to model the situation.
44. A taxi driver’s fare (F) is $7 plus $0.4 per mile (m)
45. An icicle’s length (y) is 14 inches long and melts at a
rate of 2 inch per hour (x)
Write an equation using the given information (Be able to choose answers in either slope-intercept or point-slope
form)
46. Through the point (0, 9) and with slope = –2
48. Write in point-slope form: (–2, 6), m =
47. Through the points (–1, –15) and (–7, 9)
49. Write in slope-intercept form: y + 5 = –4(x + 1)
Write the equation in slope-intercept form.
50.
y+4=−
𝟐
(x – 1)
𝟑
Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph
of the equation.
51. (5, -4);
3𝑥 − 4𝑦 = 5
Write the slope-intercept form of an equation of the line that passes through the given point and is perpendicular to the
graph of the equation.
52. (2, -5);
5
𝑦 = 𝑥−1
3
Use the scatter plot that shows the average cycling speed as time passes.
Average Cycling Speed
53. Predict the speed of the cyclist after 30 minutes.
a. about 6.2 miles per hour
b. about 8.8 miles per hour
c. about 12.3 miles per hour
d. about 10.5 miles per hour
Solve the inequalities. Graph the solution on a number line.
54.
57.
60.
2≥𝑤−6
3𝑥+30+3𝑥
6
<3
3
55.
− 5 𝑏 > −12
56.
45 − 6𝑎 > 15
58.
−3𝑛 + 5 ≥ −8𝑛 − 2 + 5𝑛
59.
2𝑘 + 7 > 1 𝑎𝑛𝑑 3𝑘 − 6 ≤ 9
−1 + 𝑣 ≤ −4 𝑜𝑟 − 2𝑣 ≤ 6
Solve and graph the absolute value inequalities.
62. |𝑝 − 4| ≤ 8
61. Solve |d + 3| > 5.
63.
In order to earn a grade of a C on the midterm, a student must have a score that is within 8 points of the average
score of 62 points. Which scores would earn a C?
a. {x | x ≤ 54 or x 70}
b. {x | 54 ≤ x ≤ 70}
c. {x | x < 54 or x > 70}
d. {x | 54 < x < 70}
64. Graph
65.Graph −
66.
Graph −3𝑥 + 𝑦 > 4
FREE RESPONSE
1.
Write an algebraic expression to represent the perimeter of the rectangle. Find the dimensions of the rectangle if
the perimeter is 32 centimeters.
2.
At a store, Jack bought a scientific calculator for $20 and four notebooks for $2.50 each. Write and evaluate
an expression to find how much money he spent not including sales tax. Then find the total if the tax is 10%.
3.
Express the relation as a table, graph or mapping. Determine the domain and range. State whether it is or is not
a function. Justify your answer.
(3,4) (7,1) (5,4) (3,-4)
4.
Find four consecutive integers with a sum of 138.
5.
Solve 6(3𝑥 + 1) − 30 = 20𝑥 + 8
6.
Solve 4(−5𝑥 + 1) + 11 = 2(−10𝑥 + 7) + 9
7.
Solve
8.
Find the x and y intercepts of the line with the equation: 2 x  4 y  24
9. Graph y  
10.
3x  12
9
4
1
x4
2
Write the equation of the line that goes through the following points: (3, −5) and (−1, 7)