Review for Trimester 1 Final Exam
Complete in your HW section, and show all support work! Use graph pads when necessary!
1. Evaluate the expression 72x + 15 – x3 when x = ‫־‬2.
2. Is x = – 6 a solution of the equation 23 – 3x = – 4x + 17?
Simplify the expressions:
3.
3(x – 5) – 4(x + 3x)
4.
2(x – 8) – (x – 7)
5.
30  21x
3
7.
1
2
x=7– x
3
3
8.
x + 23 = 3(2x + 1)
Solve the equations:
6.
5x – 7(3 – 2x) = 36
9. 14 – (6 – 3c) = 4c – c
12.
3𝑥+4
5
=
𝑥−3
2
10. 3y – 2(y + 19) = 9y – 3(9 – y)
13.
𝑦−3
2
−
𝑦−3
6
11. 2(a – 8) + 7 = 5(a + 2) – 3a – 19
=4
14. Find the slope of the line containing the points (-3, 8) and (5, 2).
15. Graph and label the x and y-intercepts of the equation 5x – 3y = 30.
16. Make a table of values for f(x) =
2
x – 5. Use the values – 6, – 3, 0, 3, 6, 9 for x.
3
17. Write in slope-intercept form and graph the line. 3x – 2y = 12.
18. Erik has 16 more nickels than dimes in his wallet. If he has a total of $3.50 in nickels and dimes, find the
number of each type of coin.
19. The length of a rectangle is five less than twice its width. If the perimeter is 68 cm, find the dimensions of
the rectangle.
20. The sum of four consecutive even integers is 540. Find the integers.
21. Tickets for a play cost $6 for adults and $3 for students. A total of 407 tickets worth $2037 were sold.
How many adult tickets were sold?
22. A grocer has dried apples selling for $1.50/lb. and dried bananas selling for $1.25/lb. How many pounds of
each did he use to make a mixture of 10 pounds that will sell for $1.30/lb.?
23. A small city park has a rectangular-shaped lawn surrounded on all sides by a border of crushed gravel that is 2
meters wide. The lawn is 5 meters longer than it is wide. The area of the crushed gravel border is 364 m 2. Find
the dimensions of the lawn.
24. Two trains left Chicago, one traveling east at 30 mph and the other traveling west at 40 mph. After how
many hours were the two trains 245 miles apart?
25. A car going 50 mph left Thousand Oaks, heading toward South Bend, Indiana. Three hours later a second car
going 70 mph left, traveling on the same road. How many hours will it take for the second car to overtake the first
car?
26. Is the relation a function? {(-4, 3), (1, -5), (7, 6), (9, 6), (1, 5)}
27. If f(x) = 2x2 + 1, find f(3n).
28. Identify the domain and range of the function. {(1, 4), (2, -2), (3, -6), (-6, 3), (-3, -6)}.
29. What is the slope of all horizontal lines? What is the slope of all vertical lines?
30. Graph 𝑔(𝑥) = −|𝑥 − 2| + 4. Compare the transformation to the parent function, 𝑓(𝑥) = |𝑥|
31. Solve. a) 2 − 3|𝑥 + 4| = −10
b) 4|2𝑥 − 3| = −8
32. Solve and Graph. a) |3𝑥 − 2| ≤ 4
1. ‫־‬121
6. x = 3
11. all real numbers
15. y =
17. y =
5
x – 10;
3
3
x – 6;
2
2. yes 41 = 41
7. x = 7
12. x = -23
b) 5|𝑥 + 1| > −25
c) |−3𝑥 + 2| ≥ 11
3. ‫־‬13x – 15
8. x = 4
13. w = 15
Graph with y-int of ‫־‬10, and x-int of 6.
4. x – 9
9. No solution
−3
14. 𝑚 =
5. -7x + 10
10. y = -1
4
16. y values are: ‫־‬9, ‫־‬7, ‫־‬5, ‫־‬3, ‫־‬1, 1
Graph with y-int of ‫־‬6, and a x-int of 4.
18. Let d = # dimes
Let d + 16 = # nickels
value dimes + value nickels = total
10d + 5(d + 16) = 350
He has 18 dimes and 34 nickels.
19. Let w = width
Let 2w – 5 = length
2 widths + 2 lengths = perimeter
2w + 2(2w – 5) = 68 Width is 13cm and length is 21 cm.
20. Let x = 1st integer
Let x + 2 = 2nd integer
Let x + 4 = 3rd integer
Let x + 6 = 4th integer
1st + 2nd + 3rd + 4th = total
x + (x + 2) + (x + 4) + (x + 6) = 540
The integers are 132, 134, 136, and 138.
21. Let a = # adults
Let 407 – a = # students
value adult tix + value student tix = total
6a + 3(407 – a) = 2037
272 adult tix and 135 student tix were sold.
22. Let a = # lb apples
Let 10 – a = # lb bananas
value apples + value bananas = value mix
150a + 125(10 – a) = 130(10)
There are 2 lb. apples and 8 lb. bananas.
23. Let w = lawn width Let w + 5 = lawn length
Let w + 4 = total width Let w + 9 = total length
area of lawn + area of gravel = total area
w(w+ 5) + 364 = (w + 4)(w + 9)
Lawn width is 41 meters and length is 46 meters.
24. Let t = time until the trains meet
distance eastbound + distance westbound = total
rate(time) + rate(time) = total distance
30t + 40t = 245
After 3.5 hours they were 245 miles apart.
25. Let t = 2nd car’s time Let t + 3 = 1st car’s time
distance of 1st car = distance of 2nd car
rate(time) = rate(time)
50(t + 3) = 70t
The 2nd car will catch up in 7.5 hours.
26. No; the domain of 1 has two different
ranges.
27. 18n2 + 1
28. domain {-6, -3, 1, 2, 3}
range {-6, -2, 3, 4}
29. Horizontal; Zero slope.
Vertical; Undefined slope
30. V-shape with a vertex of (2,4), opening
down. The graph of g is a reflection in the
x-axis, followed by a horizontal
translation right 2 units and vertical
translation 4 units up
31. a. 0 and -8
b. no solution
−2
32. a.
≤ 𝑥 ≤ 2 closed dots with
3
shading between -2/3 and 2
b. all real numbers (solid line)
13
c. 𝑥 ≤ −3 𝑜𝑟 𝑥 ≥
3
closed dot on -3 shading left and
closed dot on 13/3 with shading
right