Algebra I L1: Midterm Review
Word Problems
Read each problem carefully. Set up and solve. Show all work.
1.
Anna Wood invested some money at 6% and $4000 less than this amount at 4%. Find the
amount invested at each rate if her total annual interest income is $840.
2.
The sum of two numbers is 20. Three times the smaller subtracted from four times the
larger is equal to 17.
3.
Amie is now eight years older than her sister Dana. In six years Amie will be twice as old as
Dana is now. Find the age of each person now.
4.
David invested some money at 5% and $1000 more than that at 10%. His total annual
interest was $550. How much did he invest at each rate?
5.
Two cars start from the same point and travel in opposite directions. The car traveling west
leaves 1 hr later than the car traveling east. The eastbound car travels 40 mph, and the
westbound car travels 60 mph. When they are 240 mi apart, how long had they traveled?
6.
An automobile averaged 45 mph for the first part of a trip and 50 mph for the second part.
If the entire trip took 4 hours and covered 195 miles, how long was the rate 45 mph?
7.
Two cars leave from the same point at the same time, traveling in opposite directions. One
travels 15 mph slower than the other. After 6 hours, they are 630 miles apart. Find the rate
of each car.
8.
How much pure alcohol should be added to 7 liters of 10% alcohol to increase the
concentration to 30% alcohol?
9.
How much water should be added to 30 L of a 40% acid solution to reduce it to a 30%
solution?
10. John has six more dimes than quarters. He has $1.65 total. How many coins of each type
does he have?
11. Kathy has some dimes, quarters, and nickels. The quarters is 16 less than the number of
nickels, and the dimes exceeded the number of nickels by five. The total amount of the coins
is $4.50. Find the amount of each coin.
12. Find three consecutive integers whose sum is three less than twice the second.
13. Find four consecutive even integers such that the sum of the second and the forth is 16.
14. At a football game reserved seat tickets cost $4.00 each and general admission tickets cost
$3.00 each. If 1787 tickets were sold and $5792 was collected from the sale of the tickets,
how many reserved tickets and general admission tickets were sold?
15. There are two deals offered at the deli. Six sandwiches and 4 orders of fries cost $38.50.
Five sandwiches and 3 orders of fries cost $31.25. How much does each sandwich cost?
How much does each order of fries cost?
16. How many gallons of a 35% acid solution should be added to 6 gallons of a 25% acid
solution to obtain a 32% acid solution?
17. With a tail wind, a light plane can fly 720 km in 2 hours. Going against the wind, the plane
can fly the same distance in 3 hours. How fast is the plane flowing and what is the wind
speed?
18. Kim has 40 coins worth a total of $9. Some of the coins are nickels and the rest are
quarters. How many of each kind of coin does Kim Have?
19. Ann runs up the “down” escalator in 12 seconds and back down again in 8 seconds. The
escalator is 48 ft long. How fast does Ann run? How fast does the escalator move?
20. Venus and Serena measured a tennis court and found that is was 42 ft longer than it was
wide and had a perimeter of 228 ft. What were the dimensions of the tennis court?
Algebra I L1: Midterm Review
Linear Systems
Graph the linear system.(Remember to shade)
1.
3x – 4y > 12
and
3y > -2x
2. x + y < 4
or
Solve using the graphing method.
3.
-3x + y = -7
2x + 2y =10
4.
-4x + y = 8
5x – 3y = -3
Solve using the substitution method.
5.
5x – 3y = -29
x + 2y = 2
6.
6x – y = 5
y = 11x
Solve using the elimination method.
7. 5x – 3y = 17
x + 2y = 6
8. 6x – 7y = 12
5x – 4y = 10
x – 3y < 6
Algebra I L1: Midterm Review
Linear Graphing
Answer the following questions:
1. Does this ordered (-2, 5) belong to this equation 3x – 2y = - 16? ______
2. The slope of x = -3 is ___________? What type of line is this? _______
3. When graphing P( -2, -3), what quadrant is this point located in? ______
4. What is the x-intercept and y-intercept of 2x – 3y = - 6?
x-intercept: ________
y-intercept: _________
5. Given 2 points, ( -3, 5) and ( -5, -7), find the slope. _________
6. Given 2 points, ( 4, -1) and ( -2, -1), find the slope. _________
7. Given 2 points, ( -3, - 6) and ( 1, 4), find the midpoint. _________
1
2
3
4
8. Given 2 points,  , 
 2 1
 find the midpoint. _________
3 3 
and  ,
Graph.
9. x + 3y = 0
10. – 3x – 6 = – 3
11.
2x – 2y = 6
12. – 3x+ 6y = -x – 12
13. -3x – 4y > 8
14.
y x0
Write an equation of a line in standard form.
15. Given 2 points: ( -2, 3) and ( -2, 6)
16. Given 2 points: ( -4, 3) and ( 2, -1)
17. m = 0 and passes thru ( -5, 6)
18. undefined slope and passes thru ( 4, -3)
19. Parallel to 2x – 3y = 4 and
20. Perpendicular to 2x – 3y = 4 and
passes thru ( 2, -3)
21. m = - ¼
and passes thru ( 5, -7)
passes thru ( 2, -3)
22. Horizontal, passes thru ( 4, 0)
23. Perpendicular to x = 4, and passes thru (-4, 0) 24. Parallel to 4x – 2y = 8, passes thru ( -1, 1)
25. slope = -5, passes thru ( 5, 6)
26.
27. slope is 4, passes thru ( 0, -5)
28. Passes thru ( -4, 0) and ( -2, 1)
29. Perpendicular to -4x + 2y = -16 passes thru (4, 4)
m = -1, passes thru ( 3, 0)
Algebra I L1: Midterm Review
Functions
Determine whether the relation is a function. List the domain and range.
1. { ( -2, 3), ( 4, -5), ( 5, -5) } __________
2. { (-1, 3),(2, 2), (-1, 1)} ___________
D:
D:
R:
R:
3.
__________
4.
__________
D:
D:
R”
R:
5.
6.
D:
D:
D:
R:
R:
R:
Let f ( x)   x 2  4 x  3
8. f( -3)
7.
9. g( 2)
and
g ( x)   4 x  2.
10. g(1) – f (-1)
Find the following .
11. g( x + a)
12. f ( 3) + g( 4)
Algebra I L1: Midterm Review
I.
Let A  {
Number Sense/Equations/Inequalities
0
35
, 4.3, ,  2,  3 , 4 }. Simplify each element as needed , and then
2
7
from A that belong to the set.
25, 4,
list the elements
1. Whole numbers: ___________________ 2. Integers: ______________________
3. Rational Numbers: _________________
5. Irrational Numbers:
4. Real Numbers:__________________
_________________
6. Natural Numbers:_______________
Simplify
7. - 8 - | - 12 | - | 10 - 19 |
9.
8. -3( 2a - 4) – 5(6a – 2b)
2  2 4  5(9)  2(1)
3(2) 3  1
10. 7 2  4(8)  (  2) 3  9
11. 2[ - 6b – 2(c – 3b) – 10c ]
12. 3(4x – 2y) – 2(5 – 6x)
Evaluate: x = -2, y = 3, z = 
13. xz  y
14. x 2 z 2  2 y
1
2
15. | 4 y 2 z |
16. evaluate :
m 2  9k
r4
if k   4, m   3, r  
17. evaluate : | 3x  2 y |  |  d |
if x   2 , y 
1
2
1
,d   4
2
Solve each equation. Show all work.
3
x  12
4
18.

21.
x6 x4

1
10
15
19.
22.  (r  5)  (2  7r )  8r  3r  8
24. 0.05 x  0.03(1200  x)  42
26.
0.08 x  0.06( x  9)  1.24
7r  3(2r  5)  5  3r  4r  20
20. 3x  (2  x)  4 x  2  8 x  3
23.
x
5x
x
7 
2 9
3
6
2
25. 3(2 x  2)  4( x  6)  4 x  8
27. 8 p  4 p  ( p  7)  9 p  13  12 p
28.  2r  6(r  1)  3r  (4  r )  (r  5)  5
Solve for the indicated variable.
29. V  LWH for L
30.
A
1
h(b  B ) for B
2
32.  16t 2  vt  S  0 for v
31.
C  d for d
33. W  3 y  3z , for y
Solve each inequality. Graph on a number line. Write the interval notation.
34. 4 – 6(x + 3) ≤ -2 -3(x + 6) + 3x
37. 3k ≥ 6
and k – 4 < 5
35. -
4
x  16
7
36. 8≤ 3x -1< 14
38. -4x ≤ -24 or 4x – 2< 10
Isolate the absolute value first! Solve. Then graph.
39. 3 4 x  3  3  18
40. - 34  6 x  1  0
41. -2-4 7  x ≥ 2
Solve each absolute value equation.
43.
3k  2  1  8
44.
2 4 x  3  10  6
42. 2 5  6 x  24
Algebra I L1: Midterm Review
Absolute Value Graphing/Scatterplot
Graph each absolute value function.
1.
2.
3.
Use the given information to graph a scatterplot.
4. The table shows information about age and height from a group of children.
Age
(yr.)
Height
(in.)
3
5
8
11
12
10
4
9
6
7
11
36
40
45
56
64
52
37
51
42
44
60
a. Draw a line of best fit.
b. Write an equation for the line of best fit.
c. Use the equation to find the height of a 14 year old.