Algebra 1 300 – Midterm Review

Name: Date:

Directions: For the following problems, on a SEPARATE PIECE OF PAPER;

Define the unknown variable

Set up an equation (Include a sketch/chart if necessary)

Solve and show work

Answer the question

1. Twelve less than five times a number is thirty three. What is the number

2. If 32 is added to four times a number, the result is 100. Find the number.

3. The sum of three consecutive odd numbers is -219. What are the numbers?

4. Earl has 28 coins, all dimes and quarters. How many of each does he have if their total

value is $5.20?

5. Bob is six years older than his sister, and the sum of their ages is 32. How old is Bob?

6. The sum of two numbers is 33. One number exceeds the other by 9. Find the numbers.

7. John’s family is saving money for John to go to college. They currently have $2500 in

the bank and save $150 each month. Alex’s family is also saving for college. They currently

have $900 in the bank and save $250 per month. When will both families have the same amount

of savings?

Evaluate each of the following:

5)73(3)5

)4.3(36)4

5413)3

)458(4

1)2

)1012)(1

2

2

4

Evaluate if 5,3

2,3,

4

3,8 rqnpm

2

2

2

)8

)7

))(6

rn

pq

mn

Simplify:

2466

5)12

4

1

4

3)11

5.35.2)10

5)2(3)9

mm

m

yy

yyxx

aa

Evaluate if 5,7,2,4 dcba

3

22

2

7)18

)17

)16

12)15

)(5)14

)13

b

dc

d

bca

d

ab

cba

Solve:

3818)22

3412)21

5643)20

4

3

3

4)19

a

w

x

p

Simplify.

1. )7(454510 2. 8165972

3. 243 4. 326335

5. 342547 6. 82

7. 149

Evaluate for the given value(s).

8. 22 510 yx for x = 4, y= 8 9.

22qp for p = -3, q = 2

Solve. If a solution is an improper fraction, rewrite it as a mixed number.

10. 35 = 25 + w 11. y – 45 = -23 12. 14 = k – (-12)

13. 5

11

3

2d 14. 0.16 = k – 2.04 15. 7w = 105

16. 1212

a

17. 77

t 18.

7

410

n

19. 62

9p 20. 5

4

3

x

Simplify. If a solution is an improper fraction, rewrite it as a mixed number.

21. 9

71

9

22

9

57

22.

3

22

6

13

Graph each of the following using slope-intercept form. State the slope and the y-intercept.

(Graph all of the lines on the set of axes.)

1. 33

2 xy m = _______ 2. 14 yx m = ________

b = _______ b = ________

3. 1223 yx m = ________ 4. 7y m = ________

b = ________ b = ________

Determine whether each pair of equations are parallel, perpendicular, or neither.

5. 3

3

xy

yx 6.

63

33

xy

xy

7.

322

42

1

2

1

yx

yx 8.

123

123

xy

yx

Determine what type of lines these two

equations are and graph.

9. 84

24

xy

xy

10. Which of the points are on the line y = - 4x + 7? Write yes or no.

a) (7, 0) b) (-2, 1) c) (-1, 11) d) (3, 5)

11. Write the equation of a line that has a slope of 5 and a y-intercept of 6.

12. Write the equation of a line that has a slope of -4 and contains the point (1, -3).

13. 11. Write the equation of a line which contains the points (8, 0) and (-8, 2).

12. A line contains the points (9, 6) and (3, -2). What is the slope of all lines perpendicular to

that line?

13. What is the slope of a line that is parallel to 2x – 3y = 8?

14. Write the equation of a line that is parallel to the line 52

1

xy that contains the point

(-4, -3). Graph the line.

15. Write the equation of a line that is perpendicular to y = 3x + 6 and contains the point

(-12, 5). Graph the line.

Linear Apps Question:

A lease for a pre-owned Land Rover is advertised in the paper. The advertisement indicates that

a person can lease the Land Rover for 24 months and pay $11,838 or lease it for 48 months and

pay $20,454.

(a) Let x represent the number of months you lease the car for and let y represent the total cost

of your lease payments. Express the information given using two ordered pairs (x, y) and find

the slope of the line passing through the two points.

(b) Write the equation of the line passing through the two points.

(c) Based upon your equation, what does the slope represent in relation to this problem?

(d) Based upon your equation, what is the y-intercept and what does it mean in relation to this

problem?

(e) If a person’s payments total $13,992, for how many months are they leasing the Land Rover?

SYSTEMS:

Solve each system by the graphing method.

1) xy

xy

38

2)

xy

xy

222

1

3) 933

xy

xy 4)

642

3

xy

yx

5) 03

4

yx

yx 6)

632

24

xy

yx

Solve each system by the substitution method.

7) 13

2

yx

y 8)

4

8

yx

yx

9) 12

2

yx

xy 10)

1023

5

yx

yx

11) xy

yx

1293

64

12)

1064

13

nm

nm

13)

11

14

ba

ba

14) 834

56

ba

ba

15) 42

2

1

84

yx

yx

16) 432

32

yx

yx

Solve by Elimination:

1) 3x + 2y = 11 2) 3x + 2y = 19

2x – 2y = 4 3x – 5y = 5

3) -4x + 7y = 10 4) 8x + 12y = 20

4x – 2y = 5 5x + 12y = -1

5) 4x – 5y =3 6) x + y = 5

3x + 2y = -15 62

3 y

x

7) 4x – 2y = 10 8) 5x + 3y = 43

3x – y = 12 -x + 7y = -1

Translating Sentences into Equations

Examples

1. The sum of a number and fifteen is sixty five.

2. A number decreased by eight and then the quantity is multiplied by four totals sixty four.

3. A rectangle has length x and width x + 3. The perimeter is 22.

4. Three times the quantity two less than x is eight.

5. Two less than the product of three and x is ten.

6. Seven less than four times a number is eleven more than two times a number.

7. A season ticket good for 39 basketball games costs $1092. Write the equation based on one

admission with the ticket.

8. Each car in a fleet of twenty four rental cars is either red or blue. There are three more blue

cars than twice the number of red cars. Write the equation in terms of the number of red cars.

For the following problems, set up the equation and solve.

9. The sum of 5 times a number and -11 is -16.

10. The sum of four times a number and 3 is -13.

11. 5 times the sum of a number and 2 is 35.

12. Six times the difference of a number and 9 is 42.

13. The sum of seven times a number and 11 is 81.

14. Three times the sum of a number and negative 2 is -15.