Name ________________________
Reasoning with Equations Quiz 1
Date _______________
PMI Algebra
1. Explain the difference between an algebraic expression and an equation and give an
example of each.
2. Identify the constant: 4x – 3
3. Identify the coefficient: 6x + 19
4. Write an expression with a constant of -4 and a coefficient of 2
Translate the following into algebraic expressions:
5.
The sum of 4x and 5
6.
The product of x and 3
7.
The quantity 4 minus x divided by 3
8.
9 less than y
9.
3 more than the quantity x times 18
10. The quotient of 50 and the quantity of x times 7
11. x less 12
12. 3 times the quantity 15 minus x
13. The product of 15 and x divided by y
14. 6 times x minus the quantity 4 less than y
15. The product of 7 and x minus 5
16. Twice x
17. 11 more than n
18. 4 less than the product of 2 and x
19. The quantity x more than 2 divided by the quantity 3 less than y
20. Three times the quantity x minus 2
Name ________________________Date _________________
Reasoning with Equations Re-Quiz 1
PMI Algebra
1. Explain the difference between an algebraic expression and an equation and give an
example of each.
2. Identify the constant: 2x – 1
3. Identify the coefficient: x - 4
4. Write an expression with a constant of -3 and a coefficient of 1
Translate the following into algebraic expressions:
5. The product of 4x and 15
6. The sum of x and 3
7. The quantity 4 less x and the product of 3 and 2y
8. 9 less y
9. 3 less than the quantity of x divided by 18
10. The quotient of 150 and the quantity of x less than 7
11. x less 1
12. 3 times the quantity 15 plus x
13. The sum of 15 and x minus 14y
14. The sum of 6 times x and the quantity 4 less than y
15. The sum of 7 and x minus 5
16. Double x
17. n more than 12
18. 4 more than the product of 12 and x
19. The quantity x less than 2 divided by the quantity 13 more than y
20. two times the quantity of x plus 2
Name ________________________Date _________________
Reasoning with Equations Quiz 2
PMI Algebra
Evaluate the expression
1. 5x for x = 3
2. 2x – 5 for x = 8
3. 3x2 – 2 for x = 4
4. 4x + 3x – 9 for x = 5
5. 5x for x = 6
3
6. 4x + x for x = 12 and y = 6
y
7. 8x + 4y for x = 9 and y = ½
8. 4(x + 5) for x = 2
9. 5(x + 1) + y for x = 3 and y = 7
10. 6x2 + 2y for x = 7 and y = ½
Find the distance traveled for the given rate and time
11. Rate: 60 mph; Time: 2.5 hrs
12. Rate: 42 mph; Time: ½ hr
Fill in the table
13.
x
0
30
42
x÷6
14. Customers pay double what the store pays for a pack of gum. Complete
the table.
Store Pays
$0.50
$0.75
$0.85
$0.90
Customer’s price
15. Write an expression that represents the customer’s price for a pack of gum, if the store
pays “x” dollars for a pack of gum.
Name ________________________Date _________________
Reasoning with Equations Re-Quiz 2
PMI Algebra
Evaluate the expression
1. 5 - x for x = 3
2. 2x2 – 5 for x = 8
3. 3x – 2 for x = 4
4. 4x - 3x – 9 for x = 7
5. 15x for x = 3
3
6.
x + x2 for x = 12 and y = 6
y
7.
8x + 4y for x = 1/2 and y = ¼
8. 14(x + 5)2 for x = 1
9. 5(x + 1) - y for x = 3 and y = 7
10. 6x + 12y for x = 7 and y = ½
Find the distance traveled for the given rate and time
11. Rate: 50 mph; Time: 2 hrs
12. Rate: 48 mph; Time: .5 hr
Fill in the table
13.
x
0
30
40
5x
14. The number of cows is three less than the number of pigs. Complete the table.
Number of Pigs Number of cows
15
27
34
52
15. Write an expression that represents the number of cows, given that the number of pigs is
“x”.
Name ________________________
Reasoning with Equations Quiz 3
Date ________________
PMI Algebra
Use the distributive property to rewrite the expression without parentheses
1. 3(x – 1)
2. 4(x + 2)
3. (x – 5) 6
4. 10(x + 2)
5. 6(x – 2)
6. 4(x + 1)
7. 1(x – 5)
8. (x + 3) 8
9. 4(x – 2)
10. 9(x + 3)
11. Write a like term for 14xy
12. Write a like term for 15x2
13. Are x and x2 like terms?
Collect like terms
14. 6x + 7x + x
15. 7x2 + 3x + 5x + x2
16. y + y + 2y + y
17. 2xy + 3xy
18. 8x + 2x + 3
19. 4x + 5
20. -4 + y + 6 + 9y
Name ________________________Date _________________
Reasoning with Equations Re-Quiz 3
PMI Algebra
Use the distributive property to rewrite the expression without parentheses
1. 3(x + 1)
2. 4(x - 2)
3. (x – 5)16
4. -10(x - 2)
5. 16(x + 2)
6. 4(x - 1)
7. -1(x – 5)
8. (x + 3) 8
9. -4(x – 2)
10. 9(x - 3)
11. Write a like term for y
12. Write a like term for 15x
13. Are x and 6x like terms?
Collect like terms
14. 6x + 7x - x
15. 7x2 + x + 15x + 2x2
16. y2 + y + 2y + y2
17. 12xy - 3xy
18. 8x + 2x2 + 3
19. 4x + 5x + 6
20. -14 - y + 6 + 9y
Name ________________________Date _________________
Reasoning with Equations Quiz 4
PMI Algebra
Solve the following equations.
1. t + 7 = 5
2. v + 0.013 = -4.0
3. w – 2.3 = -7.5
4. 12 
y
13
5. -5g = -95
6. 6p = -7.2
7.
u
3  5
4
8. 7.5r – 2= -24.5
x
4
2
u2
10.
 12
4
9. 19 
Name ________________________Date _________________
Reasoning with Equations Re-Quiz 4
PMI
Algebra
Solve the following equations.
1. x + 6 = -9
2. c – 6 = -4
3. -12.1 + z = 14
4. -12 = 3x
5.
x
 5
5
6. -0.4w = 2
7. -3 = 9 + 4c
8. -8 – 3y = 25
9. 
1
d  1  12
5
10. 12 – 9w = 75
Name ________________________Date _________________
Reasoning with Equations Quiz 5
PMI
Algebra
Solve the following equations.
1. x  3( x  4)  20
2.
3.
4.
5.
6.
7.
8.
16  2n  5  8n  65
5x  x  30  4x  x  360
-7x + 18 + 2x = 33
2(k – 5) – 3k = 35
-8m + 21 + m = 35
4
-10 = - 5 𝑦 + 6
1
2
(6s + 12) = 21
2
(4 y  2)  4
9
2
10. (9 − 2𝑏) = −14
9.
5
Name ________________________Date _________________
Reasoning with Equations Re-Quiz 5
PMI Algebra
Solve the following equations.
1. 5(k  2)  8k  34
2. 
3
2
b  7  b  19
5
5
3. 3(p – 5) = 45
4. -4(y – 2) + 9y = 3
5
5.  30 
( x  15)
3
6. 8 = 3y + 5y -24 + 16
7. 25x – 400 + 28x + 90 = 3061
2
8. 3 (3𝑥 + 12) = 32
9.
3
2
10.
(𝑥 − 5) = −6
8
7
(3𝑤 − 1) = −32
Name ________________________Date _________________
Reasoning with Equations Quiz 6
PMI
Algebra
1. 5(𝑥 + 1) = 55 − 5𝑥
2. 3𝑏 + 3 = 4𝑏 − 2
3. 9 − 4𝑎 = −3𝑎 + 9
4. −5𝑥 − 2 = 14 − 𝑥
5. 2(𝑦 − 2) + 16 = 5𝑦 − 9
6. 5𝑝 + 9 = 2𝑝 − 12
7. −7𝑡 + 9 = 𝑡 + 1
8. 5 (𝑦 − 6) = 3 (y – 4)
9. -5(3x – 4) = 2(9 – 6x)
10. Robert and Sarah both left their houses at 8 a.m. It took Robert a half hour
longer to get to school by walking 3 mph than Mary who jogged 5 mph. How
long did it take for Sarah to get to school?
Name ________________________Date _________________
Reasoning with Equations Re-Quiz 6
PMI
Algebra
1. 4𝑚 − 17 = 13 + 6𝑚
2. 3(𝑥 − 3) + 12 = 4𝑥 − 2
3. 5𝑏 − 9 = 𝑏 − 9
4. 10 − 2𝑡 = 7𝑡 + 17
5. 8 + 𝑎 = 6𝑎 − 7
6. −5 − 𝑥 = −3𝑥 − 17
7. 8(𝑥 − 3) + 8 = 5𝑥 − 22
8. 5(y – 6) = 3(y – 4)
9. -5(3x – 4) = 2(9 – 6x)
10. Alice and Sue left school at 4 p.m. It took Alice an hour longer than Sue to
get home. Alice walked 2.5 mph while Sue walked 5 miles an hour. What
time did Sue get home?
Name ________________________Date _________________
Reasoning with Equations Quiz 7
PMI Algebra
Solve for the given variable.
1. V = LWH, solve for H
2. P = 2L + 2W, solve for L
3. A = 𝜋𝑟 2 , solve for r
1
4. A = (𝑏1 + 𝑏2)ℎ, solve for h
2
5. SA = 2𝜋𝑟ℎ, solve for r
Name ________________________Date _________________
Reasoning with Equations Re-Quiz 7
PMI Algebra
Solve for the given variable.
1. I = PRT, solve for R
2. D =
3. A =
4.
1
3
𝑚
𝑉
, solve for m
𝑏ℎ
2
solve for h
𝜋𝑟 2 ℎ = 𝑉, solve for r
5. T =
𝑚𝑣 2
𝐿
, solve for m