Transcript TOPICS COVERED ON “Expressions” TEST

Name:
Date:
Note: Many problems in this packet will be completed together in class during review time.
Students should complete several problems from each page-- in addition to studying the notes and
past quizzes– in order to be fully prepared for test.
TOPICS COVERED ON “Expressions” TEST:
•Integer Operations (Add, Subtract, Multiply, and Divide with both negative and positive numbers)
•Order of Operations-- (1) Parentheses
(2) Exponents
(3) x or ÷ (left to right)
(4) + or – (left to right)
•Algebraic Expressions (substitute given numbers in for variables and solve)
•Combining Like Terms (simplify expressions by combining like terms)
•Distributive Property (simplify expressions by applying the distributive property)
NOTES SPACE/HELPFUL TIPS (to be filled out in class):
Integers
Adding Integers:
1) 16+ -2 =
2) -5 + 34 =
3) -8 + -45 =
4) -40 + 50 =
5) -62 + -44 =
6) 420 + 628 =
7) 30 + -51 =
8) -520 + 750 =
9) 42 + -154 =
10) 4 – (-8) =
11) -9 - 33 =
12) -8 - (-60) =
13) -40 - 73 =
14) -70 – (-30) =
15) 299 - 23 =
16) 3 – (-48) =
17) -82 – (-64) =
18) 921 – (-104) =
Subtracting Integers (KCC):
Multiplying and Dividing Integers:
19) 4(-8) =
20) -5(12) =
21) -7(-11) =
22) -35 ÷ 7 =
23) -54 ÷ -9 =
24) 115 ÷ -5 =
25) 47(-22)=
26) -322 ÷ 2 =
27) 325 (-15) =
2
Order of Operations
Evaluate – (1) Parentheses, (2) Exponents, (3) Multiply or Divide , & (4) Add or Subtract:
(left to right)
1.
3(12 − 6) −8
4. -4 ∙│-2 -4│ ÷ 8 + 12
7.
-4 2 + 14 x 3
10. 3 + 81/2 – (6 ÷ 3 + 42)
(left to right)
2.
12 + 4(5 − 19)0
3.
-4(3 − 2)3 − 21
5.
1 + (- 2) − 2 ⋅ 27 ÷ 32
6. [52 – (23-8) ÷5] + 30
8.
(-23 −7)2 + 23
9. │5+(-8)│ − (3⋅ 8) ÷ 90
11.
-2 + 2(-8)
3(3)-4
12. (12-9)2 + √49
3
Algebraic Expressions
Evaluate the following by substituting the given #’s for each variable:
1.
xy – y -- when x = -3 and y = -1
2.
mp + ⃓ m + p⃓ -- when m = 4 and p = -6
3.
(x + y)2 -- when x = -4 and y = 6
4.
(x + y2) -- when x = -4 and y = 6
5.
[ -3(x – y) + 2] -- when x = -7 and y = -2
6.
x  y + (y – x ÷ 5) -- when x = 5 and y = 4
7.
5[ (n + m2) ÷ 4] -- when m = 6 and n = 4
8.
72 ÷⃓ x(y)⃓ + 13  x -- when x = 3 and y = -3
4
Combining Like Terms
Simplify the following by combining like terms:
2. 1 + a + 3 -3a
3.
v2 + 1 – 2v2 + 6v
4. 5 – 8n – 4n
5.
7 + 6x + 9x +9
6.
-(1 – 5n) -7n
7.
8.
x2 + x + 4 -7
9.
5 - 2(8x + 4)
1.
9+3x +1 -2x
2 + 5 + x -9
10. 6b2 + 4 + c - 3
11. 4x + 5(3x -3)
12. 5 –x2 - 4 + 1 +6x2
13. 4z – z + xz + 3z
14. -2x + 3y – 7y +x
15.
16. 5 – a – 1 + c + 5c
17.
18. - 4 + 3y – y + 4y
19. 3y(3 +2) – 6y
20. 7x – 5x +3x -6x
3 -3(x -2)
21.
5 – n +4n + n3
2x(3x-5) +2x -3
5
Distributive Property
Simplify the following by applying the distributive property:
1.
-9(-7 -7m)
2.
4.
(-6 + 9h)6
5.
7.
(2c + 6) (-8)
8.
10.
-9(-8p -8)
-5 (-3f -6)
3.
8(1 + j)
6.
-3(-2x +1)
-(1 – 6n)
9.
(7 + 5y)7
11.
(-7 + w) 6
12. -3 (8 +2k)
13. 2x (y + 4)
14.
-9(6 + 4y)
15.
-2w (5 – 4)
16.
(4y – 8) 9
17.
(c - 6)1
18.
2(1-8g)
19.
4 (-3x + 2)
20
4(7+9x)
9(-3 – r)
21.
2x(3-5)
6
Multiple Choice
1.
Which equation illustrates the distributive property?
a.
2(7-8) = 2(7) + 2(8)
b. 2 (7-8) = 2(-1)
c.
2(7-8) = 14 + 2(-8)
d. 2(7-8) = 2(7) – 2(8)
2.
Simplify the expression: 7 + 4(5 - 2)2 ÷12
a.
3.58
b. 8.25
c.
9
d. 10
3.
Which expression has a value of 9?
a.
17 - 4 ÷ 2 ⋅ (1+3)
b. 6(3+9) ÷ 3
c.
5 + (18-4) ÷ 2 -7
d. (32+24) ÷8 + 26
4.
What is the value of this expression if m = 4 and k = 2 : m [7k – (20÷k)] ?
a.
16
b. 20
c.
36
d. 51
5.
Evaluate –t2 + (5 - t)3 when t = 3
a.
-3
b. -1
c.
15
d. 17
6.
What is the value of the expression (5x + 2y ) When x = 3 and y = 15 ?
3
1/
a.
1 3
b. 15
c.
20
d. 34
7.
What is the value of the following expression? [4(6 - 3) + 24 ]÷4
a.
5
b. 7
c.
14
d. 16
7
8. Which of the following expressions is equal to 2.1 (7.5 + 1.8)?
a.
b.
c.
d.
9.
(2.1 ⋅7.5)⋅1.8
(2.1 ⋅7.5) + (2.1⋅1.8)
(2.1 +7.5)⋅ (2.1 + 1.8)
(2.1 +7.5)+ (2.1 + 1.8)
Estella makes $6.50 per hour working at her parents’ restaurant. She worked x hours last
week and y hours this week. The following expression represents the amount of Estrella’s next
paycheck:
(6.5 ⋅ x) + (6.5 ⋅ y)
Which expression can also be used to figure the amount of Estrella’s next paycheck?
a.
b.
c.
d.
6.5 ⋅ (x+y)
6.5 + (x ⋅ y)
(6.5 ⋅ 6.5) + (x ⋅ y)
(6.5 + 6.5) ⋅ (x + y)
10. Kelly is buying snacks for the school dance. She needs 15 bags of chips and 11 bags of pretzels.
Each bag of chips costs $4 and each bag of pretzels costs $4. Which expression gives Kelly the
total cost for the snacks?
a.
b.
c.
d.
4 + 15 + 4+ 11
8(15 + 11)
4(15+11)
26 (4+4)
11. Which expression is equivalent to 5(n +8) ?
a.
b.
c.
d.
(5+n)8
5n + 40
n +13
5n +8
12. Simplify: 3x2 + 2x – x2 + 3x - 1
a.
b.
c.
d.
3x2 + 5x -1
3(x2 – x) -1
7x2 – 1
2x2 + 5x -1
8