Download Class 1 Handout

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Class 1 Handout
Review Activity for Chapters 1 and 2
Section 1.1
1. Write each of the following in words.
a) 267
b) 34,100
c) 101,276
2. Consider the number 39,268
a) What number is in the hundred’s place?
b) What number is in the ten-thousand’s place?
c) What number is in the ones place?
3. Write each number in standard notation:
a) Three thousand seven hundred thirty-seven
b) Nine hundred thirty
c) Eighty-six thousand twelve
Section 1.2
4. What property of addition is shown by each of the following:
a) 4+8 = 8+4
b) (2+7)+3 = 2+(7+3)
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5. Find the perimeter of the following rectangle:
32 feet
12 feet
6. For a 17 mile trip, Joe paid the taxi driver a total of $23. If $5 was a tip, how much
was the fare?
Section 1.3
7. Write 5+5+5+5 as a multiplication.
8. A cook worked 12 hours at $11 an hour. How much did she earn?
9. Perform the indicated operation, showing remainders when necessary:
a) 25  3
d)
0
1
b) 7 6 2
e)
5
0
c) 132 11
f) 273  31
10. The members of a marching band need to make 6 foot banners. They have 50 feet of
material to work with.
a) How many banners can be made?
b) How many feet of material will be left over?
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11. a) Estimate the sum of 456 and 19,643 using front end estimation.
Show the values you are using and then find the sum.
b) Find the exact sum of 456 and 19,643.
Section 1.4
12. a) List all the factors of 24.
b) Find the prime factorization of 24.
13. a) Find all the prime factors of 20.
b) Find all the prime factors of 35.
c) What prime factors do they have in common?
14.
a) Evaluate the following exponential expression: 32 43 52
b) Write a a b b a c in exponential notation.
15.
For 73 :
a) What is the base?
b) What is the exponent?
c) Evaluate.
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Section 1.5
16. Evaluate each expression, using the following steps:
i) List all the operations in each problem as they appear from left to right.
ii) Give the first operation to be performed.
iii) Evaluate. Show all steps.
a) 7  4 5
d) 4  2(9  4  2)
b) 50  2(4) 2
e) 25  5 5
c) (2 6  4)2
f)
39  5(6)
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17. At the supermarket, Carlos has 2 cases of soda, 4 bags of potato chips, and 2 cans of
dip in his cart. Each case of soda costs $6, each bag of chips costs $2, and each can
of dip costs $1. Find the total cost of the groceries.
18. Explain the difference in the steps used to evaluate the following expressions:
Expression 1: 5 23
Expression 2: (5 2)3
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Section 1.6
19. Determine whether each statement is an equation:
a) x  2
c) x  y
b) 7 x  9
d) 5  a  2
20. Solve each equation. Show all steps. Write the complete check of the solution.
a) x  7  3
c) 1  b  2
b) x  307  513
d) x  1339  3454
21. A man needs $345 for a new set of golf clubs. You want to find how much more
money he needs if he now has $317.
a)
Define your variable: X =
b)
Set up your equation:
c)
Solve your equation:
d)
Answer: He needs
more.
Section 1.7
22. Name the steps in solving each of the following equations:
a) x  5  10
c) 5x  10
b) x  5  10
d)
x
 10
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23. Solve each equation. Show all steps. Write the complete check of the solution.
a) 3x  3
b)
c)
d
 11
100
x
 21
7
d) 288  96t
24. A high school PE teacher had the students in her class form three-person teams for a
basketball tournament. Eight teams participated in the tournament. How many
students were in the PE class?
a) Define your variable: Let K =
b) Set up your equation:
c) Solve your equation:
d) Answer: There were
kids in the PE class.
Section 2.1
25. If a number is less than 0, what type of number must it be?
26. Use <, >, or = to compare the following sets of numbers, then graph both numbers on
a number line to verify.
a)  6
5
b) 0
c)
(12)
d) 3
3
7
e)  8
 12
 12
f) 9
 9
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27. Simplify each expression:
a) 14
c)  19
b)  5
d)   5
Section 2.2
28. Explain why the expression 6  5 is not written correctly. How should it be
written?
29. Find each sum without a calculator:
a) (6)  (3)
c) 8  (20)
b) 4  14
d) 24  (45)
30. The maintenance costs, utilities, and taxes on a duplex are $900 a month. The owner
of the apartments receives monthly rental payments of $450 and $380. Does this
investment produce a positive amount of money?
Section 2.3
31. To subtract two integers, change the subtraction sign to an addition sign and add the
_______________ of the second number. For example, 15  3  15  ______ .
32. Evaluate each expression without a calculator:
a) 8  (1)
d) 0  8
b) 4  9
e) 3  (6  12)
c) 4  (9)
f) 4  5  (8)
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33. A diver jumps from his boat into the water and descends 50 feet. He pauses to check
his equipment and then descends an additional 70 feet. Use a signed number to
represent the diver’s final depth.
Section 2.4
34. a) The product of two integers with like signs is _______________.
b) The product of two integers with unlike signs is _______________.
35. Evaluate each expression without a calculator:
36.
a) 0(27)
c) 3(2)(3)
b) 7(1)
d) 6(0)(12)
A levee, which is an embankment designed to prevent the flooding of a river,
protects a town in a low-lying area. According to geologists, the banks of the
levee are eroding at a rate of 2 feet per year. If something isn’t done to correct the
problem, what signed number indicates the distance from the levee’s current
location to where it will be in 10 years?
Section 2.5
37. How do the rules for dividing integers compare with the rules for multiplying
integers?
38. Evaluate each expression without a calculator:
81
9
d)
50
25
b) 5  (5)
e)
12
1
c) 53  0
f) 0  (12)
a)
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39.
Over a week’s time, engineers at a city water reservoir released enough water to
lower the water level 35 feet. Use a signed number to indicate how much the
water level changed each day during this period, on average?
Section 2.6
40.
Use front end estimation for each of the following.
Show the numbers you are using.
5267
a) 379  (103)  287
c)
5
b) 19 3
d) (3887)  (5106)
41. Explain the difference between 32 and (3)2 , then evaluate each one.
42. Evaluate each expression, using the following instructions:
i) List all the operations in each problem as they appear from left to right.
ii) Give the first operation to be performed.
iii) Evaluate. Show all steps.
a) 15  (3 4  8)
c) 8 5  2 5
b) (5  9)2  (2  10)2
d)
25  46
42  58
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Section 2.7
43. Solve each equation. Show all steps. Write the complete check of the solution.
a
 7  6
a) 9h  3(3)
f)
5
b) r  4  4
c) 0  6 
s
3
g) 8  3x  2
h) 5(0)  2 y  10
d) 4  2x  8
i) 17  2x  3
e) 5x  6  14
j) 5x  4  1
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Class 1 Handout Answer Key
1.
a) Two hundred sixty-seven
b) Thirty-four thousand, one
hundred
c) One hundred one thousand,
two hundred seventy-six
13.
a) 2,5
b) 5,7
c) 5
14.
a) 14,400
b) a 3b 2 c
2.
a) 2
b) 3
c) 8
15.
a) 7
b) 3
c) 343
3.
a) 3737
b) 930
c) 86,012
16.
a) i) addition, multiplication
ii) multiplication
iii) 27
4.
a) Commutative property of
addition
b) i) subtraction, multiplication,
exponent
ii) exponent
iii) 18
b) Associative property of
addition
5.
88 ft
6.
$18
7.
54
8.
$132
9.
a) 8 R 1
b) 84
c) 12
10.
a) 8 banners
b) 2 feet
11.
a) 20500
b) 20099
12.
a) 1,2,3,4,6,8,12,24
b) 2 2 2 3
c) i) multiplication, subtraction,
exponent
ii) multiplication
iii) 64
d) i) addition, multiplication,
subtraction, addition
ii) subtraction
iii) 18
d) 0
e) undefined
f) 8 R 25
17.
18.
e) i) division, multiplication
ii) division
iii) 25
f) i) subtraction, multiplication,
division
ii) multiplication
iii) 3
$22
For expression 1, the exponent is
done first, followed by the
multiplication.
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For expression 2, the
multiplication is done first,
followed by the exponent.
19.
a) yes
b) no
20.
a) x = 10
b) x = 206
21.
22.
23.
24.
c) b = 3
d) x = 4793
a) x = Amount of additional
money he needs
b) 345 = 317 + x
c) x = $28
d) He needs $28 more.
a) Subtract 5 from both sides of
the equation.
b) Add 5 to both sides of the
equation.
c) Divide both sides of the
equation by 5.
d) Multiply both sides of the
equation by 5.
a) x = 1
c) d = 1100
c) x = 147
d) t = 3
a) K = The number of students in
the class.
b) K = 3 8
c) K = 24
d) There were 24 kids in the PE
class.
30.
No, costs are greater than
payments. 900 > 830
31.
Opposite, ( 3 )
32.
a) 9
b) 13
c) 5
33.
120 feet
34.
a) Positive
b) Negative
35.
a) 0
b) 7
36.
20 feet
37.
The are the same, except that you
can multiply by 0, but you can’t
divide by 0.
38.
a) 9
b) 1
c) undefined
39.
5 feet per day
40.
a) 400  (100)  300  200
c) 12
d) 21
d) 8
e) 3
f) 9
c) 18
d) 0
d) 2
e)  12
f) 0
b) 20 3  60
A negative number.
26.
a) <
b) >
c) >
d) >
e) >
f) =
a) 14
b) 5
c) 19
d) 5
28.
a) 9
b) 10
c) no
d) yes
25.
27.
29.
The  5 should be in parentheses
c)
5000
 1000
5
d) (4000)  (5000)  9000
41.
For 32 , the base is 3 whereas
for (3)2 , the base is 3
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32  3 3  9
and
2
(3)  (3) (3)  9
42.
a) i) addition, multiplication,
subtraction
ii) multiplication
iii) 5
b) i) subtraction, exponent,
subtraction, subtraction,
exponent
ii) subtraction
iii) 48
c) i) multiplication, subtraction,
multiplication
ii) multiplication
iii) 50
d) i) exponent, subtraction,
exponent, division, addition
ii) exponent
iii)  254
43.
a) h = 1
b) r = 0
c) s = 18
d) x = 2
e) x = 4
f) a = 5
g) x = 2
h) y = 5
i) x = 7
j) x = 1
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