Description
In This collection, we will go deep into math.
This collection will help all math and high school students.
Study Set Content:
Luttrell 2012
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Name: ______________________
Date: _____
3d-Adding and Subtracting Decimals
Use your calculator only to check your answer.
1. Find the perimeter of the room with dimensions: 8.35' by 11.24'.
2. Find the perimeter of a triangle whose sides are 4.3", 6.71", and 5.901".
3. Find the perimeter of the room with dimensions 9.12' by 10.8'.
4. Find the perimeter of the room with dimensions 7.02' by 11.76'.
5. If the perimeter of a room is 48' and the length is known to be 10.8', what is the other
dimension?
6. If the perimeter of a room is 65' and the length is known to be 12.5', what is the other
dimension?
7. The perimeter of an equilateral (all sides equal) triangle is 34.8". What is the side length?
8. The perimeter of a square is 38". What is the side length?
9. The perimeter of a regular hexagon (6-sided shape with equal sides) is 39'. What is the side
length?
Luttrell 2012
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Name: ______________________
Date: _____
3e-Multiplying & Dividing Decimals
Only use your calculator to check your answer.
1. (-14.3)×(-2.1)
2. (-0.05)×(-0.05)×(-0.05)
3. -0.003 × 16.1
4. 15.2 × 5.2
5. -18.34(-1.02)
6. 0.0003(-1.2)
7. -18.46 – (-18.79) – 18.46
8. -15.37 – 14.35 + 6.2
9. -83.26 – (-15.6) +(-18.2)
10. 9.3 • 1.23
11. 0.0023 • 1.57
12. 3.14 • 2.718
Solve the following problems with the aid of a calculator.
13. Your bank account started off with $40. Over the course of the week you either put money
or took money out of your account. Here are the pile of ATM transactions: 15.50, - 4.75,
-20, 55.75. How much did you have at the end of the week?
14. Your room has dimensions of 11.23 feet by 9.56 feet. What is its perimeter and area?
15. The monkey cage at a laboratory is 5.3 feet by 5.3 feet. What is the perimeter of the cage
and it’s area?
16. A zoologist recommended that captive monkeys should have AT LEAST a cage 10 feet by
20 feet. What is its perimeter and area?
17. What is the difference in areas between the two cages in problems #15 and #16?
Luttrell 2012
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Name: ______________________
Date: _____
3f-Decimals with Area and Perimeter
Use your calculator to check your answer. You must show ALL your work!!!
1. Find the area of the rectangle with dimensions 4.1' by 8.24'.
2. Find the length of the rectangle which has width 3.2' and area 64 feet squared.
3. Find the area of the rectangle with dimensions 3.201' by 8.9'.
4. Find the width of a 32 feet squared rectangle with length 6.4'.
5. Find the area of the triangle with height 5.4" and base 8.2".
6. Find the area of the triangle with height 4.35" and base 2".
7. Find the base of the triangle with area of 35 squared inches and height of 1.5".
8. Find the height of the triangle with area of 36 squared inches and base of 1.8".
Luttrell 2012
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Name: ______________________
Date: _____
3g-Multiplying & Dividing Decimals
Simplify without the use of a calculator.
1. 13.5 ÷ 1000
2. 1.004 ×100
3. 0.36 ÷ 0.009
4. 2.3 × 3.5
5. 4.56 × 3.2
6. 3.4 ×5.6
7. 2.3 ÷ 100
8. 5.34 × 1000
9. 1002.1 ÷ 10
10. 3.2 ÷ 0.8
11. 0.42 ÷ 0.07
12. 0.0036 ÷ 0.06
Solve without the use of a calculator.
13. If the available cars hold only 4 people, and 34 are going to the beach, how many cars
will be needed?
14. If you spent $48.75 on three pair of jeans, how much is each?
15. If you drive 450 miles in a car that uses 27 gallons, what is your average mile per gallon?
16. If a sack of potatoes weigh 1.2 kilograms, then how much is it in grams? How much in
milligrams?
17. A teacher wants to show a video in her 45 minute class. If the video lasts 153 minutes, how
many classes must she reserve for its use?
18. A lawn of 150 ft by 250 ft will have a house built on it. If the house will be 75 ft by 45 ft,
how much lawn will remain? Put answer in units of feet and yard.
Luttrell 2012
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Name: ______________________
Date: _____
3h-More Multiplying & Dividing Decimals
Simplify without the use of a calculator.
1. 2.9 × 3.1
2. 4.06 × 1.2
3. 27 ÷ 100
4. 34.45 ÷ 1000
5. 0.45 × 100
6. 53.4 × 10,000
7. 3.2 ÷ 0.4
8. 0.45 ÷ 0.9
Solve without the use of a calculator.
9. If 42 people are going to the beach, and cars seat at most 5, how many cars are needed?
(We are omitting vans and other modes of transportation.)
10. If you spent $39.75 on three pair of jeans, what is the average price of one?
11. If you drive 500 miles in a car that uses 22 gallons, what is your average mile per gallon?
12. If a can weighs 10 grams, then how much is it in kilograms? How much in milligrams?
13. A teacher wants to show a video in her 35 minute class. If the video lasts 112 minutes, how
many classes must she reserve for its use?
14. A lawn of 162 ft by 210 ft will have a house built on it. If the house will be 51 ft by 81 ft,
how much lawn will remain? Put answer in units of feet and yard.
Luttrell 2012
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Name: ______________________
Date: _____
3i-Circumference with Decimals
No calculator is allowed. Use 3.14 when approximating π. Round to the nearest hundredth.
1. Calculate the circumference of the circle with radius 9".
2. Calculate the circumference of the circle with diameter 2".
3. Calculate the circumference of the circle with radius 3".
4. Find the radius of a circle with circumference of 31.41 inches.
5. Find the diameter of a circle with circumference of 6.28 inches.
6. Find the radius of a circle with circumference of 9.42 inches.
7. Find the diameter of a circle with circumference of 4.71 inches.
Luttrell 2012
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Name: ______________________
Date: _____
3j-Area with Decimals
No calculator is allowed. Use 3.14 when approximating π. Round to the nearest tenth.
1. Calculate the area of the circle with radius 9".
2. Calculate the area of the circle with diameter 2".
3. Calculate the area of the circle with radius 3".
4. Calculate the area of the circle with diameter 3".
5. Calculate the radius of a circle with area of 28.26 squared inches.
6. Calculate the radius of the circle with area of 50.24 squared inches.
7. Calculate the diameter of the circle with area of 314 squared inches.
Luttrell 2012
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Name: ______________________
Date: _____
3k-Surface Area & Volume with Decimals
A calculator is allowed. If your calculator does
not have a π button, use 3.14 to approximate π.
1. Find the surface area and volume of the box:
8
20
10
2. Find the surface area and volume of the box with dimensions 6” by 8” by 10”.
6 10
8
3. Find the surface area and volume of the cylinder with a radius of 5” and height of 15”.
5
15
Luttrell 2012
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Name: ______________________
Date: _____
3L- Similar Shapes and their Surface Area & Volume
Show your work in spite of having a calculator. If your calculator does not have a π button, use
3.14 to approximate π.
1. Find the volume of a box with dimensions of 3 by 4 by 5.
2. Find the volume of a box with dimensions 6 by 8 by 10.
3. Find the volume of a box with dimensions of 12 by 16 by 20.
4. By how much, are the dimensions of the second box bigger than the first box? How does that
compare to their volumes?
5. By how much, are the dimensions of the third box bigger than the first box? How does that
compare to their volumes?
6. Find the volume of a cylinder that has a diameter of 2 and height of 4.
7. Find the volume of a cylinder that has a diameter of 4 and a height of 8.
8. Find a volume of a cylinder that has a diameter of 6 and a height of 12.
9. How do the dimensions in problems #6 and #7 compare? How do their volumes compare?
10. How do the dimensions in problems #6 and #8 compare? How do their volumes compare?
11. What rule can you create to make it easier to compare the volumes of similar shapes?
Luttrell 2012
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Name: ______________________
Date: _____
3m-Surface Area & Volume of Pyramids & Spheres
A calculator is allowed. If your calculator does
not have a π button, use 3.14 to approximate π.
1. A pyramid is twice as big as a similar pyramid with volume of 25 in
3
. Find the volume of the
other pyramid.
2. A pyramid has a square base of sides 5 inches and a height of 3 inches. What’s the volume of
the pyramid?
3. A triangular pyramid is made up of equilateral triangles with a side of 2 feet. What is the
pyramid’s surface area? (Use Pythagorean Theorem to find the height of a triangle.)
4. A pyramid has a triangular base with area of 15 squared inches and a height of 6 inches.
What’s the volume of the pyramid.
5. A man decides to make a playhouse that’s a triangular pyramid like the one in question #4,
but three times as large. What would be the new volume?
6. Find the volume of a sphere that has a radius of 9 inches.
7. Find the volume of a sphere that has a radius of 4 inches.
8. Find the surface area of a sphere that has a radius of 9 inches.
9. Find the surface area of a sphere that has 4 inches.
10. A. Finding the amount of leather to cover a basketball is an example of (area, volume).
B. Finding the amount of air contained in a basketball is an example of (area, volume).
Luttrell 2012
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Name: ______________________
Date: _____
3n-Mixed Review of Shapes and Objects
A calculator is allowed. If your calculator does not have a π button, use 3.14 to approximate π.
1. The area of a square is 625 cm
2
. Find the length of the sides.
2. The area of a rectangle is 600 cm
2
. Find the width of the rectangle if the length is 40 cm.
3. The area of a triangle is 45 cm
2
. Find the base of the triangle if the height is 9 cm.
4. The area of the circle is 8π cm
2
. Find the circumference of the circle.
5. The area of a square is 400 cm
2
. Find the perimeter of the square.
6. The perimeter of a rectangle is 30 cm with the length being 8 cm. Find the area of the
rectangle.
7. If the surface area of a box is known to be 300 cm
2
and have a base of 5 cm by 4 cm, what is
the height of the box?
8. If the surface area of a box is known to be 320 cm
2
and have a height of 36 cm and a width of
2 cm, what is the depth of the box?
9. If the surface area of a sphere is 400
π cm
2
, what is its volume?
10. If the surface area of a sphere is 100π cm
2
, what is its volume?
11. If the surface area of a cube is 600 cm
2
, what is its volume?
12. If the surface area of a cube is 96 cm
2
, what is its volume?
13. If the volume of a cube is 27 cm
3
, then what is its surface area?
14. If a square pyramid has height of 10 cm and a volume of 60 cm
3
, what is the dimension of
its base?
15. If a square pyramid has a height of 5 cm and a base side of 6 cm, what is its volume?
Luttrell 2012
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Name: ______________________
Date: _____
3o-Mixed Review of Volume & Surface Area
A calculator is allowed. Leave answers in terms of
π.
1. A cube has surface area of 72 in².
2. A tetrahedron has surface area of
What is the area of each face?
of 27.7128 in². What is the length
of each
e
d
g
e
?
3. A prism has a base of 4" by 8" and surface area
4. A prism has dimensions
of 112 in². What is its height?
of 3" by 4" by 5".
What’s its surface area?
5. A cylinder has radius of 2" and
6. A cylinder has diameter of 2"
height of 6". What’s the surface area?
and height of 3". What’s the
surface area?
Luttrell 2012
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Name: ______________________
Date: _____
3p-Mixed Review of Volume & Surface Area
A calculator is allowed. Leave your answer in terms of
π.
1. What the volume of a cylinder
2. A cylinder has radius of 4" and
whose diameter is 10 and height is 3?
surface area of 64π. What’s the
height?
3. What’s the volume of a rectangular
4. What’s the volume of a right
prism of dimensions 3 by 4 by 5? triangular prism whose base has
sides 3, 4, and 5 and height of 10?
5. What the volume of a cylinder whose
*6. A cylinder has height of 3" and
radius is 6 and height is 10?
surface area of 36π. What is the
radius?
Luttrell 2012
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Chapter 3 Test
Name: ___________________________
Date: ______
SHOW WORK
. A calculator is NOT allowed on this test. You must work alone.
1. Put in order from smallest to greatest.
a. 6.1, 6.01, 6.11, 6.001
B. -3.2, -3.22, -3.3
2. A. Write as decimal:
6
3
4
.
B. Write as a decimal:
23
8
.
3. Add:
a. 4.3 + 7
b. 4.3 + 13.7
c. 4.3 + 8.007
4. Subtract:
a. 12.3 - 3.4
b. 12.3 - 5.444
c. 1.23 - 5.444
5. Multiply:
a. 1.3 × 6
b. 1.3 × 6.44
c. -2.3 × (-8.55)
6. Divide:
a. 17.34 ÷ 1.7
b. 42.9 ÷0.03
c. -12.56 ÷ (-8)
5
5
5
5
5
5
Luttrell 2012
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Chapter 3 Test, continued
7. Find the perimeter of the rectangle whose dimensions are 2.45 cm by 3.1 cm.
8. Find the area of the rectangle whose dimensions are 4.03” by 11".
9. Simplify
a. 4(3 - 4)
2
- 5 ÷ 10
b. [3(2-1)×5- 4] ÷ 10 + 1
10. Find the volume and surface area of a cylinder whose diameter is 10 cm and its height
‘ is 20 cm.
Bonus: (3 pts) The sum of ten positive odd numbers is 20. What is the largest number
which can be used as an addend in this sum?
Bonus: (3 pts) Two 5×5 squares overlap to form a 5×7 rectangle, as shown. What is the
area of the region in which the two squares overlap?
5
5
10
5
10
Luttrell 2012
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Chapter 4 Percents and Proportions
Prior Skills:
•
For sheet 4f, placement values
•
For sheet 4g, powers of ten
•
For sheet 4h, an introduction to other bases would be good for students to get a historical
sense of mathematics.
•
For sheet 4i, decimal representations of fractions
•
For sheet 4k, practice understanding and solving with percents
•
For sheet 4m, practice with understanding and solving proportions
Luttrell 2012
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Name: ______________________
Date: _____
4a- Field Axioms
Simplifying any expression or solving any equation requires the use of the following axioms:
Closure
: A set of numbers is closed if the unique sum or product of an operation is also in the
same set. For example: 3+8 = 11, so the set of reals would be closed, but not digits.
Commutativity
:
x
+
y
=
y + x
or
xy = yx.
The order to how the sum or product is obtain is not
important, e.g. 2 + 1 = 1 + 2.
Associativity
: How the sum or product is grouped isn’t important. Examples can be seen in
x
+ (
y + z
) = (
x + y
) +
z
or 2(3×4) = (2×3)×4.
Distribution
of
Multiplication
Over
Addition
:
x
(
y + z
) =
xy + xz
Identity
: Zero plus any number remains that number. One times any number remains that
number. For example: 0+2 = 2, 1×2 = 2. Identity is about leaving the value unchanged!
Inverse
: To obtain zero, sum the number and its opposite. To obtain a one, multiply the number
and its reciprocal. The Inverse defines subtraction and division! For example:
2 + (-2) = 0 which is the same as 2 - 2 = 0. You can see it with 2(½) = 1 which is 2/2 = 1.
1. What is the additive inverse of ⅝?
2. Write an example of the distribution property.
3. What is the multiplicative invers
e of ⅓?
4. What is the multiplicative inverse of
x
?
5. Rewrite the following using addition: 5 - 5 = 0.
6. Rewrite the following using multiplication: 5/3.
7. Fill in the justifications (axioms) used in the proof of the Multiplicative Property of Zero:
a. 0 = 0
Reflexive Property
b. 0 + 0 = 0
________________
c.
x
(0 + 0) =
x
(0)
Multiplication Property of Equality
d.
x
(0+0) = 0 +
x
(0)
________________
e.
x
(0) +
x
(0) = 0 +
x
(0)
________________
f.
x
(0) = 0
Add/Subtraction Property of Equality
8. Fill in the justifications to the following problem:
a. 4
x
- 3 = 5
Given
b. 4
x
- 3 + 3 = 5 + 3
_______________, Add Property of Equality
c. 4
x
+ 0 = 8
_______________
d. 4
x
= 8
Add Property of Zero
e. (¼)(4
x
) = (¼)(8)
_______________
f. (¼*4)
x
= 2
_______________
g. 1*
x
= 2
_______________
h.
x
= 2
Identity
Luttrell 2012
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Name: ______________________
Date: _____
4b – Exponents
An exponent is a shorthand notation for multiplication. A power is an expression that uses exponents.
In the example, 5
3
= 5∙5∙5 =125, the three is the exponent and five is the base. The exponent of three says
to multiply five three times. 4
2
=16 because 4∙4 is 16.
Write the following as a product and then simplify:
1.
3
2
2.
2
4
3.
5
3
4.
10
6
5. 4
2
6. 3
3
7. 8
2
8. 4
5
9. 10
3
10. 1
10
11. 0
2
12. (- 4)
2
13. (-3)
4
14. (-2)
3
15. (-3)
5
16. 4
0
Please note that anything with a zero in the exponent is reduced to equal 1.
Negative exponents are first simplified by making them positive. By definition they mean to reciprocate
the value.
17. 10
–2
= 1/10
2
= 1/100
18. 2
–4
= 1/2
4
= 1/16
19. 3
–3
20. 4
–2
21. 3
3
−
22. 2
5
−
23. 6
3
−
24. 10
5
−
Luttrell 2012
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Name: ______________________
Date: _____
4c- Order of Operations
In English, there is a standard way of writing; there is an order of words that belie the meaning.
The subject is first, followed by verb, and then the direct object. The sentence, “the dog chased
the cat” has a different meaning from “the cat chased the dog”. The same can be said about
mathematical operations. There is a prescribed order of simplifying expressions. This order can
be remembered by the mnemonic “Please excuse my dear aunt Sally” or “Please eat Ms. Daisy’s
apple sauce.” The first letter of each word represents the mathematical operations:
Parentheses,
Exponents, Multiplication, Division, Addition
, and
Subtraction
.
Actually division and subtraction are a special type of multiplication and addition. So whenever
you have multiplication and division (addition and subtraction) together, they are treated equally.
That means you do the operations as they present themselves from
left to right
.
Example A: 2×3÷2 + 1 - 2
Example B: -(-3) - [-(- 4) + 2] + 7
6 ÷2 + 1 - 2
3 - [4+2] + 7
3 + 1 - 2
3 - 6 + 7
4 - 2 -3 + 7
2 4
Simplify the following expressions:
1. (2×3×4 - 1×3)
2
2. 3(2 - 3)
2
×3 - 1
3. (2+2
2
) ÷ 3 - 6 ÷ 3
4. 1 + 4
2
÷ (5-3)
5. 2 - 2 ×3
2
+ 1
6. (2÷2)×[3
2
-1]
7. 2
x
- 3
x
(5
x
) + 3
x
8. 2
x
- 2
x
(5
x
+ 3)
9. (2-3)
x
+ 4
x
+ 3
Luttrell 2012
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Name: ______________________
Date: _____
4d- Using Absolute Values within the Order of Operations
The American way to remember the order is to say “Please Excuse My Dear Aunt Sally” where the
beginning of each word represents the operation: Parentheses, Exponents, Multiplication, Division,
Addition, and Subtraction. Since division is definition a multiplication of fractions, whenever you see
them together, you go left to right. This can explain why the Canadian expression “Bed Mas” is still valid
in spite of them listing division first. Again when multiplication and division are together, the order is the
left operator goes first. The same can be said of addition and subtraction.
1. 2 –
3(4+5) +3∙5
2. 2∙3 + 3(2-1)
3. 4(3-2
2
)-
3∙7+8∙4
4. 3÷9
⋅
6–4
2
+5(3-3
2
)
5. 5 – 2
2
+ 3
4
6. –4*2*6 – 12/3 + 3
3
7.
2
3
4 3
2
6
8
2
+ ×
−
÷ +
(
)
8.
(
)(
)
3
3
4
3
5
2
−
− ×
9.
3
4
6
5
2
× ÷ + ×
There are various ways to write a parenthesis: { }, ( ), [ ],
----
, | |. The absolute value is a special type of
parenthesis because it makes the expression contained within a positive value. The first two questions
have been done for you.
1. | -3 | = 3
2. | 1-4 | = | -3| = 3
3. –2 | 3+8-10 |
4. | 2-6 |
∙3
5. | -½ |
6. (-3+4
2
)(-6)
7. –3(2
3
+ 4) ∙5
8. 1-5 | 5 – (9+1)|
9. -2|3-(7-3)|
10. [3 - (2 - 4)][3 + | 2 - 4 |]
11. 4 - | 1 - 7 |
12. 8 - 3| 5- 4
2
+ 1|
