TSI Math 2

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Volume of a Sphere

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1

Volume of a Sphere

V= 4/3 pi r^3

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2

Volume of a pyramid

V=1/3 b* h

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3

Volume of a cone

V= 1/3 pi r^2 *h

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4

Volume of a Rectangular prism

V= lwh

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5

Volume of a cube

V= s^3

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6

Surface Area of a Sphere

4 pi r^2

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7

Surface Area of a Cylinder

2 pi r^2 + pi* d*h

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8

Surface Area of a Rectangular Cube

2* lh + 2h*w + 2 lw

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9

Surface Area of a Cube

S^2 * 6

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10

Area of a Circle

Pi r^2

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11

Pythagorean Theorem

for Rt. Triangle= a^2*b^2=c^2

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12

Area of a triangle

1/2bh

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13

Area of a parallelogram

b*h

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14

Area of a trapezoid

1/2 *h (b+ b)

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15

Circumference of a circle

pi* d

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16

Change a % to a decimal

Move decimal point 2 places to the left EX. 63% = .62

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17

Change a decimal to a percent

Move the decimal point two places to the right. EX. .54 = 54%

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18

Change a percent to a fraction

25% = 25/100

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19

Change fraction to percent

2/5 = 40/100 Mult. top and bottom of fraction by number that makes denominator 100. (20)

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20

Fractions that are mixed numbers or improper fractions equal are greater than or equal to...

100%

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21

Finding the percent of a number: 25% of 12

.25 * 12 = 3 , so 3 is 25% of 12

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22

Part/whole method of percent

Part/whole= %/100

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23

30 is 75% of what number

30/x = 75/100 and solve for x

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24

10% of 60 = 6 so 20% of 60 =

12

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25

Percent change problems

change(difference)/orig. amount =%/100

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26

Mental Math with 10%: what is 20% of 50?

10% of 50=5 therefore: 20% of 50= 10

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27

Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?

First, calculate 18% of 23. 23 × 0.18 = 4.14 Then, add this value (the increase) to the original value of 23. 23 + 4.14 = 27.14 Rounding off, we get 27.

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28

What is the formula for Area?

Area = L*W

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29

Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?

The formula for the area of a rectangle:

A = Width * Length

From the question we know that L = 2W and that A = 50. So we can plug these values into our equation and solve for W:

50 = W * L 50 = W * 2W 50 = 2W² W² = 25 W = 5

We know that L = 2W, so L = 10 Perimeter = 2L + 2W Perimeter = 2 * 10 + 2 * 5 Perimeter = 30

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30

Diego's current age is five times Martina's age ten years ago. If Martina is currently m years old, what is Diego's current age in terms of m?

Martina's age ten years ago is: m − 10

So Diego's age is: 5(m − 10) = 5m − 50

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31

The variables x and y are directly proportional, and y = 2 when x = 3. What is the value of y when x = 9?

Y= KX 2= K3 2/3 = K3 /3 K = 2/3 Plug in K for the second formula Y=2/3(9) Y = 23 = 6 The correct answer is 6

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32

The yard behind Cindy's house is rectangular in shape and has a perimeter of 72 feet. If the length L of the yard is 18 feet longer than the width W of the yard, what is the area of the yard, in square feet?

Area= L*W Perimeter= 2l + 2w L = W + 18 = 9+ 18 = 27

72 = 2 ( W+18) = 2w 72 = 2w+ 36+ 2w 72 = 4w + 36 36/4 = 4w/4 ----> 9= W 27* 9 = 243 The answer is 243

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33

There are 20 children in the cast of a class play, and 8 of the children are boys. Of the boys, 4 have a speaking part in the play, and of the girls, 8 do not have a speaking part in the play. If a child from the cast of the play is chosen at random, what is the probability that the child has a speaking part?

Boys + girls = 20 8 of the children are boys + 12 girls = 20 the boys have 4 speaking parts and 4 do NOT have a speaking part. And of the girls 4 have a speaking part, but 8 of the girls do NOT have a speaking part. all of that added up should give you 20. 8 out of 20 have a speaking part, so we write that in a fraction form reduce it down which gives you the answer: 2/5

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34

There are 20 children in the cast of a class play, and 8 of the children are boys. Of the boys, 4 have a speaking part in the play, and of the girls, 8 do not have a speaking part in the play. If a child from the cast of the play is chosen at random, what is the probability that the child has a speaking part?

Boys + girls = 20 8 of the children are boys + 12 girls = 20 the boys have 4 speaking parts and 4 do NOT have a speaking part. And of the girls 4 have a speaking part, but 8 of the girl do NOT have a speaking part. all of that added up should give you 20. 8 out of 20 have a speaking part, so we write that in a fraction form reduce it down which gives you the answer: 2/5

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35

A ball was kicked into the air from a balcony 20 feet above the ground, and the ball's height above the ground, in feet, t seconds after the ball was kicked was h(t) = 20 − 16t2 + 32t. What was the maximum height, in feet, of the ball above the ground after it was kicked?

h(t) = 20-16t^2 + 32t h(t) = -16t^2 +32+20

x= -b /2a = -(32)/2(-16) = -32/-32 = 1 Plug one in the original equation. h(1) = -16(1)^2 +32+20 = -16+32+20 The answer is 36 ft

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36

In the xy-plane, what is the y-intercept of the graph of the equation y = 2(x + 3)(x − 4)?

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37

There are 3x-2 trees planted in each row of a rectangular parcel of land. If there are a total of 24x-16 trees planted in the parcel, how many rows of trees are there in the parcel?

Formula: ( trees / rows) (rows) = # of trees ( 3x-2/3x-2)/ rows = 24x-16/(3x-2) Rows= 8

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38

10 people can paint a building in 5 days. If each person paints as quickly as the others then how much of the building could 7 people paint in 5 days?

10 people can paint a building in 5 days. Each person paints 1/10 of the building in 5 days. In 5 days 7 people would paint 7 × 1/10 of the building In 5 days 7 people would paint 7/10 of the building.

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39

What is the x value such that y =15 - 3x and y = 0?

y =15 - 3x and y = 0

Hence 15 - 3x = 0

Hence 3x = 15

x = 5 : The answer

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40

Put these four fractions in order from smallest to largest: 1/4, 2/3, 4/7, 1/2

If 1/4, 2/3, 4/7, 1/2 are converted to decimals we get 0.25, 0.6666...., 0.571....., 0.5 then the correct order is obvious

or

If 1/4, 2/3, 4/7, 1/2 are converted to fractions with a common denominator 21/84, 56/84, 48/84, 42/84 then the correct order is obvious.

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41

An isosceles triangle has two equal sides. If two of the sides are 5 inches and 2 inches how long is the perimeter?

The other side must be 5 inches otherwise the two shorter sides could not meet. The perimeter is the distance around the outside of the triangle and is 5 + 5 + 2 = 12.

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