Second 9-Weeks Review

Transformations

Identify the transformation and the rule. The pre-image is marked with an “x”.

X

Transformations

Identify the transformation and the rule. The pre-image is marked with an “x”.

X

The transformation is a “translation” that moves 3 units left (x – 3) and 4 units up (y + 4). The rule is:(x - 3, y + 4)

• Solve for x

a

b

1 2

3 4

5 6

7 1050

x

8 9

10 670

dc

a || b

• Solve for x

a

b

1 2

3 4

5 6

7 1050

x

8 9

10

670

Angle 8 = 670 because it is vertical to the 670 angle on transversal d.

Angle 2 = 750 because it is supplementary to the 1050 angle on transversal c.

Angles 2, 8 and x add up to 1800 because the sum of the interior angles of any triangle is 1800.

67 + 75 = 142180 – 142 = 38, so x = 38d

c

a || b

• Solve for x

• Solve for x

• Write the following in scientific notation

0.000000075

• Write the following in scientific notation

0.000000075

The coefficient in scientific notation must be greater than or equal to one, and less than ten; so, the decimal must be moved between the 7 and 5 to make a coefficient of 7.5 For numbers less than 1 (small numbers), each decimal place is equal to a negative power of ten, so moving the decimal 8 places gives us a scientific notation value of:

7.5 x 10-8

• Write the following in scientific notation

9,520,000,000

• Write the following in scientific notation

9,520,000,000

The coefficient in scientific notation must be greater than or equal to one, and less than ten; so, the decimal must be moved between the 9 and 5 to make a coefficient of 9.52 For numbers greater than 1 (large numbers), each decimal place is equal to a postive power of ten, so moving the decimal 9 places gives us a scientific notation value of:

9.52 x 109

• Simplify

√256

• Simplify

√256This problem wants to know the side lengths in a square with an area of 256 square units.

The length of each side in a square with 256 square units is 16, because 16 x 16 = 256.

16

16

256 units2

• Simplify

√196

• Simplify

The square root of 196 is 14, because 14 x 14 = 196.

√196

• Estimate

√ 48

• Estimate to the nearest whole number.

√ 48The square root of 48 is between the perfect squares 36 and 49. It is closer to 49, so ~ 7.

1. Which point represents 600 on this number line?

2.

. . . . . 5 10 15 20 25 30 35 40 45 50 0

R S

R

T V

1. Which point represents 600 on this number line?

2.

. . . . . 5 10 15 20 25 30 35 40 45 50 0

R S

R

T V

The square root of 600 is between so it is between 24 and 25.The closest point on the number line is T, between 24 and 25.

• What are the square roots of 81?

• What are the square roots of 81?

Every square has 2 roots, a positive root and a negative root. The square roots of 81 are 9 and -9, because 9 x 9 = 81, and -9 x -9 = 81.

• What is

• What is

The negative root of 361 is -19, because -19 x -19 = 361.

• Mr. Langley has a square garden with an area of 196 square feet. Mrs. Langley wants him to put a fence around the garden to keep the armadillos out

• How many feet of fence does Mr. Langley need to buy?

• Mr. Langley has a square garden with an area of 196 square feet. Mrs. Langley wants him to put a fence around the garden to keep the armadillos out

• How many feet of fence does Mr. Langley need to buy?

This is a two-part question. First you have to find the square root of 196, which is 14 to find the length of one side of the garden. Then you have to multiply 14 x 4 to find the perimeter of the garden. You need 56 feet of fence.

• Find the root of the radical expressions.

• Find the root of the radical expressions.

The cube root of 257 is 3, because 3 x 3 x 3 = 27.

• Order the numbers from least to greatest.

5, , 5.4,

• Simplify. Write your solution with a positive exponent:

(63)4

• Order the numbers from least to greatest.

5.4, , 5, ,

• Simplify. Write your solution with a positive exponent:

• Simplify. Write your solution with a positive exponent:

When you divide exponents with the same base, keep the base and subtract the exponents. 212 – (-3) = 215

• Simplify. Write your solution with a positive exponent:

86 * 8-4

• Simplify. Write your solution with a positive exponent:

86 * 8-4

When you multiply exponents with the same base, keep the base and add the exponents. 86 + (-4) = 82

Simplify. Write your solution in scientific notation

Simplify. Write your solution in scientific notation

Multiply your coefficients, then use the properties of exponents to multiply the powers of 10.3 x 3 = 9 and 105 + (-3) = 102

9 x 102

Simplify. Write your solution in scientific notation

One micrometer is equal to 0.00003937 inch. What is 0.00003937 written in scientific notation?

• Solve and check

6 – 4x = 12 – 2x

• Solve and check

12 – 4a = -4a -6

• Solve an dgraph

• Write an inequality for the graph

• The length of the legs of a triangle are 5 inches and 12 inches. How long is the hypotenuse of the right triangle?

• You are asked to design a new wheelchair ramp over a set of steps that is 12 feet long and 5 feet high. How long will the ramp be?

• Does the combinations of legs and hypotenuse form a right triangle?

a = 7, b = 8, c = 9

• Calculate the distance between the two points

• A golf ball has a radius of approximately 2 centimeters. Calculate the volume of the golf ball.

•

• Soda is sold in cylindrical aluminum cans that measure 15cm in height and 7cm in diameter. Calculate the volume of a full soda can.

• A sno-cone cup has the dimensions listed below. Calculate the volume of ice needed to fill the cone to the top.

• height of cone: 12cmradius of cone base: 5cm

• A cube has a side length of 6cm. What is the longest piece of string you can fit in the cube? Estimate to the nearest centimeter.

• Decide whether the relation is a function of x. Write yes or no and explain your reasoning.

{(1, 0), (2, 0), (3, 0), (4, 0)}

• Decide whether the relation is a function of x. Write yes or no and explain your reasoning.

• Decide whether the relation is a function of x. Write yes or no and explain your reasoning.

Bob

Chris

Jon

a b c d

e f g h

Liz

Cara

Kayla

• Akil made a $75 down payment on a bicycle. His monthly payments are $15.00 per month. If he has 18 monthly payments, what is the total cost of the bicycle?

• Your summer job is cutting lawns. You charge a flat fee of $15 and an additional $5 per hour. Write a function to determine how much you earn.

• Determine whether the representations below are linear functions, non-linear functions, or not functions.

Months Saved 1 1 2 4 3 9 4 16 5 25 6 36

y = x3 - 3