7th grade math honors - miller place high school · 2020. 3. 13. · 7th grade math honors you have...

7th grade Math Honors

You have 2 assignments. You may do them in any order and some parts of one may help you with the other.

You will need access to a calculator.

Delta Math assignment will be a review of topics that we have covered in class.Some of the topics are more current than others.

The 7H packet you were given in class for "Emergency Use Only" You can download it here if necessary.

We will go over this material when we return to school. You may contact Mr. O'Brien via REMIND or email if you have any questions or concerns.

Period 4 text @sobrien4a to 81010 to signup for RemindPeriod 6 text @sobrien6a to 81010 to signup for RemindPeriod 9 text @sobrien9a to 81010 to signup for Remind

[1] Shari has $2.35 in nickels and dimes. If she has a total of thirtytwo coins, how many of each coin does she have?

[2] The length of a rectangle is twice the width. If the length is increased by three and the width is decreased by two, the new rectangle has a perimeter of 86. Identify the variables. Then write an equation that can be used to find the length and the width of the new rectangle. Solve the equation!

[3] Find two consecutive integers such that the sum of the first and 3 times the second is 55.

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[4] Find two consecutive even integers such that the sum of three times the smaller and 4 times the larger is 92.

[5] The width of rectangle is 5 less than 3 times the length. The of the perimeter of the rectangle is 102 centimeters. Find the dimensions of the rectangle.

[6] Two numbers are in the ratio 3:8. The difference of the numbers is 45. Find the two numbers.

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[7] In Δ TRE the ratio of the measures of the three angles is 3:5:7. Find the measure of the three angles.

[8] Manny has $3.45 in quarters and dimes. The number of dimes he has is 3 more than twice the number of quarters. Find the number he has of each coin.

[9] Suppose you have a coin collection of dimes and nickels containing 70 coins. If you have $6.05, how many of each type of coin do you have?

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[10] The attendance at a ball game was 275 people. Adult tickets cost $8 each and child tickets cost $3 each. If the $1,285 was collected in ticket sales, how many of each type of ticket were sold?

[11] Ron bought 23cent stamps, 25cent stamps, and 40cent stamps for $15.61. The number of 25cent stamps was 9 more than the number of 23cent stamps. The number of 40cent stamps was 5 less than twice the number of 23cent stamps. How many of each kind did he buy?

[12] The length of the second side of a triangle is 4 inches less than twice the first side. The third side of the triangle is 13 inches more than the length of the first side. The perimeter of the triangle is 101 inches. Find the length of each side of the triangle.

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[13] Find three consecutive integers such that three times the second is 9 more than the sum of the first and the third.

[14] Kristin has $3.95 in nickel, dimes, and quarters in her coin bank. The number of nickels is 4 more than twice the number of quarters. The number of dimes is 6 more than the number of quarters. Find the number she has of each kind of coin.

[16] Mario buys 12 tshirts for $78. White tshirts cost $5 each and black tshirts cost $7 each. How many of each type did he buy?

[15] The owner of a movie theater was counting the money from 1 day's ticket sales. He knew that a total of 180 tickets were sold. Adult tickets cost $6.25 each and children's tickets cost $3.75 each. If the total receipts for the day were $832.50, how many of each kind were sold?

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Inequality Word Problems

3. The seventh grade class is putting on a variety show to raise money. It cost $700 to rent the banquet hall that they are going to use. If they charge $15 for each ticket, how many tickets will the need to sell in order to raise at least $1,000? (Hint: First set up an inequality)

Example:The cost of renting a car is $25 per day plus a one time fee of $75.50 for insurance. How many days can the car be rented if the total cost is to be no more than $525?

b) Solve the inequality.

a) Write an inequality to model the situation.

Let x =

c) Graph the solution.

13 14 15 16 17 18

[1] Mr. Young plans to fence in his pool. It needs to have a rectangular shape and a perimeter of at least 190 feet. To have it look nice around the pool the length must be 11 feet more than twice the width. Write an inequality to find the dimensions of the rectangle to the nearest foot with the smallest perimeter with at least 190 feet of fence.

[2] Tiana is having a graduation party. She has at most $450 to spend. She has already bought drinks for $67.29. She will buy sandwiches that cost $4.25 each. Write and solve an inequality to show how many sandwiches she can buy. Show your work and interpret your solution.

[3] A tank filled with 800 gallons of water is losing 6 gallons of water per minute. How long will it take before the tank to has less than 200 gallons of water?

[4] To cater a brunch, Applebees charges a $130 setup fee plus $12.50 per person. The cost of the end of the season baseball party is at most $1500. What is the maximum amount of people that can attend the baseball party?

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Types of angles

Acute angle an angle that measures less than 90°

Right angle an angle that measures exactly 90°

Obtuse angle an angle that is greater than 90° and less than 180°.

Straight angle an angle that measures exactly 180°

Complementary angles two angles that add up to 90°

35°

55°

The angles can be connected to form a right angle or just two angles whose sum is 90°

Supplementary angles two angles that add up to 180°

65° 115°

The angles can be connected to form a straight angle or just two angles whose sum is 180°

Vertical angles are two angles that are opposite each other and are congruent.

A B1

2

A ≅ B because they are vertical angles

1 ≅ 2 because they are vertical angles

A is vertical to B because it is across from it.

1 is vertical to 2 because it is across from it.

Adjacent angles: Are any two angles that are next to each other.

How to name angles:

Angles can be named in a number of different ways, but will usually be described with three letters where the middle letter is the vertex of the angle.

A

B

C

The way to read this angle would be ABC or CBA

Vertex of the angle

12

In this example you can name the angle using the number inside the angle and you would read this 1 and 2

D

E

F

G

H

In this diagram when two lines intersect each other it is important to use the right letters when describing an angle. The GEH is the one highlighted here.

[1] What type of angles are shown below? Explain how you know what type of angles are shown below.


Pairs of Angles



[5] Name the angles in the diagram below.A

B M

N

[6] Name the angles in the diagram below.

X

YZ

W

[7] Name the angles in the diagram below.

Q R S

P

[8] Name all the angles in the diagram below.

J

K

LH

G

54°

x

[1] What type of angles are shown here? Explain how you can find the value of angle x.

Working with Pairs of Angles

[2] What type of angles are shown here. Explain how you can find the value of angle y.

y 112°

[3] What angle is congruent to FEM? Explain how you know that it is congruent to FEM.

F

E

M

J

R

[4] What type of angles are shown here? Explain how to find the value of angle x and the value of angle y.

x° 148°

y°

[6] ABC is complementary to CBS. If the measure of ABC is 24°, what is the measure of CBS?

[7] DEF is supplementary to FEK. If the measure of DEF is 123°, what is the measure of FEK?

[8] BIN is vertical to SIP. If the measure of BIN is 114°, what is the measure of SIP?

[5] EMA is vertical to TYL. If the measure of EMA is 74°, what is the measure of TYL?

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1)

2)

3)

4)

6)

7)

[1] What type of angles are shown here? Explain how you can find the value of angle x. Then find the value of x.

43°

x

[2] What type of angles are shown here? Explain how you can find the value of y. Then find the value of y.

y

109°

[3] What angle is congruent to SAD? Explain how you know that is congruent to SAD.

S

A

D

J

R

[4] What type of angles are shown here? Explain how to find the value of angle x and the value of angle y.

x°

52°

y°

In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x.

Angle Problems and Solving Equations 2

CD and EF are intersecting lines. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship in the figure and solve for y.

In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for b.

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The following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship shown in the diagram. Write an equation for the angle relationship shown in the figure and solve for z.

Write an equation for the angle relationship shown in the figure and solve for x. In a complete sentence, describe the angle relationship in the diagram. Find the measurements of

EPB and CPA.

Example 1The following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x.

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Exercise 1The following figure shows four lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x and y.

Example 2In a complete sentence, describe the angle relationship in the diagram. You may label the diagram to help describe the angle relationships. Write an equation for the angle relationship shown in the figure and solve for x.

Exercise 2In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x and y.

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Example 3In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship in the figure and solve for x. Find the measures of JAH and GAF.

Exercise 3In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship in the figure and solve for x. Find the measure of LKM represented by 5x.

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Problem SetIdentify the angle relationship. Write an equation for the angle relationship(s) shown in the figure, and solve for the unknown angle(s).

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Homework:

(3x)°

(4x + 27)°

What is the value of x in the diagram?[1]

(3x + 79)°

(9x 5)°

y°

What is the value of x in the diagram?

What is the measure of the two vertical angles?

What is the measure of angle y?

[2]

What is the value of x in the diagram to the left?(3x + 12)°

(10x 79)°

A

B

C

D

What is the m ABC?

[3]

.

In the diagram below, ABD is vertical to CBE. What is the value of x in the diagram, and what is the measure of CBE?

(8x 27)°

(3x + 38)°

A

B CD

E

[4]

Identify the type of angles here. What is the value of x in the diagram to the left?

What is the m A?

(11x 15)° (7x + 29)°

A

[5]

Identify the type of angles then solve for x in the diagram to the left.

(5x + 38)°

(8x + 25)°B

Find the measure of angle B.

[6]

.

23°x°

[7] In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x.

CD and EF are intersecting lines. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship in the figure and solve for y.

153°

57°

[8]

78°78°64°

[9] The following figure shows three lines intersecting at a point. In a complete sentence, describe the angle relationship in the diagram. Write an equation for the angle relationship shown in the figure and solve for x.

.

3x°

27°

1) What is the value of x in the diagram to the left?

(2x 14)°(6x)°

What is the value of x in the diagram to the left?

B

(5x + 8)°

A

(2x + 5)° If angle A and angle B are complementary, find the value of angle A.

2)

3)

Complementary, Supplementary, and Vertical Angle Examples

3x° 126°

Find the value of x.


(9x 31)°

A

B

C

D

What is the m ABC?

4)

5)

6)

(5x + 12)°

(3x)°


x° 124°

y°

What is the value of x in the diagram? Why?

What is the value of y in the diagram? Why?

(2x)°

76°y°

Find the value of x in the diagram.

What is the value of y in the diagram?

(3x + 8)°140°

y°


What is the value of y?

7)

8)

9)

(5x 6)°

(3x + 18)°

A

B CD

E


10)


What is the m A?

(7x 36)° (3x + 48)°

A

11)

.

(2x + 2)°

(x + 7)°

1) What is the value of the missing angles in the diagram?

2) Angle A and Angle B are complementary. If the measure of angle A is 53°, what is the measure of angle B?

3) Angle C and Angle D are supplementary. If the measure of angle C is (3x + 5)° and the measure of angle D is (4x + 14)°, what is the value of x?

4)

(6x + 14)°

(3x + 15)°


Give the measure of each of the angles in the diagram now that you know x.

.

5) Angle C and Angle D are complementary angles. If Angle C is (5x + 6)° and the Angle D is (3x + 12)°, what is the measure of Angle C?

(5x + 18)°

(6x + 19)°

6)


What is the measure of the two angles in the diagram?

7) Angle X and Angle Y are supplementary angles. If angle X is (4x + 14)° and angle Y is (8x + 22)°, what is the measure of angle X?

.

127°x°

y°

8)



4x°y°

120°



9)

10) Angle H and Angle G are vertical angles. If angle H is (3x + 23)° and angle G is (10x 33)°, what is the measure of angle H?

.

(4x + 39)°(9x 16)°

y°


What is the measure of the two vertical angles?

What is the measure of angle y?


(10x 45)°

A

B

C

D

What is the m ABC?

(2x + 1)°

(x 10)°What is the value of x in the diagram?

What is the measure of each of the angles?

(12x 19)°

(5x + 16)°

A

B CD

E



What is the m A?

(11x 14)°

(7x + 34)°

A

What is the value of y in the diagram to the left?

(3y + 3)°

(7y + 27)°

What is the measure of the angle represented by (7y + 27)°?

(3x + 25)°

(6x + 29)°

What is the value of x in the diagram?A

B

C

DWhat is the m ABC?

Homework:

25°

x

[1] Write an equation and then find the measure of angle x.

[2] Write an equation and then find the measure of angles.

(4x + 9)° (x + 6)°

[3] Write an equation and then find the measure of the ∠ ABC.

4(2x 7)°

(3x + 12)°A

B

C

[4] Write an equation and then solve for x.

(3x + 17)° (2x + 18)°

.

(6x + 11)° 23°

118°

[5] Write an equation for the angle relationship shown and solve for x.

[6] Write an equation for the angle relationship shown and solve for x.

(2x + 15)°

79°

(9x + 27)°

(4x + 119)°

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MORE Angles and Algebra

7th grade math honors - miller place high school · 2020. 3. 13. · 7th grade math honors you have...

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