Extra practice problems from previous reviews this year. Only practice what you need help on. The answers are at the end of the questions (not the work). You should still have the reviews from this year.

- The freshman class at Christian Brothers High School is having an election. Cara randomly asked 50 students whom they would vote for, and 30 said that McKenzie was their choice. If all 350 members of the freshman class vote, how many votes can you expect McKenzie to receive? Show all your work.

- Solve each equation below.

- b.

3.Solve the following equations using any method. Show your work and check your solution.

a. 4*x– 6 =x+ 3 b. 5x+ 2 = 4x– 10 c. 3x+ 7 = 8x+ 2 d. 9x– 4 = 2(x*+ 3)

4.The Geology Club is on a trip to study the Grand Canyon during Spring Break. While waiting in the airport securityline, Courtney notices that it takes about 4 minutes for 15 people to pass through security. Courtney estimates that there are about 100 people ahead of her school group in line.

a.Write a proportion from your table then write a few sentences explaining why your proportion makes sense.

b.Solve your proportion forx, then check that your solution is correct.

c.How long should Courtney expect to wait in line?

5. Juan is buying soda for a class party. He can go to the vending machine and buy 12-oz cans for $0.60 each, to the corner store and get 20-oz bottles for $0.95 or to the grocery store and get 32-oz jugs for $1.55. Which is the best deal? Be sure to organize, label and justify your work.

6. Below are the prices of snowboards at two competing snowboard stores:

**Middletown Snowboards Snowboard Central**

** 345, 360, 405, 356, 375, 350, 355, 362, 377 392, 387, 375, 380, 370, 395, 402, 386, 343**

a)Identify the 5 main statistics of each set of data (5 number summary).

b)Draw a double box-and-whisker plot of the above data on the scale below:

Middletown Snowboards Snowboard Central

c)What is the median price for a snowboard at Middletown Snowboards?

What is the lowest price you could pay for a snowboard at Snowboard Central?

What is the most expensive board at Middletown Snowboards?

What is the range of prices for snowboards at Snowboard Central?

Which price represents the 75th percentile for Middletown Snowboards?

Which store would you rather buy a snowboard from? Why?

What percent of the prices fall below 376 on the Middletown Snowboards?

What is the interquartile range for snowboard central?

7. Find the mean absolute deviation for the set below. S = {85, 90, 68, 75, 79}8. Find the rates for each of the following situations. Show your work on each.

- Jennifer babysat for 7 hours and earned $52.50. What is her hourly rate of pay?

- Zeke drove 346 miles in 8 hours. What is his average rate of speed (mph)?

- Will bought 14 feet of rope for $ 10.50. What does the rope cost, per foot?

- What math operation do all of the above problems have in common?

- Solve each equation below.

a) c)

- Solve the word problem and make sure you provide the answer in a complete sentence.

Matt and Ming are selling fruit for a fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes and 14 large boxes for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes for a total of $220. Find the cost of one small box of oranges and one large box of oranges.

- Solve the following. Write as an ordered pair if possible.

a)y = 2x 3 b) y = 4x +2

y= x + 3 y = 4x +3

- Solve the following. Write as an ordered pair if possible.

a)7x + 2y = 24b) -4x + 9y = 9

8x +2y =30 x- 3y = -6

13. Consider the equation .

a.Solve this equation for y.

b.What is the slope of this line?

c. What is the y-intercept?

14. For each situation, state what the slope is and how it can be interpreted in terms of the situation.

a.The amount of money in Julio’s savings account after x weeks can be calculated using the equation 6y = 20 +18x

b.The bean plant is growing 9 inches every four days.

15. Solve the equations for x. (Fraction Busters might be helpful.) Check your solutions.

a. b.

**For all of the following problems write and solve an inequality and then graph the solution (make sure that you write an inequality for every problem and show your work and do not skip steps!!).**

- In math class this quarter, Kayla scored 89, 87, 92, 88, and 88 on five exams. If she is to earn an A, 90 or higher, for the quarter, what must she score on the sixth and final test for the quarter?
- James saved $74 toward the purchase of an iPod. He makes $6.50 every week for cleaning his room. The cost of the iPods started at $165. How many more times does he need to clean his room before he gets enough to buy an iPod?

- Find the value of x in the following problems.

- Solve and graph the following inequalities.

- b. 2m + 1 -7

**Which of the following statements is ALWAYS TRUE when parallel lines are cut by a transversal?**

The sum of the degree measure of corresponding angles is 180°.

The sum of the degree measure of complementary angles is 180°.

The angles in a vertical pair are acute.

Corresponding angles are supplementary.

Corresponding angles are congruent

- Martin has a very limited wardrobe. He has two pairs of pants: one black and one white. He also has three shirts: one blue, one white, one green.

- Create an area model/probability table representing Martin’s possible outfits.

- If Martin closes his eyes and grabs a shirt and a pair of pants at random, what is the probability he will be wearing:
- green shirt and black pants?
- blueshirt or white pants?
- white pants and white shirt?

- Take a break and have a snack

23. DIRECTIONS: Find the percent or number. (Think before answering and make sure it makes sense!)

a. A store advertises a cell phone 60% off. The sale price of the phone is $36. What is the original price?

b. What is 40% of 80?

24. Solve and graph the following inequalities.

a. b.

- Find the area and perimeter of each of the following composite figures. (Use the correct units.)

a.Area: ______b. Area: ______

Perimeter: ______Perimeter: ______

- Find the area and perimeter of the following shapes:

Area: ______Perimeter: ______

Area: ______Perimeter: ______

Area: ______Circumference: ______Area: ______Perimeter: ______

**The shapes at the below are similar. **

- What is the scale factor?

- Find the length of the sides labeled x and y.

**Commutative Properties**

The**Commutative Property of Addition**states that whenaddingtwo or more numbers or terms together, order is not important. That is:

a+b=b+aFor example, 2 + 7 = 7 + 2

The**Commutative Property of Multiplication**states that whenmultiplyingtwo or more numbers or terms together, order is not important. That is:

a·b=b·aFor example 3 · 5 = 5 · 3

However,subtractionanddivisionarenotcommutative, as shown below.

7− 2 ≠ 2 − 7 since 5 ≠ − 5

50 ÷ 10 ≠ 10 ÷ since 5 ≠ 0.2

**Associative and Identity Properties**

The**Associative Property of Addition**states that whenaddingthree or more numbers or terms together, grouping is not important. That is:

(a+b) +c=a+ (b+c) For example, (5 + 2) + 6 = 5 + (2 + 6)

The**Associative Property of Multiplication**states that whenmultiplyingthree or more numbers or terms together, grouping is not important. That is:

(a·b) ·c=a·(b·c) For example,(5 ·2) ·6 = 5 ·(2 ·6)

However,subtractionanddivisionarenotassociative, as shown below.

(5 − 2) −3 ≠5 −(2 −3)since 0 ≠6

(20 ÷4) ÷ 2 ≠20 ÷ (4÷ 2)since 2.5 ≠10

The**Identity Property of Addition**states that adding zero to any expression gives the same expression. That is:

a+ 0 =a For example, 6 + 0 = 6

The**Identity Property of Multiplication**states that multiplying any expression by one gives the same expression. That is:

1 ·a=a For example,1 · 6 = 6

**Inverse Properties**

The**Additive Inverse Property**states that for every number*athere is a number −asuch thata+ (−a*) = 0. A common name used for the additive inverse is theopposite. That is, −ais the opposite ofa. For example, 3 + (−3) = 0 and −5 + 5 = 0.

The**Multiplicative Inverse Property**states that for every nonzero numberathere is a numbersuch that A common name used for the multiplicative inverse is thereciprocal. That is,is the reciprocal ofa. For example,.

**The Distributive Property**

TheDistributive Propertystates that for any three termsa, b, and c:

a(b+c) =ab+ac

That is, whena multiplies a group of terms, such as (b+c), it multiplieseachterm of the group. For example, when multiplying 2(x+ 4), the 2 multiplies both thex and the 4. This can be represented with algebra tiles, as shown below.

- Predict whether each set of lengths below will form a triangle. If a set will form a triangle, state whether the triangle will be acute, obtuse, or right. Justify your conclusion.
- 5 cm, 6 cm, and 7 cm b. 2 cm, 11 cm, 15 cm

c. 10 cm, 15 cm, 20 cm d. 10 cm, 24 cm, 26 cm

e. 1 cm, 3 cm, 9 cm f. 2 cm, 10 cm, 11 cm

30. Example 1. Determine whether the triangle is a right triangle.

, 3, and 8

Which side is the biggest?

The square root of 73 (= 8.5)! This must be the hypotenuse (c).

Plug your information into the Pythagorean Theorem. It doesn’t matter which number is a or b.

- If Austin borrows $300 to purchase a new bat, how much interest will he pay if he pays interest at a rate of 4% on a 6 month loan?

I = prt

I = 300 x 4% x one half of a year

I = 300 x .04 x .5

I = 6

Austin will pay $6 on his loan.

- If you bought a new phone for $150 and then found out it was later selling for $120 what is the percent decrease?

The phone price was decreased by 20%.

- If Mrs. Larson estimated that there were 315 students in 7th grade and there were actually 350, what is the percentage error in her estimate?

Answers:

1. McKenzie should receive 210 votes

2. a. 12.5 b. 4.444…

3. a. 3 b. -12 c. 1 d. 10/7

4. She should wait in line 26 and 2/3 minutes.

5. 20 oz. bottles

6. a. Middletown

LE 345

Q1 352.5

Med. 360

Q3 376

UE 405

- Check with me if you to not know how to draw a box and whisker plot

Snowboard

LE 343

Q1 372.5

Med. 386

Q3 393.5

UE 402

- $360, $343, $405, 59, $376, Middletown, 75%, IQR 21

7. MAD 6.48

8. a. $7.50 per hour b. 43.25 miles per hour c. $0.75 per 1 foot d. division

9. a. -9 c. 8 and 1/3

10. The small box of oranges cost $7 while the large box costs $13

11. a. (2,1) b. no solution

12. a. (6, -9) b. (9, 5)

13. a. y = -1/2 x +4 b.-1/2 c. (0,4)

14. a. slope is 3 and every week his account goes up $3 b. slope 9/4 every day the bean plant grows by 9/4 inches

15. a. -1/3 b. 16.5

16. x ≥ 96

17. x≥ 14

18. x = 11

19. a m≥-5 b. m ˂-4

20. Corresponding angles are congruent

21. i. 1/6 ii. 2/3 iii. 1/6

22.Take a break and have a snack

23. a. $60 b. 32

24. a. x≤ 7 b. x≤ -6

25. a. A= 321.46 cm² P=75.7cm b. A= 370 mm² P= 11-mm

26. a. A= 149.5 in² P= 59 in b. A= 140 cm² P= 62 cm c. A= 8m² P= 14m d. A≈ 28.3in² C≈ 18.85 in

27. 1/3

28. x = 0.9 y=12

29. a. yes acute b. no c. yes obtuse d. yes right e. no f. yes obtuse

30. yes

31. answer with problem

32. answer with problem

33. answer with problem