Math 0092

Review Ch 1, Ch 2, Ch 3.1 – 3.3

Solutions

1. Which of the following are whole numbers? {18, -9, 3, ½, 4.3, 7}

The whole numbers are 18, 3 and 7.

2. Find the place value of the 7 in 274,865,123.

The ten millions spot.

3. Write the following number in expanded form and then in words. 2,345,678

Expanded Form: 2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8

In words: 2 million, three hundred forty-five thousand, six hundred seventy eight.

4. Simplify the following:

a. 3(-3+4) – (3 – 5)

3((1) – (-2)

3 + 2

5. There is a 3-degree drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 35degrees, what will the temperature be when the plane reaches an altitude of 25,000 feet?

The temperature will drop 3 degrees 25 times so the temperature at 15,000 feet will be:

35-3(25)

35-75

-40 or below zero

6. Use front end rounding to estimate the following. Then find the exact answer.

Pat had $953 in her checking account. If she wrote checks for $145 and $339, how much does she have left in her account?

Using front end rounding Pat has, 1000-100-300 = $600 left in her account.

In actuality she has $516 left.

7. The following are examples of what properties?

a. (3*4)(5)=5(3*4) commutative property of multiplication

b. 5 + 0 = 5 additive identity

c. 5 + 0 = 0 + 5 commutative property of addition

d. 5 + (-5) = 0 additive inverse

e. [(5 + 0) +3]=5 + 3 additive identity

f. [(5 + 0) + 3] = 5 + (0 + 3) associative property of addition

g. 5x + 3x = x(5 + 3) distributive property

8. Simplify expressions: make sure that you add like terms!

Section 3.1 so not on test 1

a. 5(2x + 3) - (6x -7)

b. 2 - 4(3x + 6) + 5(8x + 7)

c. 4y + 3x – (6x – 5y)

9. Solving equations:

Section 3.2 and 3.3 so not on test 1.

a. x + 7 = 9

b. x -12 = -3

c. -8 = 4x

d. –x = 12

h. 4(3x + 2) -5( 46x + 3) = -179

10. Given the following expression: 8 – 3x

Section 3.1 so not on test 1

a. Determine the variable.__________

b. Determine the constant: __________

c. Determine the coefficient: __________

11. Divide the following and then interpret the remainder.

Lj brings a bag of candy to his classroom. The bag has 120 pieces of candy in it. Lj had planned on dividing the candy evenly between all 23 students and the teacher. However, the teacher can’t eat candy. How many pieces of candy does each child get?

The solution is 5 remainder 5. This means each child will receive 5 pieces of candy and there will be 5 pieces left over (the remainder).

12. Evaluate the following expressions when x = 2, y = 3 and z = -2.

13. What is the difference between an expression and an equation?

This material is covered in sections 3.1 and 3.2 so it will be on test 2.

14. Find the perimeter and area of the following figures.

Perimeter:

25 + 26 +5 +12 + 9 + 6 + 11 + 20

P = 114 ft.

I broke it into 3 rectangles though this is not the only way to do it.

A = 5(12) + 14(25) + 11(6)

A = 60 +350 + 66

A = 476 square feet.

P = 10 + 5 + 10 + 5

P = 30 meters

A = 10(4)

A = 40 square meters.

15. Ryan wishes to fence in his rectangular backyard. It is 45 feet deep and 117 feet wide. The cost of the fencing is $6 per linear foot. After fencing in his backyard he decides to sod the yard. The cost of the sod is $5 per square yard. What is the total cost of the project?

P = 2(45 + 117)

P = 2(162)

P = 324 ft.

The cost of the fencing is 6(324) or $1944.

The sod costs $5 per squared yard. One square yard is 3 feet by 3 feet and is therefore 9 square feet!!!!

A = 45(117)/9

A = 585 square YARDS

The cost of the sod is 5(585), or $2925.

The total cost of the project is $1944 + $2925 or $4869

16. Heidi and Brenda decide to paint Brenda’s living room. The room is 20 feet long 15 feet wide and has 8 foot tall ceilings. There is a picture window which is 12 feet long and 4 feet tall and two doorways, one is 3 feet wide and 6 feet tall while the other is 4 feet wide and reaches up to the ceiling. They need to prime the wall with “Kilz” which costs $16 per gallon and then put two coats of paint on. The paint costs $20 per gallon. If the Kilz covers 150 square feet per gallon and the paint covers 200 square feet per gallon, how many gallons of Kilz and paint should they but? What is the cost of the project before paintbrushes etc.?

The rest are from Chapter 3 and on Test 2.

17. Write the following as an algebraic expression.

a. 5 less than twice a number.

b. The difference of five and the product of two and a number.

c. Twice the sum of four and three times a number.

18. Solve: When the product of a number and three is increased by 5, the result is 35. Find the number.

19. Write the following as an algebraic equation and solve. On a given day, Judge Leslie drove five times as far as his wife. If the total number of miles that they drove was 630, how far did he drive?

20. While shooting trap, Jon hit 8 less than twice as many trap as Karin. If the two of them hit 52 in all, how many did Jon hit? Solve algebraically.