Midterm Review Notes

Convert to an algebraic expression

1.) the product of 9 and 3 less than p

2.) three times the sum of 11 and a number

3.) the quotient of 3 and the sum of x and 5

Convert to a word expression4.) x2 + 5 5.) -4(n – 3)

6.)

Real Numbers

Rational Numbers

Integers

Whole Numbers

Natural Numbers

Name the set(s) of numbers to which each number belongs7.) 3.6 8.) 0 9.) -7

Evaluate each expression: 10.) 11.)

12.) 5 + 42 × 8 – 23 ÷ 22

Name the property that each equation illustrates : 13.) 83 + 6 = 6 + 83 14.) (1)(4y) = 4y 15.) 15x + 15y = 15(x + y)

16.) (8 ∙ 7) ∙ 6 = 8 ∙ (7 ∙ 6) 17.) (8 ∙ 7) ∙ 6 = (7 ∙ 8) ∙ 6 18.) 0 + (-5m) = -5m

19.) 0 = 0 ∙ 18 20.) -2xy + 2xy = 021.)

Midterm Review Notes

Midterm Review Notes

Solve each equation:22.) 24 – 2(2m +1) = -6 23.) 4(3 + 5y) – 4 = 3 + 2(y – 2) 24.)

25.) 26.) 27.)

Write equations and solve each word problem:28.) The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions.

29.) The sum of three consecutive integers is 126. What are the integers?

30.) Two cars leave town at the same time heading in the same direction. One car travels at 60mph and the other travels at 40mph. After how many hours will they be 50 miles apart?

Distance Rate TimeSlow Car

Fast Car

Midterm Review Notes

31.) Two cars leave town at the same time going in opposite directions. One of them travels 60mph and the other travels at 30mph. In how many hours will they be 150 miles apart?

Distance Rate TimeSlow Car

Fast Car

32.) Raisins cost $2 per pound and nuts cost $5 per pound. How many pounds of each should you use to make a 30-lb mixture that costs $4 per pound?

Raisins

Nuts

Mixture

33.) A chemist has a 10% acid solution and a 60% acid solution. How many liters of each solution does the chemist need to make 200 L of a solution that is 50% acid?

Solution 1

Solution 2

Midterm Review Notes

Final Solution

Solve and graph each solution:34.) -8z – 6 < 3z + 12

35.)

36.) -3 < 2x – 1 13 37.) 4v + 3 < -1 or -2v + 7 < 1

Solve each absolute value equality:38.) 39.)

Solve and graph each absolute value inequality:40.) 41.)

Chapters 4-6

Midterm Review Notes

Find the domain and range of each relation. Is the relation a function?

1.) {(3, 2), (7, 0), (2, 1), (3, 4)} 2.) {(3, 1), (4, 1), (5, 1), (6, 1)}

3.) Sketch a graph of a relation that is a function 4.) Sketch a graph of a relation that is not a function

5.) Find the range of each function for the domain {-2, 0, 3}

h(x) = -x2 + 3x – 1

6.) Write a function for each:

the value v(d) of a pile of d dimes

a worker’s earnings e(h) for h hours of work at $9.50 per hour

the distance d(t) traveled at 55 miles per hour in t hours

Midterm Review Notes

7.) Write a function rule for the table:

xf(x)

1 -42 -33 -24 -1

Zero Exponents Negative Exponents

8.) Simplify each expression:

a) b) (-4)-2 c) -5-2

9.) Simplify each expression:

a) b)

10.) Evaluate each expression for r = -2 and s = 3

a) 4s-2 b) c) (-r2)(-s2)

11.) Find the slope of the line passing through the pair of points:

a) (-4, 7) and (2, 9)

b) (3, 8) and (3, -1)

Slope-Intercept Form Standard Form Intercepts

12.) Write the equation in slope-intercept form. State the slope (m) and y-intercept (b)

13.) Write the equation in standard form and find the x and y intercepts.

Midterm Review Notes

14.) Write the equation of the line with slope of and y-intercept 4 in standard form.

15.) Graph the line by finding the slope and y-intercept.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10-9-8

-7

-6-5

-4

-3-2

-1

12

3

45

67

89

10y

16.) Graph the line by finding the x and y intercepts.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10-9-8

-7

-6-5

-4

-3-2

-1

12

3

45

67

89

10y

17.) Write the equation of the line with slope -4 and passing through the point (6, -1) in standard form.

18.) Write the equation of the line passing through the points (-3, 2) and (1, 4) in slope-intercept form

19.) Write the equation of the line parallel to y = -2x + 3 and passing through the point (4, -1) in standard form.

20.) Write the equation of the line perpendicular to 3x – y = 2 and passing through the point (-1, -2) in standard form.

Midterm Review Notes

21.) Solve for a and b using the substitution method

22.) Solve for x and y by using the addition/elimination method:

Midterm Review Notes

23.) Graph the linear inequality:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6-5-4

-3-2

-1

123

45

6

7

89

10y

24.) Graph the set of linear inequalities and shade the solution region.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6-5-4

-3-2

-1

123

45

6

7

89

10y

Write a system of equations to model each problem and solve.

25.) You have 32 coins that are only nickels and quarters. The coins total $5.00. How many of each coin do you have?a) write let statements to define your variables b) write two equations

c) solve

26.) Kim bought 2 popsicles and 3 cokes for her friends for $5.50. Rick bought 3 popsicles and 2 cokes for $5.75. Find the cost of a popsicle and a drink.a) write let statements to define your variables b) write two equations

c) solve

Midterm Review Notes

27.) The sum of two numbers is 105. The difference of the two numbers is 59. Find the numbers. a) write let statements to define your variables b) write two equations

c) solve

28.) Susan and Katie each have a savings account. Susan started with $140 and is saving $5 a week. Katie started with $200 and is withdrawing $10 per week. After how many weeks will they have the same amount of money in their accounts?a) write let statements to define your variables b) write two equations

c) solve