Download Exam 2 Review

Math 090 Exam 2 Review – Chapter 3
Remember that material from the first exam may be on this exam also – your exams will build on
each other!
Section 3.1 Introduction to Algebra
Variable – a placeholder for a number (we use letters of the alphabet)
Algebraic Expressions – a combination of numbers, variables, and operation signs
Substitute – to replace a variable by a number
Evaluate – substitute and simplify
Translations:
English phrases meaning addition:
The sum of x and 7
x+7
y more than 2
2+y
x increased by y
x+y
English phrases meaning subtraction:
9 less than x
x–9
x minus 4
x–4
subtract 11 from y
y – 11
the difference of x and y
x–y
the value after w is subtracted from 58 58 – w
a number decreased by 11
x – 11
English phrases meaning multiplication:
3 times y
3(y) or 3y
x multiplied by 3
3(x) or 3x
the product of 4 and y
4y
x squared or the square of a number
x2
x cubed or the cube of a number x 3
twice a number
2x
ex. 7 x 2  8 y
English phrases meaning division:
x divided by 6
x ÷ 6 or
the quotient of x and y
x
6
x
y
a number divided into 16
16
x
Translate to algebraic expressions:
1. 76 more than a number
2. A number squared less than 48
3. The difference of 4 more than a number and 7
4. Subtract twice a number from 36
5. The quotient of 3 less than a number and 15
6. The product of a number divided by 3 and 4
7. A number divided into that same number increased by 4
8. The quotient of 3y 2 and the difference of 2x and 5y
Evaluate:
9.
10.
3  4 x2   5  y  7 
for x  2 and y  9
5x2  3  x  y 
for x  3 and y  5
7
Section 3.2 Equations and Formulas
Equation – states that 2 expressions are equal, with an equal sign,”=”, separating the two sides or
members of the equation
Solution – a number that makes the equation true, when it is substituted for the variable
Formula – an equation that describes a relationship between two or more quantities
Evaluate:
11. Is 8 a solution of
2 x2  3x  4  x  18 ?
12. Is 15 a solution of
3x  5
 25  x ?
10
Evaluate:
13.
14.
A
s
P
4
bh
2
if b = 7 inches and h = 4 inches
if P = 256 inches
(Area of a triangle)
(side of a square)
Section 3.3 Adding and Subtracting Polynomials (Whole Numbers)
Terms – numbers (or numbers multiplied by one or more variables) that are added.
Constant – a term without a variable.
Monomial – a term that contains a number, a variable, or combined numbers and variables with no
variable occurring in a denominator. Ex. 3x
Binomial – a polynomial with two terms
Ex. 4x + 7
Trinomial – a polynomial with three terms Ex. 9 x 2  7 x  1
Polynomials – monomials or sums or differences of monomials.
Coefficient – the numerical factor of a term. Ex. in 3x, 3 is the coefficient.
Like Terms – have precisely the same variable factors (same variables (if any) to the same power.)
Combine Like Terms – adding or subtracting the like terms
For the algebraic expression 16x + 5 define the:
15. constant
16. numerical coefficient
17. two factors
18. two terms
Simplify:
19. 32p  16p + 10p =
20. 26y + 18y  18y =
Add or subtract the polynomial:
21. Find the difference of (32a + 57b + 49c) and (12a + 45b + 18c)
22.
 92 x
23.
 45x  69 y    26x  12 y 
2
 16  34 x    51x 2  71x  81
Section 3.4 Multiplying and Dividing Polynomials (Whole Numbers)
Find the product of:
24.
 5x y 15x y 
4
6
9
5

25. 2 x5 y 3 14 x 2 y 5  12 y 20

26. 20 x 4 16 xy 7  12 xy 7


Translate and simplify:
27. The product of 10xy 2 and the difference of 11x3 and 8x 4 y 7
Multiply:
28.
 4x  12 7 x  10
29. 13x  6 5x  9
Divide:
30.
39 x5 y12  63x 4 y10  15x3 y 2
3x3 y 2
31.
26 x 2 y 2  13x 4 y 5  65x6 y 9
13x 2 y
Story Problem
Write an expression:
32. Joel opened up a new savings account. He makes an initial deposit of $2000 and then plans
to make deposits of $300 per month. Write an expression to describe how much he will have
saved after x months. (Ignore interest.)
Section 3.5 Solving Equations of the Form x + a = b or x – a = b
Equivalent equations – equations with the same solutions
Solving an equation – finding replacements for the variable that make the equation true.
Symmetric property of equality:
If x = a then a = x, that is the sides of an equation may be interchanged.
Properties of Equality for Addition and Subtraction:
Adding the same number to both sides of an equation yields an equivalent equation:
If a = b, then a + c = b + c
Subtracting the same number from both sides of an equation yields an equivalent equation.
If a = b, then a – c = b – c
Use the equality properties to solve for p:
33. p – 45 = 24
34. 165 + p = 178
Section 3.6 Solving Equations of the Form ax = b or x / a = b
Properties of Equality for Multiplication and Division:
Multiplying the same number times both sides of an equation yields an equivalent equation:
if a = b, then ac = bc
Dividing the same number into both sides of an equation yields an equivalent equation:
if a = b, and c ≠ 0 then
Solve for y:
35. 9y = 441
36. 429 = 3y
a b

c c
Solve for x:
37.
x
8
24
38. 27 
x
5
Section 3.7 Solving Equations of the form ax + b = c or ax – b = c
Solve for x:
39. 16x + 56 = 88
40. 44 = 42 + 6x  4x  12
41. 15x + 3(x  2) = 30
42. 30 = 15 +
x
4
Story Problems:
43. If 95 cows produce an average of 760 gallons of milk a day, how many gallons does one cow
produce on average each day? Let g be the average number of gallons of milk produced by one
cow in one day. Write an equation that describes this relationship and solve it.
44. Marcus is trying to calculate how much he can spend each day on food and entertainment
expenses on his vacation. He has $1225 to spend in total for the whole vacation. He needs to
use $350 for plane fare. If he plans on spending the same amount of money each day, how much
can he spend each day of his 7 day vacation? Write an equation and then solve it.
Answers to Math 090 Exam 2 Review
1. x + 76
2.
48  x 2
3. (x + 4)  7
23. 19x + 57y
24. 75x13 y11
25. 28 x7 y8  24 x5 y 23
4.
36  2x
5.
x3
15
6.
x
  (4)
3
28. 28 x 2  124 x  120
7.
x4
x
29. 65 x 2  147 x  54
8.
3y2
2x  5 y
30. 13x 2 y10  21xy8  5
26. 80x5 y 7

27. a. 10xy 2 11x3  8 x 4 y 7

b. 110 x 4 y 2  80 x5 y 9
9. 58
31. 2 y  x 2 y 4  5 x 4 y8
10. 3
32. 2000 + 300x
11. Yes
33. p = 69
12. No
34. p = 13
13. 14 in.2
35. y = 49
14. 64 in.
36. y = 143
15. 5
37. x = 192
16. 16
38. x = 135
17. 16, x
39. x = 2
18. 16x, 5
40. x = 7
19. 26p
41. x = 2
20. 26y
42. x = 60
21. 20a+12b+31c
43. 95x = 760, 8 gallons
22. 143x 2  105 x  97
44. 350 + 7x = 1225, $125 a day