In-Class Review Packet for Mid Term (Foundations of Algebra)
Show your work on each question to recieve credit. Circle your solutions and work hard. Remember: this is a grade! If you do do have enough space, work your problems on a seperate sheet and attach for credit.
UNIT 1 (Questions 1-14)
1To which subsets of the real numbers does the number belong?
2An office building is 111 ft high. About how tall is this in meters?
3A car is driving at a speed of 40 mi/h. What is the speed of the car in feet per minute?
4On a certain day 1 US dollar is equivalent in value to 90 Japanese yen. Lucy is going on a trip to Japan. She has $900 to spend. How many yen is this?
5Multiply –2x2(–5x2 + 4x3)
6Multiply then simplify the radical
7Write in standard form, then name the polynomial based on its degree and number of terms
2 – 11x2 – 8x + 6x2
8Subtract (–7x – 5x4 + 5) – (–7x4 – 5 – 9x)
9Add. (8u3 + 2u2 + 7) + (3u3 – 7u + 8)
10Multiply.
11Simplify the radical
12Simplify the Radical
13Simplify the radical
14Subtract
UNIT 2 (Questions 15-40)
15Solve for x.
16What equation do you get when you solve for x?
17Solve.
18The total cost to rent a row boat is $16 times the number of hours the boat is used. How long can you rent the boat for $224?
19Sove the equation , for U
20Steven wants to buy a $540 bicycle. Steven has no money saved, but will be able to deposit $40 per week into a savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he must give his sister $60 that he owes her. For how many weeks will Steven need to deposit money into his savings account before he can pay back his sister and buy the bike?
21 A copy center offers its customers two different pricing plans for black and white photocopies of 8.5in. by 11in. pages. Customers can either pay $0.08 per page or pay $7.50 for a discount card that lowers the cost to $0.05 per page. Write and solve an equation to find the number of photocopies for which the cost of each plan is the same.
a. Write the equation
b. Solve the equation to determine the number of photocopies for which the cost of each plan is the same.
22Solve and graph the solution to the inequality on a number line.
23Solve the inequality and graph the solution on a number line. –2m < –14
24For , .
25Determine the domain and range and whether or not the relation is a function.
26
Find
27Deterimine the Slope of the line
28Write the equation of the line in the graph below.
29Write the equation of the line that contains the following coordinates: (4, 7), (8, 2)
30Write the equation of a line that is parallel to y = x – 5 and passes (–1, –14)?
31Graph the equation
32Write an equation of a line that is perpendicular to
y = x and passes (–1, 5)?
33The recursive formula for a sequence is , . Write the explicit rule for the sequence and find the 30th term.
34Write an explicit formula for the sequence 9, 5, 1, –3, –7
35Write an explicit formula for the sequence 7, 3, –1, –5, –9, ... Then find .
36Solve by substitution.
37Solve the system by graphing.
y = x + 5
y = –5x – 1
38What is the solution to the system? Use Elimination
39Graph the inequality . List two ordered pairs that are solutions.
40Graph the system of inequalities . List two ordered pairs that are solutions
UNIT 3 (Questions 41-50)
41Factor. x2 + 12x + 20
42Factor using the GCF. 54c3d4 + 9c4d2
43What is the factored form of the expression ?
44Factor.
45Factor completely.
46Find the solutions to the equation
47Find the zeros of the function by factoring.
48Complete the square for the expression ____. Write the resulting expression as a binomial squared.
49Find the zeros of by using the Quadratic Formula.
50Find the zeros of by completing the square.
In-Class Review Packet for Mid Term (Foundations of Algebra)
Answer Section
SHORT ANSWER
1irrational numbers
233.84 m
33,520 ft/min
481000 yen
5–8x5 + 10x4
6
7–5x2 – 8x + 2; quadratic trinomial
82x4 + 2x + 10
911u3 + 2u2 – 7u + 15
10
11
12
13
14
151
16
1712
1814 hours
19
2015 weeks
21;
22
23m > 7
246
25Domain: {x| 8 x ; Range: all real numbers; No, it is not a function.
26
27
28y = x 1
29y = x
30y = x – 10
31
32y = x
33f(n) = 10n - 13
f(30) = 287
34; –43
35; –45
36
37
38(–5, –20)
39
40
41(x + 10)(x + 2)
429c3d2(6d2 + c)
43
44
45
46
47 or
48
49
50–3 and 1