Advanced Algebra Spring Final Review
1) Find the first four terms of the arithmetic sequence an = 3n + 4
2) Find the common difference of the arithmetic sequence 20, 13, 6, -1, -8…
3) Find a7 given an =
(𝑛+4)!
(𝑛+2)!
4) Write the first four terms of the arithmetic sequence defined by the recursion formula
given: a1 = 5 and an = (2n - 1)an-1
(𝑛+1)!
5)
Find the sum of the finite series: ∑4𝑛=1
6)
Using an = a1 + (n – 1)d, find the 80th term of the arithmetic sequence 3, 20, 37, 54…….
𝑛!
7) Find the 10th term of the geometric sequence 160, -40, 10, -2.5… using an = a1 •(r)n-1.
Find the first derivative, the second derivative and evaluate at the given point.
8) f(x) = x3, x = -3
9) f(x) = 5x4, x = 5
10)f(x) = 5x2 - 8x + 4, x = -6
11) f(x) = 2x 4 - 4x 3 + 6x2 – 12x + 5, x = -1
12) An apartment complex has 300 apartments to rent. The profit is given by the equation
P(x) = -3x2 +1296x – 50000 where x is the number rented per month. How many
apartments should the company rent per month to maximize profit?
13)
1
3
5
÷ =
4
14)
17) What is 15% of 1200?
3
10
7
× =
8
15)
7
10
18) 23 is what % of 92?
1
− =
4
16)
2
3
1
+ =
4
19) 30% of what number is 27?
20) What is the percent increase from 40 to 60?
21) What is the probability of selecting a 3 a 4 or a heart from a deck of cards?
22) There are 10 green marbles, 15 red marbles and 25 blue marbles in a bag. What is the
probability of selecting a blue marble, not replacing it, and selecting another blue marble?
23) Steven has 12 dress shirts, 10 ties and 6 pairs cuff links. How many different shirt-tie-cuff
links combinations can he make if he selects one of each?
24) Mrs. Lee’s class must elect 6 representatives for student council. There are 16 students in
her class. How many ways can this be done?
25) How many different ways can 8 competitors come in first, second and third place in a race?
26) How many different ways can you order 10 DVDs?
27) Simplify: (15 – 1)2 - 24 ÷ 6
28) Given a = 3, b = -2, c = 4, evaluate the following: 5(𝑐 − 2)2 − 6𝑎 + 𝑏
29) Solve: 2n - 7 = 4(n - 5) + 5
30) Solve: 4(3n – 8) + 4 ≥ 11𝑛 − 7
31) Find the slope between (2, 6) and (-7, -3)
32) Simplify: (3√5) (6√20)
33) Multiply: (x – 4)(3x + 2)
Formulas:
nPr
=
𝒏!
(𝒏 − 𝒓)!
(no repetition, order matters)
nr (repetition is allowed, order matters)
nCr
=
nCr
=
𝒏!
𝒓!(𝒏 − 𝒓)!
(no repetition, order does not matter)
(𝒏 + 𝒓 − 𝟏)!
𝒓!(𝒏 − 𝟏)!
(repetition is allowed, order does not matter)