AFM Unit 1 Test
Counting principal problems
1. A restaurant offers four sizes of pizza, two types of crust, and eight
toppings. How many possible combinations of pizza with one topping are
there?
2. You are taking a 10 question true or false quiz. If you have no idea of any of
the answers, how many different ways can the quiz be answered?
Permutation and combination problems
3. An election ballot asks voters to select three city commissioners from a
group of six candidates. In how many ways can this be done?
4. For a segment of a radio show, a disc jockey can play 7 songs. If there are
12 songs to select from, in how many ways can the program for this
segment be arranged?
5. The ski club with ten members is to choose three officers captain, cocaptain & secretary, how many ways can those offices be filled?
Conditional probability problems
Use the chart to answer questions 6 and 7
Blue
Brown
Green
Total
Male
19
43
13
75
Female
32
78
15
125
Total
51
121
28
200
6. What is P (Female | Blue)?
7. What is P (brown | Male)?
(A standard pack of cards contains 52 cards. 26 are red (diamonds and hearts), 26
are black (clubs and spades), each suit has 13 cards with three picture cards in
each suit)
8. A single card is drawn from a standard deck of 52 cards. Find the probability it is
an ace, given it is a black card.
9. At a high school 18% of the students play football and basketball, and 32% of all
students play football. What is the probability that a student plays basketball given
that the student plays football?
Expand the following binomials
10. (𝑥 + 2)4
11. (2𝑥 − 2)3
Solve the equations by factoring
12.
𝑥 2 - 4x – 32 = 0
13.
3𝑥 2 - 15x + 12 = 0
Solve the equations using the quadratic formula
14.
𝑥 2 +6x – 16 = 0
15.
3𝑥 2 - 8x - 16 = 0