Module 1
Consider this sequence: 10, 7.5, 5, 2.5, ...
What is the equation and 201st term?
an = 12.5 – 2.5n
-490
The sum of four consecutive natural numbers is 470. What are the four numbers?
116, 117, 118, 119
Hamid is a bookseller. He sells “bundles” of books (where each bundle contains 20
books). Sometimes he allows a sale of a “halfbundle”. Here is his data for sales last
week:
Day # Bundles Sold
Sun 3
Mon 2
Tue 2
Wed 2
Thu 1.5
Fri 4
Sat 5.5
What is the average number of books he sold each day last week?
60 books each day (on average)
Carrie has a five-spinner as shown at the right (five equal regions)
and a fair 4-sided tetrahedral die. Her process (experiment) is as follows:
> Spin the spinner, and
> Toss the die
a) What are all the possible outcomes of this experiment?
b) Carrie then counted up all the occurrences of a vowel with an even number.
Write down the outcomes that would be included in that event.
a) (A, 1 ) (A, 2 ) (A, 3) (A, 4)
(B, 1 ) (B, 2 ) (B, 3) (B, 4)
(C, 1 ) (C, 2 ) (C, 3) (C, 4)
(D, 1 ) (D, 2 ) (D, 3) (D, 4)
(E, 1 ) (E, 2 ) (E, 3) (E, 4)
b) (A,2)(E,2)(A,4)(E,4)
At a carnival game, you have a 10% chance of winning 10.00 $, a 30% chance of
winning 5.00 $, and a 60% of winning 1.00$.
i) What is the expected value for this game?
ii) If the game costs 4.00 $ to play, then what is the expected average loss ?
i) $3.10
ii)$ - 0.90
Consider this sequence: 5, -15, 45, -135, ...
What is the equation and 8th term?
an = 5*( -3 )n - 1
-10935
Consider this function which accepts ordered pairs of Natural Numbers (x,y) as inputs: F(x, y) = 6x + 3y
(i) For each of the following inputs, find the corresponding output:
a) (3, 7) b) (4, 6)
c) (5, 2) d) (2, 5)
a)39
b)42
c)36
d)27
Of 120 stores in Spokane, the “MathStore” was at the 65th percentile in terms of
most money made in gross sales. How many stores had gross sales equal to or less than
the “MathStore”
78 stores made less (or equal)
The box has three Red and two Green marbles. You reach in and draw out a marble,
look at it, and put it back in the box (this is Draw 1). After remixing, you reach in and
draw out a marble again (this is Draw 2 ). What is:
i) P (Both marbles were Red )
ii) P( Both marbles were Green )
iii) P(Colors of both marbles Match)
i) 9/25
ii) 4/25
iii) 13/25
A publishing company shows that most books lose money! In fact, here’s the table for all books
published by the company last year:
Money Made/Lost Percentage of All Books
-1000$ 25%
-2500$ 40%
-5000$ 20%
+20000$ 15%
As you can see, the majority of books lose money! But some are very profitable. So, what’s the
expected earnings for this company?
$750
Find the first three terms of an arithmetic sequence if the 97th term is 473 and the 121st term is 593.
7, -2, 3
Consider the following two functions: f(x) = 6x + 7 and g(x) = -3x
(i) Find the (f o g)(x) for if x =
a) 4
b) -5/7
a) (f o g)(4) = -65
b)(f o g)(-5/7) = 139/7
A herd of 250 cows was taken, and each cow was weighed. How many cows had
weights that were between the 22nd and 68th percentiles?
115 cows
68-22=46%
.46*250=115
There is a four-pack of batteries. Unbeknownst to you, one these batteries is bad.
The other three are good. You randomly take out one battery (this is Draw 1),
keep it, and then you randomly take out another battery (this is Draw 2). What is:
i) P (Draw 2 is Bad)
ii) P (Draw 2 is Good)
iii) P (Both batteries are Good)
i) 3/12
ii) 9/12
iii) 6/12
A publishing company shows that most books lose money! In fact, here’s the table for all books
published by the company last year:
Money Made/Lost Percentage of All Books
-1000 $ 25%
-2500 $ 40%
-5000 $ 20%
+ (X) $ 15%
As you can see, the majority of books lose money! But some are very profitable, currently listed as the
“+ (X) $” above. Let’s call that (X) the target of money made for the profitable books.
If the company wants it’s expected earnings to be 1401 $, then what should be the value of (X) ?
(X $) = 24340
Find the first term in a geometric sequence if the 9th term is -26244 and the common ratio is (-3/8)
a1 = -67108864
Find equations for each of the following lines:
i) The line containing P: (-8, -1) and parallel to
L: -3x = 6 – 7y
ii) The line containing P: (-2, 1) and perpendicular to
L: 5x – 3y = 6
i) Original equation: y = (3/7)x + (6/7)
New equation: y = (3/7)x + (17/7)
ii)Original equation: y=2-x(5/3)
New equation: y = (-3/5)x + (-1/5)
There are 6 exams, and the average score for these exams is 88. Four of the
exam scores are 98, 86, 84, and 70. The other two exams have the same
score, which is ______ ?
95
Spinner A has 4 equal sectors: Two sectors are Red, One is Blue, & One is Black.
Spinner B has 3 equal sectors: One is Gray, One is Green, and one is Red.
You spin A and then you spin B. What is:
i) P ( [Spinner A is Blue] & [Spinner B is Red])
ii) P ( [Spinner A is (Blue or Black)] & [Spinner B is Green] )
iii) P ( [Spinner A is Red] or [Spinner B is Red] )
i) 1/12
ii) 2/12
iii) 8/12
There are 6 identical Math books and 12 identical English books.
i) How many different ways can these books be lined up on the shelf?
ii) How many different ways can they be lined up if the first book must be an English book?
i)(18C6)*(12C12)= 18564
ii)(1)*(17C11)*(6C6)= 12376
In a small town, three children deliver all the newspapers. Abby delivers 3 times as many papers as Bob, and Connie delivers 13 more papers that Abby. If the three children deliver a total of 496 papers, how
many papers does each deliver?
A = 207, B = 69, C = 220
Find equations for each of the following systems, if possible. Indicate whether the system has a unique
solution, infinitely many solutions, or no solution.
i) 40 – 5y = 12x
24x + 10y = -10
ii) 2y – 3x = 10
4.5x + 15 = 3y
iii) 5y – 3x = 1
3x – 5 = 2y
i) No Solution
ii) Infinitely Many Solutions
iii) (3,2)
Vanessa drives from A to B at 50mph. She returns along identical route at 60mph.
What is average speed for overall trip?
Depends on how long you chose the route to be.
TBD by Kortnei:
Total distance/ total time
Hunter says she is itchy. There is a test for Allergy to Cats, but this test is not always right. Here are our
assumptions:
(usually you pick your own population but for this purpose the population is 10000)
i) We know that only 1% of the population has Allergy to Cats.
ii) For people that really do have the allergy, the test says "Yes" 80% of the time.
iii) For people that do not have the allergy, the test says "Yes" 10% of the time.
If Hunter's test says "Yes", then what are the chances that Hunter really has the allergy?
P(Allergic | Test “Yes” ) = 80/1070 ≈ 7.48%
Eight club members decide to choose officers at random. They need a President, Vice President, and
Treasurer.
i) How many ways are there to do this?
ii) What is the probability that club member Heidi is chosen to be an officer?
ii) 3/8
(1*7*6+1*7*6+1*7*6/ 8P3)