Statement Tree Math Exercise

MIDTERM EXAM REVIEWName:____________________________________
Date:_______________
1. Write a word description of each set.
a. {April, August}
Solution: The sets of Months that begin with A.
2. Write ⊆ or ⊄ in each blank so that the resulting statement is true.
a. {-4, 0, 4}___⊄__{-4, -3, -1, 1, 3, 4} because 0 is not included in {-4, -3, -1, 1, 3, 4}
3. In the following exercise, let
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 3, 5, 7}
B = {1, 2, 3}
C = {2, 3, 4, 5, 6}
a. Find B ∩ C = {2, 3} because these are the common numbers in B and C.
b. Find A ∪ B = {1, 2, 3, 5, 7} because these are all the numbers in A and B.
4. Determine whether the following sentence is a statement or not a statement.
Is this the best of all possible worlds? Not a Statement. Because it is a question
5. Form the negation of the following statement.
It is not true that Albert Einstein was offered the presidency of Israel.
Solution: opposite: It is true that Albert Einstein was offered the presidency of Israel
6. In the following exercise, let p and q represent the following statements:
p: 4 + 6 = 10 T
This statement is true because 4 + 6 = 10.
q: 5 x 8 = 80 F
This statement is False because 5 x 8 = 40.
a. Determine the truth value of ~p.
Solution: F because ~ means the opposite of p.
p ~p
T F
7. Use the order of operations to find the value of each expression.
a. -5 + (-3) . 8 = -5 + (-24) = -5 – 24 = -29
8. Convert the following mixed number to an improper fraction.
2 7/9
= 9 x 2 + 7 = 25
9
9
9. Convert the following improper fraction to a mixed number.
The integer is 5 because 8 goes 5 times into 47
47 = 5 7/8
The remainder 7 goes in the denominator of the mixed fraction
8
The denominator is the same
Perform the indicated operations. If possible, reduce the answer to its lowest terms.
10a. 5
8
.
3 = 15
11
88
11a. 5 + 2 = 7
13 13 13
12. Perform the indicated operation. Simplify the answer when possible.
a. √5 . √5 = √25 = 5
13. Use properties of exponents to simplify each expression. First express the answer in
exponential form. Then evaluate the expression.
a. 38 = 38-4 = 34 = 81
34
14. Express each number in decimal notation.
a. 4.7 X 103 = 4,700
b. 3.14 X 10-2 = 0.0314
15. Express each number in scientific notation.
a. 2700 = 2.7 X 103
b. 0.00083 = 8.3 X 10-4
16. Write the first six terms of the arithmetic sequence with the first term, a1, and
common difference, d.
Because in Arithmetic Sequence you Add d
a.
a1 = 5, d = 3 5, 8, 11, 14, 17, 20 you add 3 by each term starting with a1=5
17. Write the first six terms of the geometric sequence with the first term a1, and common
ratio, r.
Because in Geometric Sequence you Multiply by r (ratio)
a. a1 = 2, r = 3
2, 6, 18, 54, 162, 486 you multiply 3 by each term staring with a1=2
The set of real numbers is composed by rational and irrational numbers. List all the
numbers from the given set that are:
_
{-9, 5/6, 0, 1.3, √5, π, 6, √64}
18. Natural Numbers: N = {6, √64} Natural number are counting numbers, not
decimals
19. Integers: Z = {-9, 0, 6,
√64} Integers include whole numbers and the negative of
the natural numbers, for example: {…, -3, -2, -1, 1, 2, 3, …}
20. Whole Numbers: W= {0, 6, √64} Whole Numbers include the natural numbers
and 0.
21. Evaluate the algebraic expression for the given values of the variables
3×2 + 2xy + 5y2
x = 2, y = 3
3(2) 2 + 2(2)(3) + 5(3)2
3(4) + 2(2)(3) + 5(9)
12 + 12 + 45
69
22. Simplify the following algebraic expression
4(2y – 6) + 3(5y + 10)
8y – 24 + 15y + 30
8y + 15y + 30 – 24
23y + 6
23. A number decreased by 20 is equal to 500. What is the number?
x – 20 = 500
x = 500 + 20
x = 520
24. A number increased by 20 is equal to 500. What is the number?
x + 20 = 500
x = 500 – 20
x = 480
25. Solve the quadratic equation x2 + 7x -18 = 0 by factoring.
(x + 9)(x – 2) = 0
x1 = -9 x2 = 2
26. Graph the equation y = x – 2 Select integers for x from -3 to 3, inclusive.
x
-3
-2
-1
0
1
2
3
y
-5
-4
-3
-2
-1
0
1
y = (-3) – 2 = -5
y = (-2) – 2 = -4
y = (-1) – 2 = -3
y = (0) – 2 = -2
y = (1) – 2 = -1
y = (2) – 2 = 0
y = (3) – 2 = 1
27. Evaluate f (x) for the given value of x. Then use the ordered pairs from your table to
graph the function.
f (x) = x2 – 1
x
-2
-1
0
1
2
f (x2 – 1)
3
0
-1
0
3
f(-2) = (-2)2 – 1 = 3
f(-1) = (-1)2 – 1 = 0
f(0) = (0)2 – 1 = -1
f(1) = (1)2 – 1 = 0
f(2) = (2)2 – 1 = 3
28. Use a vertical line to identify graphs in which y is a function or not a function of x.
Figure A
Figure B
A. ___Function_________
B. ___Not a Function__
29. Calculate the slope of the line passing through the given points (2, 6) and (3, 5). Use
the formula:
m=
y2 – y1 = _5 – 6 = -1
x2 – x1
3–2
1
= -1
30. Graph the linear function using the slope and y-intercept.
y = 1x + 3
2
31. Express the following fraction as a percent.
3 = 0.75 x 100 = 75%
4
32. Express the following percent as a decimal.
72% = 72/100 = 0.72
33. Find the simple interest owed for the use of money. Use the formula I = Prt
Principal = $4000, rate = 6%, time = 1 year
I = Prt = 4000 X 0.06 X 1 = $240
34. In the following exercise, the principal, $10000 represents and amount of money
deposited in a savings account subject to compound interest rate of 4% annually. Find
how much money there will be in the account after 2 years. Then, find the interest earned.
Use the formula A = P (1 + r) t
A = 10000 (1 + 0.04)2 = 10000 (1.04)2 = 10000 X 1.0816 = $10816
Interest Earned 10816 – 10000 = $816
35. Use the given figure to find the area in square units. Use the formula A = s 2
4 in
A = (4)2 = 16 square inches
4 in
36. Use the given figure to find the volume in cubic units. Use the formula V = WLH
5 cm
3 cm
V = 3 X 5 X 4 = 60 cubic centimeters.
4 cm
37. Convert the given unit of weight to the unit indicated. Use (kg hg dag g dg cg mg)
74 kg to g = 74,000 g
38. Convert the given unit of weight to the unit indicated. Use (kg hg dag g dg cg mg)
342 mg to g = 0.342 g
39. Convert 10ºC from ºC to ºF. Use the formula F = 9 C + 32
5
F = 9/5 C + 32 = 1.8C + 32 = 1.8(10) + 32 = 18 + 32 = 50
40. Convert 68ºF from ºF to ºC. Use the formula C = 5 (F – 32)
9
C = 5/9 (F – 32) = 5/9 (68 – 32) = 5/9 (36) = 20