A: 56
Solution:
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Term
PROBABILITY
How to solve probability problems must be multiplied?
When all the outcomes are all equally likely, the basic formula is:
Probability = (# of favorable outcomes)/(#of possible outcomes)
Q: If 2 studnets are chosen at random to run an errand from a class with 5 boys and 5 girls, what is the probability that both students chosen will be girls?
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Definition
A: 2/9
Explanation: The probability that the 1st student chosen will be a girl is 5/10=1/2, and since there would be 4 girls and 5 boys left out of 9 students, the probabilitiy that the 2nd student chosen will be a girl (given that the first student chosen is a girl) is 4/9. Thus the probability that both students chosen will be girls is (1/2)x(4/9)=2/9
***There was a conditional probability here because the probability of choosing a second girl was affected by another girl being chosen first. |
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PROBABILITY (Q 2)
How to solve probability problems must be multiplied?
When all the outcomes are all equally likely, the basic formula is:
Probability = (# of favorable outcomes)/(#of possible outcomes)
Q: In a fair coin is tossed 4 times, what's the probability that at least 3 of the 4 tosses will be heads. |
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Definition
A: 5/16
Setup:There are 2 possible outcomes for each toss, so after 4 tosses, there are 2x2x2x2=16 possible outcomes.
We can list the different possible sequences where at least 3 of 4 tosses are heads, these sequences are:
HHHT
HHTH
HTHH
THHH
HHHH
Thus the probability that at least 3 of the 4 tosses will come up heads is (# of favorable outcomes)/(#of possible outcomes) = 5/16 |
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Term
STANDARD DEVIATION
How to deal with standard deviation?
Standard deviation is a measure of how spread out a set of numbers is (how much the numbers deviate from the mean). The greater the spread, the greater the standard deviation.
How to calculate:
1. Find the average of the set.
2. Find the differences between the mean and each value in the set.
3. Square the differences.
4. Find the average of the squared differences.
5. Take the positive square root.
Q:
High temperatures, in Farenheit, in two cities over 5 days:
September 1 2 3 4 5
City A 54 61 70 49 56
City B 62 56 60 67 65
For the 5 day period listed, which city had the greater standard deviation? |
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Definition
A: City A (standard deviation = 7.1)
City A = √(254/5) =7.1
City B = √(74/5) =3.8 |
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Term
POWERS
How to multiply with exponent powers?
Q: xa • xb = ?
Q: 23 • 24 = ?
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Definition
A: xa • xb = xa+b
A: 23 • 24 =27
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Term
POWERS
How to divide with exponent powers?
Q: xc/xd = ?
Q: 56/52 = ? |
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Definition
A: xc/xd = xc-d
A: 56/52 = 54 |
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Term
POWERS
How to handle a value with an exponent raised to an exponent?
Q: (xa)b = ?
Q: (34)5 = ? |
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Definition
A: (xa)b = xab
A: (34)5 = 320 |
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Term
POWERS
How to handle powers with a base of 0?
Q: 04 = ?
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Definition
A: 04 = 0
04 = 012 = 01 = 0
Any non-zero number raised to the exponent 0 equals 1. |
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Term
POWERS
How to handle powers with an exponent of 0?
Q: 30 = ?
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Definition
A: Q: 30 = 1
30 = 150 = (.34)0 = (-345)0 = ∏0 = 1
All numbers raised to the 0 power equal 1, except 00 which is undefined. |
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Term
POWERS
How to handle negative powers?
Q: n-1 = ?
Q: n-2 = ?
Q: 5-3 = ?
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Definition
A: n-1 = 1/n
A: n-2 = 1/n2
[image]
A number raised to the exponent -x is the reciprocal of that number raised to the x exponent. |
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Term
FRACTIONAL POWERS
How to handle fractional powers?
Q: x1/2 = ?
Q: x1/3 = ?
Q: x2/3 = ?
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Definition
Answers (separated by commas)
[image]
Note: as seen above, fractional exponents relate to roots. |
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Term
CUBE ROOTS
How to handle cube roots?
[image] |
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Definition
[image]
A1: -5 • -5 • -5 = -125
A2: 1/2 • 1/2 • 1/2 =1/8 |
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Term
ROOTS
How to add and subtract roots?
√2 + 3√2 = ?
√2 - 3√2 = ?
√2 + √3 = ? |
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Definition
√2 + 3√2 = 4√2
√2 - 3√2 = -2√2
√2 + √3 = cannot be combined
***Note: You can add/subtract roots only when the parts inside the √ are identical. |
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Term
ROOTS
How to multiply and divide roots?
(2√3)(7√5) = ?
[image] |
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Definition
A: (2 • 7)(√3 • √5) = 14√15
[image]
***Note: to multiply/divide roots, deal with what's inside the √ and outside the √ separately. |
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Term
RADICALS
How to simplify a radical?
Q: √48 = ?
Q: √180 = ? |
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Definition
A: √48 = √16 • √3 =4√3
A: √180 = √36 • √5 = 6√5
***Note: look for factors of the number under the radical sign that are perfect squares; then find the square root of those perfect squares. Keep simplifying until the term with the square root sign is as simplified sas possible: there are no other perfect square factors (4, 9, 16, 25, 36, etc.) inside the √. Write the perfect squares as separate factors and "unsquare" them. |
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Term
RADICALS
List all perfect squares up to 100.
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Definition
- 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
- 02 = 0, 12 = 1, 22 = 4, 32 = 9, 42 = 16, 52 = 25, 62 = 36, 72 = 49, 82 = 64
- 92 = 81, 102 = 100, 112 = 121, 122 = 144
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Term
QUADRATIC EQUATIONS
How to solve quadratic equations?
Solve:
1. x2+6=5x
2. x2=9
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Definition
1. x2+6=5x
x2-5x+6=0
(x-2)(x-3)=0
x-2=0 or x-3=0
x = 2 or 3
2. x2=9
x = 3 or -3
Notes: Manupulate the equation if necessary into the "_____=0" form, factor the left side (reverse FOIL by finding two numbers whose product is the constant and whose sum is the coeffecient of the term without the exponent), and break the quadratic equation into two simple expressions. Then find the value(s) for the variable that make either expression 0.
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Term
MULTIPLE EQUATIONS
How to solve multiple equations?
Q: if 5x-2y = -9 and 3y-4x = 6, what is the value of x+y?
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Definition
A:
5x-2y = -9
+[-4x+3y = 6]
x + y = -3
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Term
SEQUENCES
How to solve a sequence problem?
Q: What is the difference between the fifth and fourth terms in the sequence 0, 4, 18,... whose nth term is n2(n-1)?
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Definition
A: 52
Setup: Use the definition fiven to come up with the values for your terms:
n5 = 52(5-1) = 25(4) = 100
n4 = 42(4-1) = 16(3) = 48
So the positive difference between the 4th and 5th terms is 100-48 = 52 |
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Term
FUNCTIONS
How to solve a function problem?
Q: What is the minimum value of x in the function f(x)=x2-1?
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Definition
A: the minimum is -1
Explanation: In the function f(x)=x2-1, if x is 1, then f(1)=12-1=0. In other words, by inputting 1 into the function, the output f(x)=0. Every number inputted has one and only one output (although the reverse is not necessarily true). You're asked to find the minimum value so how would you minimize the expression value f(x)=x2-1? Since x2 cannot be negative, in this case f(x) is minimized by making x=0: f(0) = 02-1=-1, so the minimum value of the function is -1.
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Term
LINEAR EQUATIONS
How to handle linear equations?
Q: What is the common expression of linear equations? |
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Definition
A: y=mx+b
m=slope of the line = rise/run
b=the y-intercept
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Term
INTERCEPTS
How to find the x- and y-intercepts of a line?
Q: What are the x- and y-intercept for the equation y=-(3/4)x+3
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Definition
A: x-intercept = 4
y-intercept =3
solving for x
0=-(3/4)x+3 <-divide both sides by 3/4
0=-x+4
x=4 |
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Term
TRIANGLE
How to find the maximum and minimum lengths for a side of a triangle?
Q: The length of one side of a triangle is 7. Yhr length of another side is 3. What is the possible range of possible lengths for the third side?
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Definition
A: between 4 and 10
The third side is greater than the difference (7-3=4) and less than the sum (7+3=10) |
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Term
ANGLES
How to find one angle or the sum of all the angles of a regular polygon?
Q: What is the equation for the sum of the interior in a polygon with n sides?
Q: What is the equation for the degree measure of one angle in a regular polygon with n sides? |
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Definition
A: (n-2)x180
A: ((n-2)x180)/n
***Note: The term regular means all angles in the polygon are of equal measure. |
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Term
CIRCLES/ARCS
How to find the length of an arc?
Q: What is the equation for determining the length of an arc?
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Definition
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Term
CIRCLES
How to find the area of a sector?
Q: What is the equation for determing the area of a secotr?
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Definition
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Term
CIRCLES/FIGURES
If the area of the square is 36, what is the circumference of the circle?
[image] |
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Definition
A: circumference = ∏(diameter) = 6∏√2
To get the circumference, you need the diameter or radius. The circle's diameter is also the square's diagonal. The diagonal of the square is 6√2. This is because the diagonal of the square transforms it into two separate 45˚-45˚-90˚ triangles. So the diameter is 6√2.
[image] |
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Term
RECTANGLES
How to find the volume of a rectangular solid?
Q: What is the equation to find the volume of a rectangular solid? volume = ?
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Definition
| A: volume=length x width x height |
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Term
RECTANGLES
How to find the surface area of a rectangular solid?
Q: surface area = 2(lw)+2(wh)+2(lh)
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Definition
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Term
CYLINDER
How to find the volume of a cylinder?
Q: volume of a cylinder = ?
Q: what is the volume if r=6 and h=3 |
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Definition
A: volume = area of base x height =
∏r2h
A: ∏(62)(3) = 108∏ |
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Term
CYLINDER
How to find the surface area of a cylinder?
Q: What is the equation for surface area of a cylinder?
Q: Find surface arae when r=3 and h=4
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Definition
A: surface area = 2∏r2+2∏rh
A: 2∏(3)2+2∏(3)(4) = 18∏+24∏ = 42∏ |
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Term
WORK RATE
How to solve problems with combined work rate?
Q: What is the general equation for combined work rate?
Q: If it takes Daniel 9 hours to clean an office building and it takes Mark 6 hours, how long would it take the two of them, working together to clean the building?
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Definition
A:
[image]
A: According to the work formula, the inverse of the time it takes working together equals the sum of the inverses of the time it takes each individually.
1/9 + 1/6 = 1/t
2/18 + 3/18 = 1/t
5/18 = 1/t
t = 1/(5/18) = 18/5
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Term
COMBINED RATES
How to find average rate?
Q: Angelo ran 6 miles per hour for 3 miles and 8 miles per hour for 2 miles. What was his average spped in MPH?
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Definition
A: 6 2/3
The question is average speed, or distance per time. You know the total distance Angelo ran, but you don't know the total time. First determine each individual segment of time, and then add them. This will enable you to find the average. He ran 6 miles per hour for 3 miles, so he ran for half an hour. Then, he ran 8 miles per hour for 2 miles, so he ran for one-fourth of an hour. You can now find his average speed:
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Term
DISTANCE
Q: A person walking 3 miles per hour goes from point A to point B in 10 minutes. How many miles is it from point A to point B?
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Definition
Answer: 1/2 miles
Ten minutes is to 1/6 of an hour. If someone can go 3 miles in a full hour, he can go 1/6 of that in 1/6 of an hour. Multiply: 1/6 • 3 = 1/2 |
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Term
ANGLES
Q: The angles of a triangle are in the ratio of 5:6:7. What is the degree measure of the largest angle?
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Definition
Answer: 70
The angles are in the ratio of 5:6:7, so represent them as 5x, 6x, and 7x. The sum of the angles in any triangle is 180, so 5x+6x+7x=180, 18x=180, and x=10. So the largest angle has the measure of 7 x 10 = 70. |
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Term
Q: If a>1, which of the following equal to
[image]
- a
- a+3
- 2/(a-1)
- 2a/(a-3)
- (a-1)/a
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Definition
A: 2/(a-1)
Solution:
[image]
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Term
Solve:
2x2 = 32
A B
x 4
Which is bigger, are they equal or can you not tell? |
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Definition
A: you cannot tell
2x2 = 32
x2 = 16
√x2 = √16
x = +/- 4
Plus or minus because x could be 4 or -4 since it is squared. |
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Term
A square is inscribed in a circle with a circumference of 16∏√2. What is the area of the square?
• 32
• 64
•128
•256
•512 |
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Definition
A: 256
Start by drawing the circle with the square inscribed, to visualize the dimensions. If a square with a side length a is inscribed in a circle, the diagonal of the square, with length a√2, is also the diameter of the circle. The circumference of a circle is ∏d. Since the circumference is given as 16∏√2, ∏d = 16∏√2. Solve for d by dividing both sides by ∏to get 16√2. Since this diamter is also the diagonal of the square creates two 45-45-90 triangles, the sides of the square are the legs of the 45-45-90 triangle with a hypotenuse of 16√2. Recall that the sides of a 45-45-90 triangle are always in the ratio of 1:1:√2. Therefore, if the hypotenuse is 16√2 the side length of the square is 16 and the area is 256. |
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Term
In a class of 30 students the ratio of males to females is 3 to 2. What is the number of females in the class?
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Definition
A: 12
2/5 = f/30 = 60 = 5f f = 12
or 30/5 = 6 6x2 = 12 |
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Term
| If a company receives 60% of it's income from individuals and in 2009 its income from individuals was 90 million dollars, what was the company's total income? |
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Definition
A: 150 million
Let T be the toal income received: 90 = .6 • T, so T = 150 |
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Term
Question:
A B
(√6a)(5√3) √200a
Which is greater, are they equal or can you not tell? |
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Definition
A: A is larger
You need to simplify each of the quantities in order to compare them. To simplify Quantity A, multiply the radicals and simplify as shown:
(√6a)(5√3)=(5√6a • 3) = 5√18a = 5√9•√2a = 5•3•√2a=15√2a
Next simplify Quantity B:
√200a = √200 • √a = (√100•2)•√a = √100•√2√a
= 10√2a
15√2a > 10√2a |
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Term
A trail mix has a ratio of cashews to peanuts of 2:3. The ratio of cashews to raisins is 2:3. What is the ratio of cashews to raisins?
• 1:2
•2:9
•3:9
•4:6
•4:9 |
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Definition
| This question is asking about a combined ratio. To compare the ratios, the number of peanuts must be the same in each ratio. Since peaunuts are represented by 2 in one ratio and 3 in another, convert them both to 6. The ratio of cashews to peanuts is 2:3 = 4:6, and the ratio fo peanuts to raisins is 2:3 = 6:9. Now "peanuts" is the same in both ratios, so the ratio of cashews to raisins is 4:9 and the answer is E. |
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Term
| There are five employees willing to serve on one of two different committees. If each employee can only serve on one committee, how many possible ways are there for the openings on the committees to be filled? |
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Definition
A: 20
There are 5 ways for the opening on the first committee to be filled because all 5 people are willing to serve on either committee. With that opening filled, there are 4 ways for the second opening to be filled. There are 5•4=20 total ways to fill the opening. So the answer is 20. |
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Term
Triangle ABC is similar to triangle DEF. If AB=8, AC=16, and DE=48, what is EF/BC?
•2
•3
•6
•8
•16 |
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Definition
Drawing this one helps.
The question is asking for the ratio of corresponding sides of similar triangles. While you aren't given any information about BC or EF, in similar triangles, the ratio of corresponding sides is constant. Since you can calculate the ratio of the corresponding side lengths DE and AB, the ratio will be the same for EF and BC. This means that DE/AB = 48/6 = 6 gives you that EF/BC = 6 |
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Term
In 2010, the average price for Company A's laptops was $800. What are the possible prices during the 4 quarters of 2010?
A) $750, $800, $850, $800
B) $850, $950, $800, $850
C) $800, $750, $700, $700
D) $950, $950, $900, $950
E) $900, $850, $750, $700 |
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Definition
First off, look for answers that cold plausibly give you an average of $800. B and D definitely can't so eliminate them right away. C will be too low so eliminate that choice as well. You are now left with A and E as the only plausible answer.
A =750 + 800 + 850 + 800 = 3200
3200/4 = 800
B= 900 + 850 + 750 + 700 = 3200
3200/4 = 800
A and E both work. |
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