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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. HIGH: What is the Pythagorean theorem?

2. What degree angle is a line?
A line is a 180-degree angle.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Not reading the problems carefully enough!
x²-y²

3. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
(x-y)²
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
x²-y²

4. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
The factorial of a number is that number times every positive whole number smaller than that number - down to 1. Example: 6! means the factorial of 6 - which = 65432*1 = 720.
Zero is even. It is an integer. It is neither positive nor negative. Zero multiplied by any other number = zero. You cannot divide by zero.

5. An integer is divisible by 4 if...

6. Explain how to use a 'Rate Pie'
An integer is divisible by 2 if its units digit is divisible by 2.
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.
This is similar to an Average Pie - and can be used for some story problems. Draw a circle. Top half holds the Distance or other Amount. Bottom left holds Time. Bottom right holds Rate. Rate * Time = Amount
A triangle in which one of the three interior angles is 90 degrees.

7. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

8. How do you solve a combination?

9. HIGH: Explain the process to solve '56 is what percent of 80?'

10. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
S*v2
Absolute value is a number'S distance away from zero on the number line. It is always positive - regardless of whether the number is positive or negative. It is represented with | |. For example - |-5| = 5 - and |5| = 5.
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
Arrangements - orders - schedules - or lists.

11. What is a 'Right' triangle?
Find the total - or whole - first - and then set up a Ratio Box.
Not reading the problems carefully enough!
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
A triangle in which one of the three interior angles is 90 degrees.

12. How is a range expressed with inequalities?
V=s³
Find a common denominator and make equivalent fractions. Then add or subtract.
Example: 1 < x < 10
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

13. HIGH: x^-n is equal to
A radius
S²
1/x^n For example - 6-² = 1/6² = 1/36
1. Figure out how many slots you have (i.e. there are 3 winning positions in a race - 1st - 2nd - and 3rd) 2. Write down the number of possible options for each slot (i.e. 5 runners in the race - so 5 options for the 1st slot - 4 options for the 2nd

14. List all the prime numbers that are less than 30:
If order matters - then you have a permutation -- do NOT divide. If order does NOT matter - then you have a combination -- divide by the factorial of the number of available slots.
An integer is divisible by 5 if its units digit is either 0 or 5.
40%
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

15. HIGH: Describe how to deal with 2 sets of parentheses.
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
By Plugging In an actual value for the variable(s). This will be quicker - more accurate - you'll avoid built-in traps - and you can use the calculator. When Plugging In - use simple numbers but avoid 1 and 0.

16. An integer is divisible by 9 if...
PEMDAS (Please Excuse My Dear Aunt Sally): P = Parentheses. Solve anything inside of parentheses first. E = Exponents. Solve these second. MD = Multiplication - Division. From left to right - do all multiplication and division during one step through
1
This is similar to an Average Pie - and can be used for some story problems. Draw a circle. Top half holds the Distance or other Amount. Bottom left holds Time. Bottom right holds Rate. Rate * Time = Amount
An integer is divisible by 9 if the sum of its digits is divisible by 9.

17. In a coordinate system - what is the origin?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
3:4:5 5:12:13
(0 -0)
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

18. Does order matter for a permutation? How about for a combination?
A(b+c) = ab + ac a(b-c) = ab - ac - For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Arrangements - orders - schedules - or lists.
Order does matter for a permutation - but does not matter for a combination.

19. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
V=s³
The value that appears most often in a data set.
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
360 degrees

20. In a coordinate system - identify the quadrants and describe their location.
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

21. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
An integer is divisible by 5 if its units digit is either 0 or 5.

22. What is the 'Third side' rule for triangles?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.
An integer is divisible by 3 if the sum of its digits is divisible by 3. For example - adding the digits of the number 2 -145 (2+1+4+5) = 12 - which is divisible by 3.
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group

23. An integer is divisible by 2 if...
Bh
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
An integer is divisible by 2 if its units digit is divisible by 2.

24. HIGH: Define the formula for calculating slope.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
25%
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
90 degrees each.

25. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
V=pr²h (This is just the area multiplied by the height)
T = G1 + G2 - B + N Where T = Total G1 = first Group G2 = second Group B = members who are in Both groups N = members who are in Neither group
First - translate into clear math: 56 = x/100(80) ('56 is x one-hundredths of 80') = 56 = 80x/100 = 56 = 4x/5 Divide both sides by 4/5 (multiply by 5/4) 70 = x - so 70%.

26. How do you add or subtract fractions?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Find a common denominator and make equivalent fractions. Then add or subtract.
Find the total - or whole - first - and then set up a Ratio Box.
(x+y)(x-y)

27. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
PEMDAS (Please Excuse My Dear Aunt Sally): P = Parentheses. Solve anything inside of parentheses first. E = Exponents. Solve these second. MD = Multiplication - Division. From left to right - do all multiplication and division during one step through

28. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
V75 = v253 = 5v3 - and v27 = v93 = 3v3. So we have 5v3/3v3. The v3 in the top and bottom of the fraction cancel - leaving 5/3.
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
1. Given event A: A + notA = 1.

29. Probability Formula
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V=pr²h (This is just the area multiplied by the height)
(a+b)(a-b)
Favorable Outcomes/Total Possible Outcomes

30. What'S the most important thing to remember about charts you'll see on the GRE?
x²-y²
'Big' angles and 'Small' angles.
A radius
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.

31. How precise do you need to be - using p on the GRE?

32. On the GRE - should you ever assume that diagrams are truthful?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
First - translate into clear math: 56 = x/100(80) ('56 is x one-hundredths of 80') = 56 = 80x/100 = 56 = 4x/5 Divide both sides by 4/5 (multiply by 5/4) 70 = x - so 70%.

33. HIGH: how do you calculate the surface area of a rectangular box?
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.
80%
Calculate and add the areas of all of 6 its sides. Example: for a rectangle with dimensions 2 x 3 x 4 - there will be 2 sides each - for each combination of these dimensions. That is - 2 each of 2x3 - 2 each of 3x4 - and 2 each of 4x2.
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given

34. HIGH: Rough est. of v1 =
1
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
90 degrees each.

35. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Calculate and add the areas of all of 6 its sides. Example: for a rectangle with dimensions 2 x 3 x 4 - there will be 2 sides each - for each combination of these dimensions. That is - 2 each of 2x3 - 2 each of 3x4 - and 2 each of 4x2.
90 degrees each.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.

36. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Always read the answer choices first. Try to eliminate choices by ballparking or estimating. But watch out for 'Trap' answers that look temptingly correct at first glance.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
The total # of possible outcomes.
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

37. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

38. HIGH: How much of your times table should you know - for the GRE?
Favorable Outcomes/Total Possible Outcomes
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Use the FOIL method: First - Outer - Inner - Last. This simply means to multiply every term in the first parentheses by every term in the second parentheses. Example: (x+4)(x+3) = First: (xx) + Outer: (x3) + Inner: (4x) + Last: (43) = (xx)+(x3)+(x4)+
It will be a great advantage on test day to have your times table memorized from 1 through 15.

39. What is the formula to determine probability?
Order does matter for a permutation - but does not matter for a combination.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

40. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
3:4:5 5:12:13

41. HIGH: What is 'absolute value' - and how is it represented?

42. What should you do BEFORE you start to solve a GRE math problem?

43. Define 'proportionate' values
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4. 2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

44. HIGH: What is a '30:60:90' triangle?
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 4 if its last two digits form a number that'S divisible by 4. For example - 712 is divisible by 4 because its last two digits (12) is divisible by 4.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

45. HIGH: What is the equation of a line?

46. HIGH: What is the unfactored version of (x+y)² ?
Between 0 and 1.
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² + 2xy + y²
Favorable Outcomes/Total Possible Outcomes

47. HIGH: What is the unfactored version of x²-y² ?
2r
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Not necessarily. This is a trick question - because x could be either positive or negative.
(x+y)(x-y)

48. An integer is divisible by 6 if...

49. Convert to a percentage: 2/5
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.
40%
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
2

50. HIGH: What is the mode?
The value that appears most often in a data set.
Groups - teams - or committees.
40%
360 degrees

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