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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. What is the 'Third side' rule for triangles?
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
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.
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.

2. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

3. HIGH: What is a 'Right isosceles' triangle?
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
V=pr²h (This is just the area multiplied by the height)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

4. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
The average - mean - median - or mode.
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

5. HIGH: What is the formula for the diagonal of any square?
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
Favorable Outcomes/Total Possible Outcomes
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.
S*v2

6. HIGH: Rough est. of v3 =
Bh
6
1.7
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

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

8. HIGH: What is the Pythagorean theorem?

9. How do you divide fractions?
2
'Big' angles and 'Small' angles.
The total # of possible outcomes.
Invert the second fraction (reciprocal) and multiply

10. Simplify this: v32
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Favorable Outcomes/Total Possible Outcomes
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

11. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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.
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.
1.7

12. List all the prime numbers that are less than 30:
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 5 if its units digit is either 0 or 5.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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

13. If something is certain to happen - how is the probability of this event expressed mathematically?
1
Find a common denominator and make equivalent fractions. Then add or subtract.
A radius
1/1

14. Area of a parallelogram?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Bh
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
Invert the second fraction (reciprocal) and multiply

15. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
1/x^n For example - 6-² = 1/6² = 1/36
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.

16. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Invert the second fraction (reciprocal) and multiply
V=pr²h (This is just the area multiplied by the height)
Between 0 and 1.
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.

17. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

18. How many degrees does a circle contain?
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Bh

19. Convert to a percentage: 2/5
(0 -0)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
40%
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

20. The three interior angles of a triangle add up to...
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
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
180 degrees

21. What is a 'Right' angle?
A 90-degree angle.
80%
A line is a 180-degree angle.
A radius

22. HIGH: Define the formula for calculating slope.
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A triangle in which one of the three interior angles is 90 degrees.

23. An integer is divisible by 2 if...
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.
Probability A + Probability B
An integer is divisible by 2 if its units digit is divisible by 2.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

24. What causes 80% of errors on the math section of the GRE?
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.
Not reading the problems carefully enough!
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.

25. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Between 0 and 1.
'Big' angles and 'Small' angles.

26. How do you multiply fractions?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
40%
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.
Multiply numerator times numerator and denominator times denominator.

27. HIGH: What is the unfactored version of (x-y)² ?
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.
x² -2xy + y²
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.
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.

28. How do you calculate the percentage of change?
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Multiply numerator times numerator and denominator times denominator.
Percentage Change = Difference/Original * 100

29. HIGH: How do you calculate the length of an arc?

30. Solve this: v6 * -v6 = ?
6
The value that appears most often in a data set.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.

31. HIGH: Define the 'Third side' rule for triangles

32. If x² = 144 - does v144 = x?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Not necessarily. This is a trick question - because x could be either positive or negative.
3:4:5 5:12:13
4 angles are formed. Their sum is 360 degrees

33. Explain how to calculate an average (arithmetic mean)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
360 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.

34. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
Favorable Outcomes/Total Possible Outcomes
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

35. HIGH: To divide powers with the same base...
Not necessarily. This is a trick question - because x could be either positive or negative.
6
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

36. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x+y)(x-y)
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

37. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1. Given event A: A + notA = 1.
Probability A + Probability B
25%

38. HIGH: what is the side ratio for a Right Isosceles triangle?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
360 degrees
x² -2xy + y²

39. What is the formula to determine probability?
(# 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)+
Probability A * Probability B
2r

40. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
25%
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
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.
Example: 1 < x < 10

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

42. Explain the special properties of zero.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
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
360 degrees

43. HIGH: What is the unfactored version of x²-y² ?
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.
60%
(x+y)(x-y)
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.

44. HIGH: How do you calculate the circumference of a circle?
A=pr²
S*v2
2pr -or- pd
It will be a great advantage on test day to have your times table memorized from 1 through 15.

45. How do you add or subtract fractions?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.

46. An integer is divisible by 3 if...
360 degrees
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.
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.
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

47. Convert to a percentage: 4/5
80%
Favorable Outcomes/Total Possible Outcomes
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.
A line is a 180-degree angle.

48. Define the range of a set of numbers.
Not reading the problems carefully enough!
1. Figure out how many slots you have (i.e. you'Re supposed to bring home 3 different types of ice cream) 2. Write down the number of possible options for each slot (i.e. 5 flavors of ice cream at the store - 5 options for the 1st slot - 4 options fo
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.
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.

49. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
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.

50. What is the equation for a group problem?
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
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.
4 angles are formed. Their sum is 360 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.