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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. HIGH: What is the Pythagorean theorem?

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

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

4. HIGH: Area of a circle
1/x^n For example - 6-² = 1/6² = 1/36
Between 0 and 1.
Not reading the problems carefully enough!
A=pr²

5. Diameter of a circle?
2r
A 90-degree angle.
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%.
1.4

6. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Invert the second fraction (reciprocal) and multiply
90 degrees each.
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.

7. Does order matter for a permutation? How about for a combination?
180 degrees
Order does matter for a permutation - but does not matter for a combination.
1. Given event A: A + notA = 1.
80%

8. Convert to a percentage: 1/4
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
40%
'Big' angles and 'Small' angles.
25%

9. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
A 90-degree angle.
Not reading the problems carefully enough!

10. a² - b² is equal to
60%
(x-y)²
(a+b)(a-b)
Multiply numerator times numerator and denominator times denominator.

11. HIGH: Volume of a cube?
V=s³
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

12. HIGH: how do you calculate the surface area of a rectangular box?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
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%.
Order does matter for a permutation - but does not matter for a combination.

13. Explain how to calculate an average (arithmetic mean)
Bh
(x-y)²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

14. 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
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.
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
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.

15. HIGH: What is a 'Right isosceles' triangle?
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.
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.
80%
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

16. What number goes on the bottom of a probability fraction?
The 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)+
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.

17. Area of a square?
Not reading the problems carefully enough!
40%
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
S²

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

19. How do you solve a permutation?
Not reading the problems carefully enough!
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
1.7
Groups - teams - or committees.

20. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Find the total - or whole - first - and then set up a Ratio Box.
1.7
An integer is divisible by 5 if its units digit is either 0 or 5.

21. Explain the difference between a digit and a number.

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

23. HIGH: What is the median?
x² + 2xy + y²
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
The # falling in the center of an ordered data set
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

24. In a coordinate system - identify the quadrants and describe their location.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find a common denominator and make equivalent fractions. Then add or subtract.

25. HIGH: Rough est. of v1 =
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% |
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)+
60%

26. An integer is divisible by 2 if...
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
Bh
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.
An integer is divisible by 2 if its units digit is divisible by 2.

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

28. Explain how to use a 'Rate Pie'
A=pr²
1.4
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
The value that appears most often in a data set.

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

30. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
25%

31. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Groups - teams - or committees.

32. An integer is divisible by 3 if...
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
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.
1.7

33. The three interior angles of a triangle add up to...
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.
180 degrees
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S²

34. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The # falling in the center of an ordered data set
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.
Arrangements - orders - schedules - or lists.

35. HIGH: What is the unfactored version of (x-y)² ?
A radius
Find a common denominator and make equivalent fractions. Then add or subtract.
x² -2xy + y²
A=pr²

36. How do you calculate the probability of two events in a row? (Probability of A and B)
6
Probability A * Probability B
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
90 degrees each.

37. Convert to a percentage: 4/5
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
80%
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Arrangements - orders - schedules - or lists.

38. Area of a parallelogram?
Bh
Invert the second fraction (reciprocal) and multiply
(0 -0)
360 degrees

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

40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(a+b)(a-b)
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.
1
Length of an Arc = (n/360)(2pr) - where 'n' equals the central angle (the angle formed by the two edge radii of the arc). For example: if n=60 - then n/360 = 1/6 - which means the arc formed by the 60-degree central angle will be 1/6 of the circle'S

41. What'S the most important thing to remember about charts you'll see on the GRE?
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.
Order does matter for a permutation - but does not matter for a combination.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

42. HIGH: what is the side ratio for a Right Isosceles triangle?
A 90-degree angle.
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.
A=pr²

43. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Groups - teams - or committees.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
The total # of possible outcomes.

44. How do you calculate the percentage of change?
V=pr²h (This is just the area multiplied by the height)
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Percentage Change = Difference/Original * 100
90 degrees each.

45. HIGH: What must be true before a quadratic equation can be solved?

46. Explain the special properties of zero.
An integer is divisible by 5 if its units digit is either 0 or 5.
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
Bh
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.

47. How is a range expressed with inequalities?
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Example: 1 < x < 10
The average - mean - median - or mode.

48. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
4 angles are formed. Their sum is 360 degrees
360 degrees
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.

49. HIGH: What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S*v2
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.

50. What is the equation for a group problem?
The average - mean - median - or mode.
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
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.
A radius