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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. An integer is divisible by 6 if...

2. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

3. What causes 80% of errors on the math section of the GRE?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Not reading the problems carefully enough!
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

4. If x² = 144 - does v144 = x?
(x-y)²
Not necessarily. This is a trick question - because x could be either positive or negative.
Probability A * Probability B
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.

5. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
A radius
6
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.

6. How do you solve a combination?

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

8. How do you solve a permutation?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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
A triangle in which one of the three interior angles is 90 degrees.
V=s³

9. Explain how to use an 'Average Pie'
80%
Probability A * Probability B
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

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

11. HIGH: Define the formula for calculating slope.
Probability A * Probability B
1/1
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

12. How do you add or subtract fractions?
Probability A * Probability B
Find a common denominator and make equivalent fractions. Then add or subtract.
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.

13. HIGH: What is the factored version of (x+y)(x-y) ?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
x²-y²
x² -2xy + y²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

14. Explain how to solve for 7/¼
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Favorable Outcomes/Total Possible Outcomes
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
An integer is divisible by 2 if its units digit is divisible by 2.

15. What is the 'distributive law'?
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.
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%.
Bh
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

16. Explain the difference between handling a permutation versus a combination.
(a+b)(a-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.
Probability A * Probability B
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.

17. Explain the special properties of zero.
Probability A * Probability B
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
180 degrees.

18. 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
1/x^n For example - 6-² = 1/6² = 1/36
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

19. An integer is divisible by 2 if...
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.
180 degrees.
An integer is divisible by 2 if its units digit is divisible by 2.
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

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

21. How many degrees does a circle contain?
Percentage Change = Difference/Original * 100
180 degrees
An integer is divisible by 9 if the sum of its digits is divisible by 9.
360 degrees

22. The three interior angles of a triangle add up to...
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
180 degrees

23. 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.
V=pr²h (This is just the area multiplied by the height)
Example: 1 < x < 10

24. HIGH: Volume of a cylinder?
2pr -or- pd
V=pr²h (This is just the area multiplied by the height)
180 degrees.
Favorable Outcomes/Total Possible Outcomes

25. Area of a parallelogram?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Bh
60%
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)+

26. List all the prime numbers that are less than 30:
1/1
x² + 2xy + y²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

27. HIGH: How much of your times table should you know - for the GRE?
'Big' angles and 'Small' angles.
360 degrees
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

28. Explain how to calculate an average (arithmetic mean)
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide 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

29. HIGH: What is a 'Right isosceles' triangle?
An integer is divisible by 5 if its units digit is either 0 or 5.
1
'Big' angles and 'Small' angles.
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.

30. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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)+
(x-y)²
1. Given event A: A + notA = 1.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

31. What is the sum of any 'big' angle and any 'Small' angle?
x² -2xy + y²
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
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
180 degrees.

32. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
V=s³
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.
The # falling in the center of an ordered data set
S*v2

33. Define the range of a set of numbers.
Groups - teams - or committees.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
1.7

34. Define the mode of a set of numbers.
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.
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
Find a common denominator and make equivalent fractions. Then add or subtract.
V=pr²h (This is just the area multiplied by the height)

35. 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)+
(x-y)²
180 degrees.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

36. Define a factorial of a number - and how it is written.
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.
2r
6
V=pr²h (This is just the area multiplied by the height)

37. What'S one way to avoid mistakes on algebra questions in the GRE?

38. If something is possible but not certain - what is the numeric range of probability of it happening?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x²-y²
Between 0 and 1.
x² + 2xy + y²

39. 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.
Bh
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

40. What do combination problems usually ask for?
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Between 0 and 1.
Groups - teams - or committees.

41. What is a 'Right' angle?
A 90-degree angle.
The # falling in the center of an ordered data set
Percentage Change = Difference/Original * 100
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

42. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
An integer is divisible by 5 if its units digit is either 0 or 5.
1/x^n For example - 6-² = 1/6² = 1/36
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.

43. How do you calculate the percentage of change?
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.
Percentage Change = Difference/Original * 100
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.
(a+b)(a-b)

44. HIGH: How do you multiply and divide square roots?
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
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'.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

45. Probability Formula
Find a common denominator and make equivalent fractions. Then add or subtract.
Favorable Outcomes/Total Possible Outcomes
A triangle in which one of the three interior angles is 90 degrees.
2pr -or- pd

46. Define 'proportionate' values
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
An integer is divisible by 5 if its units digit is either 0 or 5.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

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

48. What degree angle is a line?
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)+
(x-y)²
A line is a 180-degree angle.
60%

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

50. HIGH: Area of a circle
360 degrees
Invert the second fraction (reciprocal) and multiply
A=pr²
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.