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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. Define the mode of a set of numbers.
Find the total - or whole - first - and then set up a Ratio Box.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.

2. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
1.4
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'.

3. Explain how to use a 'Rate Pie'
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
V=pr²h (This is just the area multiplied by the height)

4. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

5. What are 'vertical angles'?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
V=s³
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

6. HIGH: What is the factored version of x² + 2xy + y² ?
Bh
'Big' angles and 'Small' angles.
(x+y)²
6

7. HIGH: What is the formula for the diagonal of any square?
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.
S*v2
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.
Probability A * Probability B

8. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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)+
1
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
4 angles are formed. Their sum is 360 degrees

9. What do permutation problems often ask for?
S²
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.
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.
Arrangements - orders - schedules - or lists.

10. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
1
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
Percentage Change = Difference/Original * 100

11. What is the equation for a group problem?
1. Given event A: A + notA = 1.
Find the total - or whole - first - and then set up a Ratio Box.
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.

12. List all the prime numbers that are less than 30:
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

13. What is a 'Right' triangle?
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.
(x+y)(x-y)
A triangle in which one of the three interior angles is 90 degrees.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

14. HIGH: Describe how to deal with 2 sets of parentheses.
x²-y²
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.
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)+
(a+b)(a-b)

15. HIGH: Volume of a cube?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(x+y)(x-y)
80%
V=s³

16. 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.
Example: 1 < x < 10
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 9 if the sum of its digits is divisible by 9.

17. Diameter of a circle?
Multiply numerator times numerator and denominator times denominator.
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%.
2r
25%

18. Solve this: v6 * -v6 = ?
(x+y)(x-y)
6
x²-y²
1/x^n For example - 6-² = 1/6² = 1/36

19. Area of a parallelogram?
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.
Between 0 and 1.
Bh
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

20. The three interior angles of a triangle add up to...
1.4
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
A 90-degree angle.
180 degrees

21. An integer is divisible by 8 if...

22. HIGH: To divide powers with the same base...
S²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 5 if its units digit is either 0 or 5.

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

24. What degree angle is a line?
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.
A 90-degree angle.
A line is a 180-degree angle.
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.

25. HIGH: Area of a circle
2
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.
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=pr²

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

27. How do you solve a permutation?
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.
(0 -0)
x²-y²
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

28. If something is certain to happen - how is the probability of this event expressed mathematically?
A line is a 180-degree angle.
(x+y)²
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
1/1

29. What is an 'equilateral' triangle?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

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

31. HIGH: What is the Pythagorean theorem?

32. What is the name of a line that extends from the center of a circle to the edge of a circle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A radius
An integer is divisible by 2 if its units digit is divisible by 2.
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

33. How is a range expressed with inequalities?
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)+
Example: 1 < x < 10
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.
Not reading the problems carefully enough!

34. Convert to a percentage: 1/4
25%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2

35. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
V=pr²h (This is just the area multiplied by the height)
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

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

37. Does order matter for a permutation? How about for a combination?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
2
Order does matter for a permutation - but does not matter for a combination.

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

39. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Between 0 and 1.
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.

40. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
Find a common denominator and make equivalent fractions. Then add or subtract.
Probability A + Probability B
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

41. v4 =
Probability A + Probability B
2
An integer is divisible by 2 if its units digit is divisible by 2.
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

42. HIGH: How do you multiply and divide square roots?
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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
Find a common denominator and make equivalent fractions. Then add or subtract.

43. 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.
Percentage Change = Difference/Original * 100
25%
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.

44. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
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.
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.
360 degrees

45. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
3:4:5 5:12:13
Find a common denominator and make equivalent fractions. Then add or subtract.
Between 0 and 1.
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

46. HIGH: Area of a triangle?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

47. On the GRE - should you ever assume that diagrams are truthful?
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)+
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

48. HIGH: What is the unfactored version of (x+y)² ?
x²-y²
x² + 2xy + y²
(0 -0)
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.

49. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
3:4:5 5:12:13
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.
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

50. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
25%
(x+y)²
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.