Test your basic knowledge |

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 side ratio for a 30:60:90 triangle?
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
40%

2. Explain the special properties of zero.
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 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.
60%
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.

3. What is an 'equilateral' triangle?
The # falling in the center of an ordered data set
1.4
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2pr -or- pd

4. Probability Formula
90 degrees each.
Favorable Outcomes/Total Possible Outcomes
A triangle in which one of the three interior angles is 90 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.

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

6. HIGH: What are the percentages for standard deviation?
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Not reading the problems carefully enough!
1/x^n For example - 6-² = 1/6² = 1/36

7. Explain how to use a 'Rate Pie'
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
A triangle in which one of the three interior angles is 90 degrees.
1/x^n For example - 6-² = 1/6² = 1/36

8. Simplify this: v32
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
'Big' angles and 'Small' angles.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
6

9. Explain how to solve for 7/¼
V=pr²h (This is just the area multiplied by the height)
1/1
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

10. HIGH: Describe how to deal with 2 sets of parentheses.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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 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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

11. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
(0 -0)
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.
6

12. If x² = 144 - does v144 = x?
2pr -or- pd
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Favorable Outcomes/Total Possible Outcomes

13. 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
60%
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

14. What is the formula to determine probability?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

15. HIGH: How do you multiply and divide square roots?
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
2pr -or- pd
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

16. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
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.
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%.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

17. HIGH: What is the formula for the diagonal of any square?
S*v2
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.
1.7
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.

18. 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
2pr -or- pd
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Groups - teams - or committees.

19. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
25%
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

20. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
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
80%

21. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide 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

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

23. What is the name of a line that extends from the center of a circle to the edge of a circle?
A=pr²
Probability A + Probability B
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

24. What is the factored version of x² -2xy + y² ?
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.
V=s³
(x-y)²
80%

25. How do you solve a permutation?
Between 0 and 1.
Invert the second fraction (reciprocal) and multiply
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

26. How is a range expressed with inequalities?
Multiply numerator times numerator and denominator times denominator.
Example: 1 < x < 10
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

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
1.4
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

28. HIGH: What is the factored version of x² + 2xy + y² ?
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.
(x+y)²
V=pr²h (This is just the area multiplied by the height)
(x-y)²

29. In a coordinate system - what is the origin?
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
6
(0 -0)

30. What is the key to dealing with ratio questions?
2pr -or- pd
Find the total - or whole - first - and then set up a Ratio Box.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
180 degrees

31. Does order matter for a permutation? How about for a combination?
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'.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
6
Order does matter for a permutation - but does not matter for a combination.

32. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
360 degrees
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

33. HIGH: What is the mode?
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.
The value that appears most often in a data set.
Bh
V=s³

34. Explain the difference between handling a permutation versus a combination.
6
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.
80%
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

35. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
x² + 2xy + y²
3:4:5 5:12:13
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

36. Solve this: v6 * -v6 = ?
6
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

37. The three exterior angles of a triangle add up to...
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
80%
A line is a 180-degree angle.

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

39. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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=pr²
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=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

40. An integer is divisible by 3 if...
1/x^n For example - 6-² = 1/6² = 1/36
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 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.
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.

41. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1. Given event A: A + notA = 1.
S*v2

42. What is the sum of any 'big' angle and any 'Small' angle?
Find the total - or whole - first - and then set up a Ratio Box.
Groups - teams - or committees.
180 degrees.
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

43. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

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

45. HIGH: How do you multiply powers with the same base?
A=pr²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Order does matter for a permutation - but does not matter for a combination.
A radius

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

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

48. HIGH: Rough est. of v3 =
(x+y)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.
1.7
A 90-degree angle.

49. Area of a square?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
S²

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