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Test your basic knowledge |
GRE High Frequency Math Terms
Start Test
Study First
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. The three exterior angles of a triangle add up to...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
A triangle in which one of the three interior angles is 90 degrees.
360 degrees
2. On the GRE - should you ever assume that diagrams are truthful?
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.
V=pr²h (This is just the area multiplied by the height)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
3. Define a factorial of a number - and how it is written.
V=s³
360 degrees
1.4
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.
4. How many degrees does a circle contain?
Multiply numerator times numerator and denominator times denominator.
360 degrees
Not reading the problems carefully enough!
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
5. HIGH: How do you calculate the length of an arc?
6. Does order matter for a permutation? How about for a combination?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Order does matter for a permutation - but does not matter for a combination.
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.
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
7. An integer is divisible by 6 if...
8. What causes 80% of errors on the math section of the GRE?
1/x^n For example - 6-² = 1/6² = 1/36
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Not reading the problems carefully enough!
Probability A * Probability B
9. An integer is divisible by 9 if...
V=s³
An integer is divisible by 9 if the sum of its digits is divisible by 9.
V=pr²h (This is just the area multiplied by the height)
It will be a great advantage on test day to have your times table memorized from 1 through 15.
10. Diameter of a circle?
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.
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
2r
11. What is the equation for a group problem?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
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.
A 90-degree angle.
12. List two odd behaviors of exponents
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(0 -0)
13. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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
1.4
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.
Not reading the problems carefully enough!
14. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Order does matter for a permutation - but does not matter for a combination.
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(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.
15. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Example: 1 < x < 10
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
16. HIGH: What is a 'Right isosceles' triangle?
The total # of possible outcomes.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
17. HIGH: Volume of a cube?
V=pr²h (This is just the area multiplied by the height)
V=s³
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
1.4
18. What degree angle is a line?
S*v2
An integer is divisible by 5 if its units digit is either 0 or 5.
A line is a 180-degree angle.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
19. HIGH: What are the percentages for standard deviation?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Arrangements - orders - schedules - or lists.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x+y)²
20. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
A line is a 180-degree angle.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The value that appears most often in a data set.
21. HIGH: Describe how to deal with 2 sets of parentheses.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Favorable Outcomes/Total 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)+
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.
22. In a coordinate system - what is the origin?
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.
Find the total - or whole - first - and then set up a Ratio Box.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(0 -0)
23. List all the prime numbers that are less than 30:
Groups - teams - or committees.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
24. How is a range expressed with inequalities?
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=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Example: 1 < x < 10
Between 0 and 1.
25. Probability Formula
Groups - teams - or committees.
Favorable Outcomes/Total Possible Outcomes
A=pr²
(a+b)(a-b)
26. HIGH: Define the 'Third side' rule for triangles
27. HIGH: How do you multiply and divide square roots?
Not reading the problems carefully enough!
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
28. Convert to a percentage: 4/5
80%
V=pr²h (This is just the area multiplied by the height)
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
29. HIGH: To divide powers with the same base...
Arrangements - orders - schedules - or lists.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(0 -0)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
30. Define 'proportionate' values
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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/x^n For example - 6-² = 1/6² = 1/36
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
31. How do you solve a permutation?
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
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.
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.
V=s³
32. Area of a parallelogram?
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.
Bh
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
33. 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.
80%
(x-y)²
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.
34. 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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
35. Explain the difference between a digit and a number.
36. HIGH: What is the median?
The # falling in the center of an ordered data set
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
S*v2
37. HIGH: How do you calculate the circumference of a circle?
Bh
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.
2pr -or- pd
(a+b)(a-b)
38. HIGH: What is the Pythagorean theorem?
39. Explain how to divide fractions.
360 degrees
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.
S*v2
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
40. The three interior angles of a triangle add up to...
180 degrees
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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
41. a² - b² is equal to
(a+b)(a-b)
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)+
Not necessarily. This is a trick question - because x could be either positive or negative.
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
42. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
(0 -0)
S*v2
Bh
43. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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
(x+y)²
V=pr²h (This is just the area multiplied by the height)
44. Convert to a percentage: 2/5
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. 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.
40%
1/x^n For example - 6-² = 1/6² = 1/36
45. Explain how to solve for 7/¼
1. Given event A: A + notA = 1.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Multiply numerator times numerator and denominator times denominator.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
46. An integer is divisible by 4 if...
47. How precise do you need to be - using p on the GRE?
48. Explain the difference between handling a permutation versus a combination.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
49. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
The # falling in the center of an ordered data set
(x-y)²
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
50. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
A line is a 180-degree angle.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Favorable Outcomes/Total Possible Outcomes