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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. Probability Formula
Favorable Outcomes/Total Possible Outcomes
'Big' angles and 'Small' angles.
Example: 1 < x < 10
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
2. HIGH: What is the equation of a line?
3. How do you solve a combination?
4. HIGH: What is the mode?
2r
The total # of possible outcomes.
S²
The value that appears most often in a data set.
5. Area of a parallelogram?
6
Bh
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
6. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
x² -2xy + y²
1
1. Given event A: A + notA = 1.
7. An integer is divisible by 2 if...
(a+b)(a-b)
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 2 if its units digit is divisible by 2.
8. What do combination problems usually ask for?
Multiply numerator times numerator and denominator times denominator.
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.
Find the total - or whole - first - and then set up a Ratio Box.
Groups - teams - or committees.
9. Explain how to divide fractions.
4 angles are formed. Their sum is 360 degrees
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A 90-degree angle.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
10. How do you calculate the percentage of change?
6
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
Percentage Change = Difference/Original * 100
Arrangements - orders - schedules - or lists.
11. HIGH: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
A=pr²
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
Probability A + Probability B
12. Convert to a percentage: 2/5
Groups - teams - or committees.
(a+b)(a-b)
40%
The total # of possible outcomes.
13. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
14. What is the name of a line that extends from the center of a circle to the edge of a circle?
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
A radius
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
15. What is the equation for a group problem?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
Percentage Change = Difference/Original * 100
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
16. HIGH: What is a 'Right isosceles' triangle?
Multiply numerator times numerator and denominator times denominator.
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+b)(a-b)
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. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
2pr -or- pd
It will be a great advantage on test day to have your times table memorized from 1 through 15.
18. Explain the difference between a digit and a number.
19. In a coordinate system - identify the quadrants and describe their location.
The average - mean - median - or mode.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
A line is a 180-degree angle.
20. What is the formula to determine probability?
A=pr²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
40%
1.4
21. Area of a square?
S²
Example: 1 < x < 10
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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)+
22. Explain how to solve for 7/¼
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
The # falling in the center of an ordered data set
x² + 2xy + y²
23. An integer is divisible by 5 if...
V=pr²h (This is just the area multiplied by the height)
An integer is divisible by 5 if its units digit is either 0 or 5.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
24. a² - b² is equal to
60%
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
(a+b)(a-b)
3:4:5 5:12:13
25. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
6
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Probability A + Probability B
26. What'S the most important thing to remember about charts you'll see on the GRE?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
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.
27. List two odd behaviors of exponents
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Find a common denominator and make equivalent fractions. Then add or subtract.
28. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
29. The three exterior angles of a triangle add up to...
360 degrees
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.
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
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.
30. Does order matter for a permutation? How about for a combination?
6
Order does matter for a permutation - but does not matter for a combination.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
31. An integer is divisible by 4 if...
32. HIGH: Volume of a cube?
S*v2
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
V=s³
Not reading the problems carefully enough!
33. What is a 'Right' triangle?
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.
A radius
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.
A triangle in which one of the three interior angles is 90 degrees.
34. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
1.4
Between 0 and 1.
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.
35. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
36. HIGH: What is the unfactored version of (x-y)² ?
1/x^n For example - 6-² = 1/6² = 1/36
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
Not necessarily. This is a trick question - because x could be either positive or negative.
x² -2xy + y²
37. HIGH: What is the side ratio for a 30:60:90 triangle?
360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
38. Solve this: v6 * -v6 = ?
V=pr²h (This is just the area multiplied by the height)
180 degrees
6
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
39. Convert to a percentage: 3/5
60%
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.
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
Not reading the problems carefully enough!
40. Define the range of a set of numbers.
(a+b)(a-b)
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
41. HIGH: What is the Pythagorean theorem?
42. Convert to a percentage: 1/4
25%
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
43. What is the factored version of x² -2xy + y² ?
A=pr²
(x-y)²
V=s³
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
44. How is a range expressed with inequalities?
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.
2r
Example: 1 < x < 10
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
45. HIGH: Describe how to deal with 2 sets of parentheses.
The value that appears most often in a data set.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Not reading the problems carefully enough!
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)+
46. What do permutation problems often ask for?
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Arrangements - orders - schedules - or lists.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
47. HIGH: Simplify this: v75/v27
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
S*v2
48. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
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
360 degrees
49. What is the key to dealing with ratio questions?
Bh
Find the total - or whole - first - and then set up a Ratio Box.
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%.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
50. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
360 degrees
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.