GRE High Frequency Math Terms

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 unfactored version of x²-y² ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4 angles are formed. Their sum is 360 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
(x+y)(x-y)


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


3. What are the side ratios for a 30:60:90 triangle?
360 degrees
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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. 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.


4. What is the equation for a group problem?
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
x² + 2xy + y²
Example: 1 < x < 10
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.


5. HIGH: What is the formula for the diagonal of any square?
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.
(x+y)²
A radius
S*v2


6. Convert to a percentage: 1/4
Multiply numerator times numerator and denominator times denominator.
An integer is divisible by 5 if its units digit is either 0 or 5.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
25%


7. HIGH: What is the mode?
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%.
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.
The value that appears most often in a data set.
(x+y)²


8. What is an 'equilateral' triangle?
1. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Order does matter for a permutation - but does not matter for a combination.
60%


9. In a coordinate system - what is the origin?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
A radius
S*v2
(0 -0)


10. Convert to a percentage: 3/5
60%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


11. 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)+
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
Find the total - or whole - first - and then set up a Ratio Box.


12. HIGH: Area of a circle
2
A=pr²
x² -2xy + y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


15. On the GRE - should you ever assume that diagrams are truthful?
Order does matter for a permutation - but does not matter for a combination.
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.
90 degrees each.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.


16. HIGH: How do you multiply powers with the same base?
The total # of possible outcomes.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x²-y²


17. How do you solve a combination?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


18. For a bell curve - what three terms might be used to describe the number in the middle?
The value that appears most often in a data set.
The average - mean - median - or mode.
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.
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.


19. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
6
Probability A + Probability B
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Percentage Change = Difference/Original * 100


20. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
180 degrees
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Bh


21. What is the key to dealing with ratio questions?
(x+y)²
Find the total - or whole - first - and then set up a Ratio Box.
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.
An integer is divisible by 2 if its units digit is divisible by 2.


22. Explain how to solve for 7/¼
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!
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Between 0 and 1.


23. HIGH: Area of a triangle?
1.7
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.
(x-y)²
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


24. What do permutation problems often ask for?
1.4
(x+y)(x-y)
Arrangements - orders - schedules - or lists.
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.


25. List all the prime numbers that are less than 30:
(x+y)(x-y)
The average - mean - median - or mode.
80%
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.


26. Define the mode of a set of numbers.
(x-y)²
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.


27. What is the 'distributive law'?
40%
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.
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.
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.


28. HIGH: What is the Pythagorean theorem?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


29. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Find a common denominator and make equivalent fractions. Then add or subtract.
1


30. Define 'proportionate' values
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.


31. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
2
1/1
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.


32. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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 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. Given event A: A + notA = 1.
360 degrees


33. An integer is divisible by 2 if...
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.
Find the total - or whole - first - and then set up a Ratio Box.
An integer is divisible by 2 if its units digit is divisible by 2.


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


36. Does order matter for a permutation? How about for a combination?
Not necessarily. This is a trick question - because x could be either positive or negative.
Order does matter for a permutation - but does not matter for a combination.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')


37. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
180 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.
Arrangements - orders - schedules - or lists.
x² + 2xy + y²


38. Probability Formula
1
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Favorable Outcomes/Total Possible Outcomes
An integer is divisible by 5 if its units digit is either 0 or 5.


39. HIGH: Volume of a cube?
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.
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.
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
V=s³


40. What causes 80% of errors on the math section of the GRE?
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%.
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'.
Not reading the problems carefully enough!
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


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


42. 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.
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
x²-y²
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.


43. 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% |
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


45. HIGH: What is the median?
Favorable Outcomes/Total Possible Outcomes
The # falling in the center of an ordered data set
The average - mean - median - or mode.
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.


46. If something is possible but not certain - what is the numeric range of probability of it happening?
(a+b)(a-b)
The average - mean - median - or mode.
25%
Between 0 and 1.


47. What is the name of a line that extends from the center of a circle to the edge of a circle?
S²
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 radius
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |


48. In a coordinate system - identify the quadrants and describe their location.
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
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


49. HIGH: Rough est. of v1 =
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.
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.
A radius
1


50. HIGH: What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A + Probability B
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 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.