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. v4 =
2
6
The average - mean - median - or mode.
3:4:5 5:12:13


2. In a coordinate system - what is the origin?
Groups - teams - or committees.
(0 -0)
S²
The value that appears most often in a data set.


3. HIGH: What is the unfactored version of (x+y)² ?
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.
x² + 2xy + y²
An integer is divisible by 5 if its units digit is either 0 or 5.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


4. List all the prime numbers that are less than 30:
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.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
180 degrees.


5. How do you solve a permutation?
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
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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


6. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Order does matter for a permutation - but does not matter for a combination.
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.
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.


7. What is the key to dealing with ratio questions?
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.
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.
x²-y²
Find the total - or whole - first - and then set up a Ratio Box.


8. HIGH: Area of a circle
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
1/1
S*v2
A=pr²


9. Probability Formula
Favorable Outcomes/Total 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
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.
A 90-degree angle.


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

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11. What number goes on the bottom of a probability fraction?
1
The total # of possible outcomes.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A 90-degree angle.


12. Convert to a percentage: 4/5
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.
80%
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


13. How do you calculate the percentage of change?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Percentage Change = Difference/Original * 100


14. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
(x-y)²
90 degrees each.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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


15. HIGH: What is a '30:60:90' triangle?
60%
The value that appears most often in a data set.
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 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |


16. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


17. How do you add or subtract fractions?
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.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
V=s³


18. What is the equation for a group problem?
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.
x² + 2xy + y²
The # falling in the center of an ordered data set
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


19. What is the 'distributive law'?
Example: 1 < x < 10
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 value that appears most often in a data set.
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.


20. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
1.4
x² + 2xy + y²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


21. Area of a square?
S²
2pr -or- pd
S*v2
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


22. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.


23. An integer is divisible by 2 if...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
An integer is divisible by 2 if its units digit is divisible by 2.
S*v2
A radius


24. What causes 80% of errors on the math section of the GRE?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A 90-degree angle.
2
Not reading the problems carefully enough!


25. The three interior angles of a triangle add up to...
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
180 degrees
V=s³


26. An integer is divisible by 4 if...

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27. Explain the difference between handling a permutation versus a combination.
A 90-degree angle.
(x+y)(x-y)
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


28. Simplify this: v32
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The total # of possible outcomes.
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.


29. An integer is divisible by 6 if...

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30. Define a factorial of a number - and how it is written.
Bh
80%
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.
The # falling in the center of an ordered data set


31. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
Groups - teams - or committees.
V=pr²h (This is just the area multiplied by the height)
The # falling in the center of an ordered data set


32. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
90 degrees each.
80%
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.


33. What degree angle is a line?
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.
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 line is a 180-degree angle.
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.


34. The three exterior angles of a triangle add up to...
(0 -0)
S²
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.
360 degrees


35. HIGH: What is the median?
The # falling in the center of an ordered data set
S²
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!


36. HIGH: What is a 'Right isosceles' triangle?
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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


37. Define the mode of a set of numbers.
25%
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
x² -2xy + y²


38. An integer is divisible by 3 if...
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
4 angles are formed. Their sum is 360 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.


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

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

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41. HIGH: What is the equation of a line?

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42. Explain how to use an 'Average Pie'
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 90-degree angle.
80%
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


43. a² - b² is equal to
Groups - teams - or committees.
3:4:5 5:12:13
An integer is divisible by 5 if its units digit is either 0 or 5.
(a+b)(a-b)


44. HIGH: Rough est. of v3 =
1.7
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.
90 degrees each.
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


45. How do you solve a combination?

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46. What is the factored version of x² -2xy + y² ?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
(x-y)²
Between 0 and 1.
Multiply numerator times numerator and denominator times denominator.


47. 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.
Not reading the problems carefully enough!
60%
'Big' angles and 'Small' angles.


48. Diameter of a circle?
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.
2r
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


49. HIGH: What 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.
The value that appears most often in a data set.
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
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.


50. HIGH: How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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'.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.