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. What is an 'equilateral' triangle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/x^n For example - 6-² = 1/6² = 1/36
25%


2. HIGH: What is the factored version of x² + 2xy + y² ?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
(x+y)²
Groups - teams - or committees.
The average - mean - median - or mode.


3. How is a range expressed with inequalities?
1. Given event A: A + notA = 1.
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%.
Example: 1 < x < 10
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 key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
(a+b)(a-b)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
It will be a great advantage on test day to have your times table memorized from 1 through 15.


5. HIGH: How much of your times table should you know - for the GRE?
Groups - teams - or committees.
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.
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.


6. Diameter of a circle?
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2r
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.


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

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8. How do you add or subtract fractions?
x² -2xy + y²
60%
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.
Find a common denominator and make equivalent fractions. Then add or subtract.


9. Simplify this: v32
An integer is divisible by 9 if the sum of its digits is divisible by 9.
x² + 2xy + y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Probability A * Probability B


10. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
360 degrees
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a+b)(a-b)
(x+y)²


11. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
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'.
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.
3:4:5 5:12:13


12. HIGH: What is a '30:60:90' triangle?
2r
Not reading the problems carefully enough!
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


13. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
An integer is divisible by 2 if its units digit is divisible by 2.
S*v2
Not necessarily. This is a trick question - because x could be either positive or negative.
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.


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

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

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16. What is the 'distributive law'?
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.
1.4
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


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

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18. Define 'proportionate' values
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.
2r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(x-y)²


19. In a coordinate system - what is the origin?
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.
x² -2xy + y²
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
(0 -0)


20. How precise do you need to be - using p on the GRE?

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

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22. HIGH: To divide powers with the same base...
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
360 degrees
6


23. What is the formula to determine probability?
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1
Find the total - or whole - first - and then set up a Ratio Box.


24. HIGH: what is the side ratio for a Right Isosceles triangle?
(a+b)(a-b)
x² -2xy + y²
Probability A + Probability B
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


25. HIGH: What is the unfactored version of (x-y)² ?
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.
A radius
2pr -or- pd
x² -2xy + y²


26. What is the factored version of x² -2xy + y² ?
1. Given event A: A + notA = 1.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
S²
(x-y)²


27. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1.7


28. Define the range of a set of numbers.
S*v2
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.
Multiply numerator times numerator and denominator times denominator.
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. List all the prime numbers that are less than 30:
(x+y)²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
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.


30. HIGH: What is the unfactored version of (x+y)² ?
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 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 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.
x² + 2xy + y²


31. What is the name of a line that extends from the center of a circle to the edge of a circle?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
S*v2
A radius


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

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33. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
x² + 2xy + y²
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.
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.


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

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35. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A line is a 180-degree angle.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


36. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
2
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
3:4:5 5:12:13


37. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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 average - mean - median - or mode.
2pr -or- pd
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.


38. How do you calculate the probability of two events in a row? (Probability of A and B)
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'.
Probability A * Probability B
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
Percentage Change = Difference/Original * 100


39. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The value that appears most often in a data set.


40. HIGH: What is the unfactored version of x²-y² ?
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.
(x+y)(x-y)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.


41. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Favorable Outcomes/Total Possible Outcomes
Example: 1 < x < 10
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


42. 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
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
360 degrees


43. HIGH: What is the factored version of (x+y)(x-y) ?
Probability A * Probability B
x²-y²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Find the total - or whole - first - and then set up a Ratio Box.


44. HIGH: What is a 'Right isosceles' triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
A radius
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


45. Explain the difference between handling a permutation versus a combination.
(0 -0)
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(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.


46. HIGH: What 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.
The value that appears most often in a data set.
180 degrees.
(x+y)²


47. HIGH: Rough est. of v3 =
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1.7


48. HIGH: Define the 'Third side' rule for triangles

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49. HIGH: What is the side ratio for a 30:60:90 triangle?
A=pr²
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.


50. How do you calculate the percentage of change?
V=pr²h (This is just the area multiplied by the height)
1/1
Percentage Change = Difference/Original * 100
1. Given event A: A + notA = 1.