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: Describe how to deal with 2 sets of parentheses.
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.
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.
Between 0 and 1.


2. Diameter of a circle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
2r
25%


3. HIGH: What is the factored version of x² + 2xy + y² ?
80%
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
(x+y)²


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

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5. Define a factorial of a number - and how it is written.
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
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.
1.4
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.


6. Convert to a percentage: 3/5
(x+y)²
60%
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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%.


7. Explain how to solve for 7/¼
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.
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
360 degrees


8. 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
180 degrees
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.
(x+y)²


9. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² + 2xy + y²
3:4:5 5:12:13


10. HIGH: What is a '30:60:90' triangle?
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'.
A=pr²
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


11. What'S the most important thing to remember about charts you'll see on the GRE?
Not necessarily. This is a trick question - because x could be either positive or negative.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
(a+b)(a-b)


12. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
S²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


13. Area of a parallelogram?
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.
Bh
1


14. How is a range expressed with inequalities?
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'.
Example: 1 < x < 10
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The average - mean - median - or mode.


15. What is the 'distributive law'?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A 90-degree angle.
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 total # of possible outcomes.


16. HIGH: List the two most common side ratios for right triangles
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Bh
3:4:5 5:12:13


17. If something is possible but not certain - what is the numeric range of probability of it happening?
Multiply numerator times numerator and denominator times denominator.
S²
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
Between 0 and 1.


18. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Percentage Change = Difference/Original * 100
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
1/1
90 degrees each.


19. What is the factored version of x² -2xy + y² ?
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
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'.
(x-y)²


20. In a coordinate system - what is the origin?
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
(0 -0)
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.


21. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


22. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(x+y)(x-y)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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
1. Given event A: A + notA = 1.


23. Explain how to divide fractions.
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A triangle in which one of the three interior angles is 90 degrees.


24. How do you calculate the probability of two events in a row? (Probability of A and B)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
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.
Probability A * Probability B


25. HIGH: To divide powers with the same base...
25%
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4 angles are formed. Their sum is 360 degrees
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


26. HIGH: Rough est. of v3 =
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Example: 1 < x < 10
1.7


27. Convert to a percentage: 2/5
40%
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5


28. How do you solve a combination?

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29. How do you divide fractions?
Invert the second fraction (reciprocal) and multiply
1/1
Bh
360 degrees


30. HIGH: x^-n is equal to
360 degrees
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.
An integer is divisible by 2 if its units digit is divisible by 2.
1/x^n For example - 6-² = 1/6² = 1/36


31. An integer is divisible by 5 if...
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Order does matter for a permutation - but does not matter for a combination.


32. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Example: 1 < x < 10


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

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34. What is an 'equilateral' triangle?
4 angles are formed. Their sum is 360 degrees
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2r
2pr -or- pd


35. HIGH: What is the Pythagorean theorem?

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36. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
(x+y)²
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
2pr -or- pd


37. Explain the special properties of zero.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Between 0 and 1.


38. HIGH: Area of a circle
S*v2
A=pr²
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.
(x-y)²


39. What number goes on the bottom of a probability fraction?
180 degrees.
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
The total # of possible outcomes.


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

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41. Explain how to use a 'Rate Pie'
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
3:4:5 5:12:13
S²


42. What do permutation problems often ask for?
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
Multiply numerator times numerator and denominator times denominator.
Not reading the problems carefully enough!
Arrangements - orders - schedules - or lists.


43. HIGH: how do you calculate the surface area of a rectangular box?
180 degrees.
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.
1/x^n For example - 6-² = 1/6² = 1/36
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.


44. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
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'.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x+y)²


45. What is the 'Third side' rule for triangles?
Not reading the problems carefully enough!
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.
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 triangle in which one of the three interior angles is 90 degrees.


46. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
2
A line is a 180-degree angle.


47. a² - b² is equal to
An integer is divisible by 5 if its units digit is either 0 or 5.
6
(a+b)(a-b)
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


48. HIGH: How much of your times table should you know - for the GRE?
x² -2xy + y²
It will be a great advantage on test day to have your times table memorized from 1 through 15.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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)+


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

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

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