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 median?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x²-y²
The # falling in the center of an ordered data set
2r


2. HIGH: Area of a triangle?
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
1.7
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


3. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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


4. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

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5. HIGH: Rough est. of v2 =
It will be a great advantage on test day to have your times table memorized from 1 through 15.
1.4
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.
Groups - teams - or committees.


6. On the GRE - should you ever assume that diagrams are truthful?
Order does matter for a permutation - but does not matter for a combination.
2r
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.


7. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
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.
x² + 2xy + y²
1/1


8. HIGH: What is the Pythagorean theorem?

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9. HIGH: What is a 'Right isosceles' triangle?
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
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.


10. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/x^n For example - 6-² = 1/6² = 1/36
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
S²


11. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A triangle in which one of the three interior angles is 90 degrees.
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.
x² -2xy + y²
The average - mean - median - or mode.


12. What is the factored version of x² -2xy + y² ?
(x-y)²
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.
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


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

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14. a² - b² is equal to
25%
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.
(a+b)(a-b)


15. HIGH: Simplify this: v75/v27
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).
1. Given event A: A + notA = 1.
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.


16. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Groups - teams - or committees.
(x-y)²
Probability A + Probability B


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

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18. What is the 'Third side' rule for triangles?
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.
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.
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions


19. Area of a square?
S²
Favorable Outcomes/Total Possible Outcomes
Between 0 and 1.
1/1


20. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
An integer is divisible by 2 if its units digit is divisible by 2.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.


21. Explain how to solve for 7/¼
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.
(0 -0)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


22. An integer is divisible by 9 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
2pr -or- pd
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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


23. The three exterior angles of a triangle add up to...
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'.
360 degrees
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


24. In a coordinate system - what is the origin?
x² -2xy + y²
Arrangements - orders - schedules - or lists.
(0 -0)
The total # of possible outcomes.


25. Convert to a percentage: 2/5
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.
40%
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7


26. What are 'vertical angles'?
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.
4 angles are formed. Their sum is 360 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


27. An integer is divisible by 5 if...
2
An integer is divisible by 5 if its units digit is either 0 or 5.
1.7
180 degrees


28. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
(x-y)²
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.
S²


29. Convert to a percentage: 4/5
80%
ZONE-F numbers: Zero - One - Negatives - Extreme values - 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
An integer is divisible by 2 if its units digit is divisible by 2.


30. How do you solve a permutation?
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.
Order does matter for a permutation - but does not matter for a combination.
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
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


31. What do permutation problems often ask for?
The value that appears most often in a data set.
Arrangements - orders - schedules - or lists.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.


32. What number goes on the bottom of a probability fraction?
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
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)+
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.
The total # of possible outcomes.


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

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34. HIGH: how do you calculate the surface area of a rectangular box?
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 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.
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


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

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36. HIGH: How do you multiply and divide square roots?
Favorable Outcomes/Total Possible Outcomes
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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
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.


37. What is the key to dealing with ratio questions?
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Find the total - or whole - first - and then set up a Ratio Box.
Invert the second fraction (reciprocal) and multiply


38. What causes 80% of errors on the math section of the GRE?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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
Not reading the problems carefully enough!
Groups - teams - or committees.


39. How do you calculate the probability of two events in a row? (Probability of A and B)
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.
40%
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
Probability A * Probability B


40. What degree angle is a line?
A line is a 180-degree angle.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Percentage Change = Difference/Original * 100
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.


41. 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)+
Order does matter for a permutation - but does not matter for a combination.
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.
x² + 2xy + y²


42. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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43. What'S the most important thing to remember about charts you'll see on the GRE?
S*v2
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.
60%
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.


44. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
1/x^n For example - 6-² = 1/6² = 1/36
The # falling in the center of an ordered data set
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.
4 angles are formed. Their sum is 360 degrees


45. Diameter of a circle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
V=pr²h (This is just the area multiplied by the height)
A 90-degree angle.
2r


46. For a bell curve - what three terms might be used to describe the number in the middle?
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.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
The average - mean - median - or mode.


47. What is the equation for a group problem?
60%
(x+y)(x-y)
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
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%.


48. How do you solve a combination?

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49. HIGH: Volume of a cube?
Not reading the problems carefully enough!
V=pr²h (This is just the area multiplied by the height)
V=s³
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


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

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