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: Rough est. of v3 =
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
x² -2xy + y²
1.7
Not reading the problems carefully enough!


2. Define the mode of a set of numbers.
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.
A=pr²
S²
The # falling in the center of an ordered data set


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

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4. Probability Formula
The average - mean - median - or mode.
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)+
Favorable Outcomes/Total Possible Outcomes
(a+b)(a-b)


5. Define 'proportionate' values
(x+y)(x-y)
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.
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.


6. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Invert the second fraction (reciprocal) and multiply
(x+y)²
Multiply numerator times numerator and denominator times denominator.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


7. Define the range of a set of numbers.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A=pr²
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.
Not necessarily. This is a trick question - because x could be either positive or negative.


8. HIGH: Rough est. of v2 =
1.4
360 degrees
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.
80%


9. HIGH: what is the side ratio for a Right Isosceles triangle?
A=pr²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 2 if its units digit is divisible by 2.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


10. What are 'vertical angles'?
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
360 degrees
360 degrees


11. HIGH: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.


12. HIGH: What is the unfactored version of (x+y)² ?
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%.
'Big' angles and 'Small' angles.
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
x² + 2xy + y²


13. HIGH: List the two most common side ratios for right triangles
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.
V=pr²h (This is just the area multiplied by the height)
3:4:5 5:12:13
(a+b)(a-b)


14. 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
Not necessarily. This is a trick question - because x could be either positive or negative.
A triangle in which one of the three interior angles is 90 degrees.
1. Given event A: A + notA = 1.


15. Convert to a percentage: 4/5
80%
Not reading the problems carefully enough!
1/x^n For example - 6-² = 1/6² = 1/36
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.


16. HIGH: What is the formula for the diagonal of any square?
Arrangements - orders - schedules - or lists.
Groups - teams - or committees.
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.
S*v2


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

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18. What do combination problems usually ask for?
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
Groups - teams - or committees.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Not reading the problems carefully enough!


19. An integer is divisible by 2 if...
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 2 if its units digit is divisible by 2.
1
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.


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

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21. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
(x+y)²
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.
Order does matter for a permutation - but does not matter for a combination.
4 angles are formed. Their sum is 360 degrees


22. Simplify this: v32
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.
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'.
(0 -0)


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

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

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25. What do permutation problems often ask for?
An integer is divisible by 5 if its units digit is either 0 or 5.
A triangle in which one of the three interior angles is 90 degrees.
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
Arrangements - orders - schedules - or lists.


26. HIGH: What is the side ratio for a 30:60:90 triangle?
The # falling in the center of an ordered data set
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Not reading the problems carefully enough!
An integer is divisible by 5 if its units digit is either 0 or 5.


27. HIGH: Area of a triangle?
1/1
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
1. Given event A: A + notA = 1.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


28. HIGH: Define the formula for calculating slope.
The total # of possible outcomes.
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.
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


29. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
Not reading the problems carefully enough!
Favorable Outcomes/Total Possible Outcomes
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)+


30. Explain the difference between handling a permutation versus a combination.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
90 degrees each.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.


31. What'S the most important thing to remember about charts you'll see on the GRE?
An integer is divisible by 2 if its units digit is divisible by 2.
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.
Arrangements - orders - schedules - or lists.
A line is a 180-degree angle.


32. HIGH: What is the unfactored version of x²-y² ?
A radius
(x+y)(x-y)
80%
(0 -0)


33. The three exterior angles of a triangle add up to...
(x-y)²
360 degrees
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A line is a 180-degree angle.


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

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35. Solve this: v6 * -v6 = ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
6
1.4
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


36. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a+b)(a-b)
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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


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

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38. What degree angle is a line?
A line is a 180-degree angle.
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 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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4


39. In a coordinate system - what is the origin?
(0 -0)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
An integer is divisible by 5 if its units digit is either 0 or 5.
60%


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

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41. Convert to a percentage: 3/5
A line is a 180-degree angle.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
60%
A radius


42. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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.
Probability A + Probability B
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.
Favorable Outcomes/Total Possible Outcomes


43. How do you solve a permutation?
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. 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
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.


44. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
1. Given event A: A + notA = 1.
2r
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.


45. What causes 80% of errors on the math section of the GRE?
A 90-degree angle.
1/1
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 reading the problems carefully enough!


46. How do you calculate the percentage of change?
x² -2xy + y²
2pr -or- pd
2r
Percentage Change = Difference/Original * 100


47. How is a range expressed with inequalities?
Bh
Example: 1 < x < 10
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.
(a+b)(a-b)


48. An integer is divisible by 9 if...
(x+y)(x-y)
(x+y)²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
An integer is divisible by 9 if the sum of its digits is divisible by 9.


49. HIGH: Simplify this: v75/v27
'Big' angles and 'Small' angles.
180 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.
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.


50. What is an 'equilateral' triangle?
1/x^n For example - 6-² = 1/6² = 1/36
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.
360 degrees
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.