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: Define the formula for calculating slope.
Percentage Change = Difference/Original * 100
S²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.


2. Explain how to solve for 7/¼
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
'Big' angles and 'Small' angles.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


4. Convert to a percentage: 3/5
'Big' angles and 'Small' angles.
60%
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
1/1


5. What is the sum of any 'big' angle and any 'Small' angle?
V=s³
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.
4 angles are formed. Their sum is 360 degrees
180 degrees.


6. HIGH: What is the formula for the diagonal of any square?
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.
An integer is divisible by 2 if its units digit is divisible by 2.
S*v2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.


7. How do you solve a permutation?
Groups - teams - or committees.
Percentage Change = Difference/Original * 100
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. 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


8. An integer is divisible by 5 if...
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
A line is a 180-degree angle.


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


10. If x² = 144 - does v144 = x?
80%
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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'.


11. HIGH: What is the side ratio for a 30:60:90 triangle?
Probability A + Probability B
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
Find a common denominator and make equivalent fractions. Then add or subtract.


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


13. What should you do BEFORE you start to solve a GRE math problem?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


14. The three interior angles of a triangle add up to...
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
180 degrees
4 angles are formed. Their sum is 360 degrees


15. How do you solve a combination?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


16. HIGH: What is a '30:60:90' triangle?
S*v2
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.
1/x^n For example - 6-² = 1/6² = 1/36
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


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


18. How many degrees does a circle contain?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
360 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.


19. Probability Formula
Favorable Outcomes/Total Possible Outcomes
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
x² + 2xy + y²


20. HIGH: How do you multiply and divide square roots?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
The # falling in the center of an ordered data set
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


21. What is the factored version of x² -2xy + y² ?
(x-y)²
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.


22. What is the name of a line that extends from the center of a circle to the edge of a circle?
(x-y)²
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Bh
A radius


23. Define the range of a set of numbers.
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.
80%
Groups - teams - or committees.
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


24. 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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Between 0 and 1.
180 degrees.


25. What is the formula to determine probability?
3:4:5 5:12:13
V=s³
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)


26. Area of a square?
25%
S²
V=s³
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


27. Explain the difference between handling a permutation versus a combination.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
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'.
25%


28. Area of a parallelogram?
An integer is divisible by 2 if its units digit is divisible by 2.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
V=s³
Bh


29. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
180 degrees.


30. List two odd behaviors of exponents
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.
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.
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.
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.


31. How do you divide fractions?
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.
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.
Invert the second fraction (reciprocal) and multiply
1/1


32. HIGH: How do you calculate the length of an arc?

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


33. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The total # of possible outcomes.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.


34. An integer is divisible by 3 if...
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
40%


35. HIGH: What is the mode?
180 degrees
Groups - teams - or committees.
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 value that appears most often in a data set.


36. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Bh
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.
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'.
1/1


37. HIGH: Rough est. of v3 =
1.7
The value that appears most often in a data set.
Not reading the problems carefully enough!
(a+b)(a-b)


38. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
6
x² -2xy + y²
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
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...

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


40. HIGH: What are the percentages for standard deviation?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Multiply numerator times numerator and denominator times denominator.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.


41. What is the 'distributive law'?
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.
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.


42. Solve this: v6 * -v6 = ?
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
6
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.


43. v4 =
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Between 0 and 1.
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
2


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


45. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Arrangements - orders - schedules - or lists.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
Find a common denominator and make equivalent fractions. Then add or subtract.


46. Does order matter for a permutation? How about for a combination?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Order does matter for a permutation - but does not matter for a combination.
Probability A * Probability B


47. An integer is divisible by 9 if...
1.7
Example: 1 < x < 10
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.


48. 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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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=pr²


49. Explain how to use a 'Rate Pie'
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.
Between 0 and 1.
2pr -or- pd
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


50. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Not reading the problems carefully enough!
4 angles are formed. Their sum is 360 degrees
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 5 if its units digit is either 0 or 5.