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: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
360 degrees
2
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.


2. How is a range expressed with inequalities?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2pr -or- pd
180 degrees.
Example: 1 < x < 10


3. What are the side ratios for a 30:60:90 triangle?
A triangle in which one of the three interior angles is 90 degrees.
Arrangements - orders - schedules - or lists.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x 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.


4. The three interior angles of a triangle add up to...
2pr -or- pd
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
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.


5. HIGH: What is the factored version of x² + 2xy + y² ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
(x+y)²


6. Convert to a percentage: 4/5
Groups - teams - or committees.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
80%
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


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


8. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
V=s³
4 angles are formed. Their sum is 360 degrees
A=pr²


9. HIGH: Simplify this: v75/v27
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.
V=s³
Probability A * Probability B
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3


10. What degree angle is a line?
Percentage Change = Difference/Original * 100
A line is a 180-degree angle.
90 degrees each.
4 angles are formed. Their sum is 360 degrees


11. Define a factorial of a number - and how it is written.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1. Given event A: A + notA = 1.
Find the total - or whole - first - and then set up a Ratio Box.
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.


12. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
90 degrees each.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.


13. HIGH: How do you multiply and divide square roots?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
x² -2xy + y²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


14. 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


15. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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. 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.


16. 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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A radius


17. What do permutation problems often ask for?
The total # of possible outcomes.
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.
Arrangements - orders - schedules - or lists.


18. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
1.4
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.
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


19. An integer is divisible by 2 if...
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
360 degrees
An integer is divisible by 2 if its units digit is divisible by 2.
2pr -or- pd


20. Explain how to use an 'Average Pie'
A line is a 180-degree angle.
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.
S²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.


21. HIGH: Define the formula for calculating slope.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The value that appears most often in a data set.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
'Big' angles and 'Small' angles.


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


23. In a coordinate system - identify the quadrants and describe their location.
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
A 90-degree angle.
3:4:5 5:12:13
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.


24. HIGH: What is the Pythagorean theorem?

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


25. What is a 'Right' angle?
Probability A + Probability B
S*v2
Arrangements - orders - schedules - or lists.
A 90-degree angle.


26. Define 'proportionate' values
Not reading the problems carefully enough!
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.


27. 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


28. Diameter of a circle?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2r
25%
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.


29. 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


30. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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.
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
2pr -or- pd


31. The three exterior angles of a triangle add up to...
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
2pr -or- pd
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
360 degrees


32. 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


33. What do combination problems usually ask for?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1.7
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.


34. What is the sum of any 'big' angle and any 'Small' angle?
A triangle in which one of the three interior angles is 90 degrees.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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)+
180 degrees.


35. Area of a parallelogram?
360 degrees
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Bh


36. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
180 degrees


37. Convert to a percentage: 3/5
Bh
(x-y)²
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.
60%


38. How do you divide fractions?
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Invert the second fraction (reciprocal) and multiply
A=pr²


39. HIGH: What is a '30:60:90' triangle?
A line is a 180-degree angle.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.


40. Explain how to solve for 7/¼
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2


41. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Order does matter for a permutation - but does not matter for a combination.
Probability A + Probability 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.


42. What causes 80% of errors on the math section of the GRE?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/1
Not reading the problems carefully enough!


43. How do you solve a combination?

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


44. a² - b² is equal to
180 degrees.
Order does matter for a permutation - but does not matter for a combination.
(a+b)(a-b)
x²-y²


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

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


46. HIGH: What is the unfactored version of (x-y)² ?
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'.
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
(x-y)²


47. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.


48. Explain the difference between handling a permutation versus a combination.
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
x² -2xy + y²
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.


49. What is the key to dealing with ratio questions?
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
Find the total - or whole - first - and then set up a Ratio Box.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
1


50. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
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
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.
Between 0 and 1.