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GRE High Frequency Math Terms

Subjects : gre, math

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. What is the factored version of x² -2xy + y² ?
(x-y)²
4 angles are formed. Their sum is 360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.
x²-y²

2. HIGH: Area of a circle
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.
A triangle in which one of the three interior angles is 90 degrees.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A=pr²

3. HIGH: What is the mode?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Invert the second fraction (reciprocal) and multiply
Probability A + Probability B
The value that appears most often in a data set.

4. How do you divide fractions?
1
Favorable Outcomes/Total Possible Outcomes
Invert the second fraction (reciprocal) and multiply
80%

5. HIGH: What is the side ratio for a 30:60:90 triangle?
(x+y)²
180 degrees.
A 90-degree angle.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

6. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
(a+b)(a-b)
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.
Example: 1 < x < 10

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

8. What is the formula to determine probability?
(x+y)(x-y)
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
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'.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

9. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Probability A + Probability B
The 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.

10. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A=pr²
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

11. 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.
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
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
Probability A * Probability B

12. HIGH: What is the median?
2pr -or- pd
The # falling in the center of an ordered data set
Find the total - or whole - first - and then set up a Ratio Box.
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

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

14. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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 90-degree angle.
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.

15. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
90 degrees each.
4 angles are formed. Their sum is 360 degrees
V=s³
Percentage Change = Difference/Original * 100

16. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Probability A * Probability B
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
x² -2xy + y²

17. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
(0 -0)
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.
180 degrees.

18. An integer is divisible by 2 if...
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
An integer is divisible by 2 if its units digit is divisible by 2.
S*v2
1/1

19. HIGH: Rough est. of v3 =
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
25%
1.7
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

20. In a coordinate system - identify the quadrants and describe their location.
2pr -or- pd
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Between 0 and 1.
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.

21. Explain how to use an 'Average Pie'
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(# 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.

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

23. HIGH: Describe how to deal with 2 sets of parentheses.
An integer is divisible by 2 if its units digit is divisible by 2.
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.
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)+
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

24. How do you add or subtract fractions?
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.
1.4
Find a common denominator and make equivalent fractions. Then add or subtract.
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

25. 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.
The total # of possible outcomes.
Not necessarily. This is a trick question - because x could be either positive or negative.
Probability A + Probability B

26. HIGH: What is a 'Right isosceles' triangle?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
90 degrees each.
(x+y)²
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.

27. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
The average - mean - median - or mode.
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

28. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Find a common denominator and make equivalent fractions. Then add or subtract.
80%
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
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

29. If x² = 144 - does v144 = x?
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
V=pr²h (This is just the area multiplied by the height)
360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.

30. What is the sum of any 'big' angle and any 'Small' angle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
180 degrees.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

31. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

32. How do you solve a combination?

33. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
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.
Probability A * Probability B
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

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

35. HIGH: Rough est. of v2 =
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1.4

36. HIGH: What is the unfactored version of x²-y² ?
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%.
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.
A line is a 180-degree angle.
(x+y)(x-y)

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

38. Explain the difference between handling a permutation versus a combination.
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.
S*v2
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
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.

39. What is the key to dealing with ratio questions?
6
Find the total - or whole - first - and then set up a Ratio Box.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

40. Solve this: v6 * -v6 = ?
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.
6
The value that appears most often in a data set.

41. Define the range of a set of numbers.
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.
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.
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.

42. Convert to a percentage: 1/4
25%
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.

43. How do you solve a permutation?
1
360 degrees
4 angles are formed. Their sum is 360 degrees
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

44. HIGH: Area of a triangle?
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=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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

45. HIGH: Volume of a cylinder?
180 degrees
1
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.
V=pr²h (This is just the area multiplied by the height)

46. The three exterior angles of a triangle add up to...
360 degrees
x² + 2xy + y²
1/x^n For example - 6-² = 1/6² = 1/36
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

47. Explain how to use a 'Rate Pie'
180 degrees.
1/1
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

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

49. HIGH: To divide powers with the same base...
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
360 degrees

50. Explain the difference between a digit and a number.