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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. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
An integer is divisible by 5 if its units digit is either 0 or 5.
Not reading the problems carefully enough!
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Multiply numerator times numerator and denominator times denominator.

2. What'S one way to avoid mistakes on algebra questions in the GRE?

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

4. HIGH: Volume of a cube?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V=s³
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

5. HIGH: What is the unfactored version of x²-y² ?
x² + 2xy + y²
(x+y)(x-y)
x² -2xy + y²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

6. HIGH: What is the median?
x² + 2xy + y²
360 degrees
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The # falling in the center of an ordered data set

7. Explain how to calculate an average (arithmetic mean)
A triangle in which one of the three interior angles is 90 degrees.
x² -2xy + y²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
3:4:5 5:12:13

8. HIGH: How do you multiply and divide square roots?
An integer is divisible by 5 if its units digit is either 0 or 5.
6
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A radius

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

10. HIGH: What is the unfactored version of (x-y)² ?
V=s³
A triangle in which one of the three interior angles is 90 degrees.
x² -2xy + y²
Not necessarily. This is a trick question - because x could be either positive or negative.

11. Diameter of a circle?
2r
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

12. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

13. HIGH: What is the formula for the diagonal of any square?
1.4
The value that appears most often in a data set.
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.
S*v2

14. What is the key to dealing with ratio questions?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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%.
Favorable Outcomes/Total Possible Outcomes
Find the total - or whole - first - and then set up a Ratio Box.

15. Area of a parallelogram?
Bh
6
S²
90 degrees each.

16. 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)+
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
The # falling in the center of an ordered data set

17. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
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.

18. Probability Formula
Groups - teams - or committees.
Favorable Outcomes/Total Possible Outcomes
2pr -or- pd
A 90-degree angle.

19. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
2r
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
S²

20. Explain how to use a 'Rate Pie'
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Order does matter for a permutation - but does not matter for a combination.
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.

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

22. Simplify this: v32
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
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
360 degrees

23. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Between 0 and 1.
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
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
A line is a 180-degree angle.

24. What is the equation for a group problem?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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/x^n For example - 6-² = 1/6² = 1/36

25. What number goes on the bottom of a probability fraction?
A=pr²
The total # of possible outcomes.
S²
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

26. How do you solve a combination?

27. What is an 'equilateral' triangle?
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.
Not reading the problems carefully enough!
2pr -or- pd
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

28. What is the formula to determine probability?
(0 -0)
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A radius

29. HIGH: x^-n is equal to
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
1/x^n For example - 6-² = 1/6² = 1/36
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

30. 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% |
4 angles are formed. Their sum is 360 degrees
60%
V=s³

31. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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 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.
Example: 1 < x < 10
4 angles are formed. Their sum is 360 degrees

32. HIGH: What is a 'Right isosceles' triangle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
The # falling in the center of an ordered data set

33. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

34. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
The total # of possible outcomes.

35. Area of a square?
S²
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.
Bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

36. Define the range of a set of numbers.
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
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.
180 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.

37. How is a range expressed with inequalities?
Invert the second fraction (reciprocal) and multiply
Probability A * Probability B
Example: 1 < x < 10
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

38. How do you calculate the probability of two events in a row? (Probability of A and B)
(x+y)²
60%
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

39. The three exterior angles of a triangle add up to...
360 degrees
Find a common denominator and make equivalent fractions. Then add or subtract.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Multiply numerator times numerator and denominator times denominator.

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

41. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
(x-y)²
Between 0 and 1.
Arrangements - orders - schedules - or lists.

42. HIGH: Rough est. of v1 =
80%
1
Between 0 and 1.
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'.

43. HIGH: Define the formula for calculating slope.
Order does matter for a permutation - but does not matter for a combination.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

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

45. What causes 80% of errors on the math section of the GRE?
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.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
Not reading the problems carefully enough!

46. What is the 'distributive law'?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
Arrangements - orders - schedules - or lists.
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.

47. HIGH: How much of your times table should you know - for the GRE?
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.
3:4:5 5:12:13
It will be a great advantage on test day to have your times table memorized from 1 through 15.
S²

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

49. How many degrees does a circle contain?
An integer is divisible by 2 if its units digit is divisible by 2.
The # falling in the center of an ordered data set
360 degrees
Find the total - or whole - first - and then set up a Ratio Box.

50. What is a 'Right' angle?
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
A 90-degree angle.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.