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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. An integer is divisible by 8 if...

2. How do you divide fractions?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Invert the second fraction (reciprocal) and multiply
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.
2

3. Simplify this: v32
(x+y)(x-y)
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

4. HIGH: What is a 'Right isosceles' triangle?
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.
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.
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

5. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

6. What number goes on the bottom of a probability fraction?
Find the total - or whole - first - and then set up a Ratio Box.
The total # of possible outcomes.
1/1
V=pr²h (This is just the area multiplied by the height)

7. Solve this: v6 * -v6 = ?
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
6
Invert the second fraction (reciprocal) and multiply
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'.

8. HIGH: What is a '30:60:90' triangle?
(0 -0)
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Example: 1 < x < 10

9. Convert to a percentage: 3/5
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.
60%
A triangle in which one of the three interior angles is 90 degrees.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

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

11. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
360 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Find the total - or whole - first - and then set up a Ratio Box.

12. What degree angle is a line?
25%
A line is a 180-degree angle.
The # falling in the center of an ordered data set
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

13. HIGH: How do you calculate the circumference of a circle?
1/x^n For example - 6-² = 1/6² = 1/36
90 degrees each.
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
2pr -or- pd

14. What is the 'distributive law'?
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(0 -0)
2r

15. HIGH: What is the unfactored version of x²-y² ?
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
The total # of possible outcomes.
(x+y)(x-y)

16. HIGH: What is the side ratio for a 30:60:90 triangle?
V=pr²h (This is just the area multiplied by the height)
3:4:5 5:12:13
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

17. What is the factored version of x² -2xy + y² ?
(x-y)²
S*v2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

18. What is the sum of any 'big' angle and any 'Small' angle?
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.
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.
180 degrees.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

19. In a coordinate system - what is the origin?
A triangle in which one of the three interior angles is 90 degrees.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(0 -0)
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.

20. HIGH: How do you multiply and divide square roots?
25%
Example: 1 < x < 10
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.

21. 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.
1/1
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.

22. What is the formula to determine probability?
80%
Groups - teams - or committees.
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)

23. HIGH: Rough est. of v1 =
1.4
Invert the second fraction (reciprocal) and multiply
1
A line is a 180-degree angle.

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

25. The three exterior angles of a triangle add up to...
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
360 degrees
(0 -0)

26. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
x² -2xy + y²
4 angles are formed. Their sum is 360 degrees
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

27. HIGH: Describe how to deal with 2 sets of parentheses.
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.
1
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.
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)+

28. Area of a square?
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
2
S²

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

30. The three interior angles of a triangle add up to...
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 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.
180 degrees
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

31. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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

33. HIGH: What is the unfactored version of (x-y)² ?
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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
x² -2xy + y²
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

34. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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
Invert the second fraction (reciprocal) and multiply
2

35. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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 90-degree angle.

36. HIGH: How much of your times table should you know - for 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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
V=s³
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

37. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
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.

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

39. Probability Formula
2r
(x+y)(x-y)
Favorable Outcomes/Total Possible Outcomes
90 degrees each.

40. What are the side ratios for a 30:60:90 triangle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
1.7
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

41. HIGH: How do you multiply powers with the same base?
A triangle in which one of the three interior angles is 90 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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Bh

42. HIGH: how do you calculate the surface area of a rectangular box?
Probability A + Probability B
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.
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.

43. Define a factorial of a number - and how it is written.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.
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.

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

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

46. HIGH: What is the Pythagorean theorem?

47. Explain how to use a 'Rate Pie'
180 degrees.
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
'Big' angles and 'Small' angles.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

48. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The # falling in the center of an ordered data set
180 degrees
Between 0 and 1.

49. What is a 'Right' triangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Probability A + Probability B
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.
A triangle in which one of the three interior angles is 90 degrees.

50. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
'Big' angles and 'Small' angles.
(x+y)²
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)+