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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 4 if...

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

3. HIGH: What is a 'Right isosceles' triangle?
Probability A * Probability B
6
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

4. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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%.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

5. Area of a parallelogram?
360 degrees
Bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

6. Convert to a percentage: 1/4
Probability A * Probability B
25%
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.

7. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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 integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
x² -2xy + y²

8. Explain how to use a 'Rate Pie'
(0 -0)
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.
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.

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

10. Define a factorial of a number - and how it is written.
180 degrees
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.
(x-y)²
(x+y)(x-y)

11. HIGH: Rough est. of v2 =
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Invert the second fraction (reciprocal) and multiply
1.4

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

13. HIGH: What is the order of math operations - and the mnemonic to remember it?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.
V=pr²h (This is just the area multiplied by the height)

14. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
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
Find the total - or whole - first - and then set up a Ratio Box.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

15. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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. Given event A: A + notA = 1.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1/1

16. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
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')
1.7

17. HIGH: What is the formula for the diagonal of any square?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
S*v2
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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

18. How do you solve a permutation?
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
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)+
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.
180 degrees

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

20. What do permutation problems often ask for?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Arrangements - orders - schedules - or lists.
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 total # of possible outcomes.

21. If x² = 144 - does v144 = x?
180 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.
Bh
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.

22. Does order matter for a permutation? How about for a combination?
1/1
Order does matter for a permutation - but does not matter for a combination.
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.
x² -2xy + y²

23. Explain how to divide fractions.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Not necessarily. This is a trick question - because x could be either positive or negative.
Between 0 and 1.

24. An integer is divisible by 9 if...
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
1. Given event A: A + notA = 1.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

25. List all the prime numbers that are less than 30:
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Probability A * Probability B
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
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%.

26. Simplify this: v32
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
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
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

27. In a coordinate system - identify the quadrants and describe their location.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

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

29. How is a range expressed with inequalities?
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.
A triangle in which one of the three interior angles is 90 degrees.
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%.
Example: 1 < x < 10

30. HIGH: What is the mode?
25%
The # falling in the center of an ordered data set
The value that appears most often in a data set.
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

31. What is the sum of any 'big' angle and any 'Small' angle?
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.
1
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
180 degrees.

32. HIGH: What is the factored version of x² + 2xy + y² ?
The # falling in the center of an ordered data set
Example: 1 < x < 10
80%
(x+y)²

33. What is the 'distributive law'?
Not reading the problems carefully enough!
The average - mean - median - or mode.
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.
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.

34. HIGH: Simplify this: v75/v27
Find the total - or whole - first - and then set up a Ratio Box.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A radius
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.

35. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
Order does matter for a permutation - but does not matter for a combination.
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
1/1

36. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
Multiply numerator times numerator and denominator times denominator.
90 degrees each.
(x+y)(x-y)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

37. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
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. 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=pr²

38. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
25%
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

39. HIGH: how do you calculate the surface area of a rectangular box?
The average - mean - median - or mode.
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.
80%
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%.

40. Define the range of a set of numbers.
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.
80%
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.

41. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
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
4 angles are formed. Their sum is 360 degrees

42. The three interior angles of a triangle add up to...
V=pr²h (This is just the area multiplied by the height)
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
180 degrees

43. In a coordinate system - what is the origin?
(0 -0)
Arrangements - orders - schedules - or lists.
60%
'Big' angles and 'Small' angles.

44. HIGH: Rough est. of v1 =
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
Not reading the problems carefully enough!
An integer is divisible by 2 if its units digit is divisible by 2.
1

45. What do combination problems usually ask for?
Groups - teams - or committees.
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.
80%
x² + 2xy + y²

46. What is a 'Right' angle?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
A 90-degree angle.
6
3:4:5 5:12:13

47. Define 'proportionate' values
An integer is divisible by 2 if its units digit is divisible by 2.
The average - mean - median - or mode.
Not necessarily. This is a trick question - because x could be either positive or negative.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

48. HIGH: What is the unfactored version of (x+y)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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
x² + 2xy + y²

49. On the GRE - should you ever assume that diagrams are truthful?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Example: 1 < x < 10
Order does matter for a permutation - but does not matter for a combination.

50. a² - b² is equal to
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.
(a+b)(a-b)
Find the total - or whole - first - and then set up a Ratio Box.
x² + 2xy + y²