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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. HIGH: What is the side ratio for a 30:60:90 triangle?
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2pr -or- pd
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

2. What are the side ratios for a 30:60:90 triangle?
x² -2xy + y²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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%.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

4. 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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
Not reading the problems carefully enough!

5. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 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)+
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
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.

6. What is the factored version of x² -2xy + y² ?
1/1
(x-y)²
60%
'Big' angles and 'Small' angles.

7. HIGH: How do you multiply and divide square roots?
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The value that appears most often in a data set.
A line is a 180-degree angle.

8. HIGH: Volume of a cube?
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
V=pr²h (This is just the area multiplied by the height)
V=s³
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'.

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

10. HIGH: What is the median?
Between 0 and 1.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
The # falling in the center of an ordered data set
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.

11. HIGH: What is a 'Right isosceles' 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.
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.
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 90-degree angle.

12. HIGH: Rough est. of v3 =
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.
1.7
A radius
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.

13. What'S the most important thing to remember about charts you'll see on the GRE?
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
Bh
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
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.

14. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

15. Does order matter for a permutation? How about for a combination?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
S²
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

16. 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.
Find the total - or whole - first - and then set up a Ratio Box.
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 5 if its units digit is either 0 or 5.

17. Explain how to divide fractions.
(0 -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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

18. The three interior angles of a triangle add up to...
The total # of possible outcomes.
180 degrees
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
V=s³

19. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
(x-y)²
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

20. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
A line is a 180-degree angle.
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

21. Simplify this: v32
Multiply numerator times numerator and denominator times denominator.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
Percentage Change = Difference/Original * 100

22. HIGH: What is the factored version of x² + 2xy + y² ?
(x+y)²
90 degrees each.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A radius

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

24. What causes 80% of errors on the math section of 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.
Not reading the problems carefully enough!
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
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.

25. Define the range of a set of numbers.
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.
Order does matter for a permutation - but does not matter for a combination.
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.
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.

26. How do you calculate the probability of two events in a row? (Probability of A and B)
Arrangements - orders - schedules - or lists.
Probability A * Probability B
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

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

28. Convert to a percentage: 1/4
25%
Between 0 and 1.
1/1
An integer is divisible by 2 if its units digit is divisible by 2.

29. In a coordinate system - identify the quadrants and describe their location.
Order does matter for a permutation - but does not matter for a combination.
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
1/1
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

30. HIGH: Simplify this: v75/v27
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
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.

31. What do combination problems usually ask for?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The total # of possible outcomes.
Groups - teams - or committees.

32. What is a 'Right' angle?
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%.
A 90-degree angle.
1/1
1.4

33. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Groups - teams - or committees.
Find the total - or whole - first - and then set up a Ratio Box.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

34. Convert to a percentage: 2/5
180 degrees.
40%
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

35. HIGH: List the two most common side ratios for right triangles
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
1.4
3:4:5 5:12:13
Bh

36. 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.
2pr -or- pd
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.

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

38. 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% |
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.
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 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.

39. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Groups - teams - or committees.
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. Given event A: A + notA = 1.
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.

40. HIGH: Area of a triangle?
An integer is divisible by 5 if its units digit is either 0 or 5.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
V=pr²h (This is just the area multiplied by the height)
1/1

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

42. For a bell curve - what three terms might be used to describe the number in the middle?
Favorable Outcomes/Total Possible Outcomes
The average - mean - median - or mode.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

43. How do you solve a permutation?
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.
(x-y)²
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
1/x^n For example - 6-² = 1/6² = 1/36

44. HIGH: Rough est. of v1 =
1
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

45. HIGH: Volume of a cylinder?
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)
4 angles are formed. Their sum is 360 degrees
1/x^n For example - 6-² = 1/6² = 1/36

46. HIGH: What is the unfactored version of (x+y)² ?
25%
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
x² + 2xy + y²
A triangle in which one of the three interior angles is 90 degrees.

47. Explain how to calculate an average (arithmetic mean)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
(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.

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

49. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
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.
x²-y²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

50. What is the 'Third side' rule for triangles?
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
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.
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.