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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: 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)+
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=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

2. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Find the total - or whole - first - and then set up a Ratio Box.

3. How is a range expressed with inequalities?
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Example: 1 < x < 10
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(x-y)²

4. HIGH: What is the unfactored version of x²-y² ?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(x+y)(x-y)
1.4
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.

5. Define the mode of a set of numbers.
6
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.
1/1
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.

6. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
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.
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.
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.

7. HIGH: Area of a triangle?
S*v2
V=pr²h (This is just the area multiplied by the height)
4 angles are formed. Their sum is 360 degrees
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

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

9. What is the 'distributive law'?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
(x+y)(x-y)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

10. HIGH: x^-n is equal to
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.
Example: 1 < x < 10
1/x^n For example - 6-² = 1/6² = 1/36
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

11. How do you solve a combination?

12. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
(x+y)(x-y)
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

13. How do you multiply fractions?
V=s³
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
An integer is divisible by 2 if its units digit is divisible by 2.
Multiply numerator times numerator and denominator times denominator.

14. HIGH: what is the side ratio for a Right Isosceles triangle?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
80%
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.

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

16. Probability Formula
Bh
Not necessarily. This is a trick question - because x could be either positive or negative.
Favorable Outcomes/Total Possible Outcomes
V=s³

17. Define the range of a set of numbers.
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.
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.
(x+y)(x-y)
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.

18. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
1/1
360 degrees
2pr -or- pd

19. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
4 angles are formed. Their sum is 360 degrees
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
25%

20. HIGH: What is the unfactored version of (x-y)² ?
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
x² -2xy + y²

21. Area of a square?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
S²
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.
90 degrees each.

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

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

24. Explain how to solve for 7/¼
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Groups - teams - or committees.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

25. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
'Big' angles and 'Small' angles.
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.
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

26. What is a 'Right' triangle?
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.
A triangle in which one of the three interior angles is 90 degrees.
(a+b)(a-b)
180 degrees.

27. The three exterior angles of a triangle add up to...
360 degrees
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
x²-y²

28. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
80%
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
40%

29. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
360 degrees
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

30. An integer is divisible by 8 if...

31. Explain how to use an 'Average Pie'
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
60%

32. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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.

33. Convert to a percentage: 1/4
A 90-degree angle.
25%
3:4:5 5:12:13
V=pr²h (This is just the area multiplied by the height)

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

35. 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
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

36. What is a 'Right' angle?
Order does matter for a permutation - but does not matter for a combination.
Not necessarily. This is a trick question - because x could be either positive or negative.
360 degrees
A 90-degree angle.

37. How do you calculate the percentage of change?
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)+
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Percentage Change = Difference/Original * 100
An integer is divisible by 5 if its units digit is either 0 or 5.

38. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
2pr -or- pd
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.
Invert the second fraction (reciprocal) and multiply

39. a² - b² is equal to
(a+b)(a-b)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(0 -0)
'Big' angles and 'Small' angles.

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

41. HIGH: How do you multiply and divide square roots?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
4 angles are formed. Their sum is 360 degrees

42. Convert to a percentage: 4/5
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
80%

43. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
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'.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Invert the second fraction (reciprocal) and multiply

44. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
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.
S*v2

45. How many degrees does a circle contain?
A triangle in which one of the three interior angles is 90 degrees.
6
1/x^n For example - 6-² = 1/6² = 1/36
360 degrees

46. HIGH: Rough est. of v3 =
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1.7
80%
V=pr²h (This is just the area multiplied by the height)

47. What is the factored version of x² -2xy + y² ?
A 90-degree angle.
60%
(x-y)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

48. HIGH: Volume of a cylinder?
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.
A=pr²
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
V=pr²h (This is just the area multiplied by the height)

49. Define 'proportionate' values
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
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

50. An integer is divisible by 5 if...
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
A line is a 180-degree angle.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.