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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. In a coordinate system - identify the quadrants and describe their location.
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.
360 degrees
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
180 degrees

2. What is the key to dealing with ratio questions?
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.
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Find the total - or whole - first - and then set up a Ratio Box.

3. HIGH: What is the side ratio for a 30:60:90 triangle?
(a+b)(a-b)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

4. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
The # falling in the center of an ordered data set
90 degrees each.
S*v2

5. HIGH: What is the unfactored version of x²-y² ?
2r
(x+y)(x-y)
An integer is divisible by 5 if its units digit is either 0 or 5.
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.

6. HIGH: What is the unfactored version of (x+y)² ?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Favorable Outcomes/Total Possible Outcomes
x² + 2xy + y²
180 degrees

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

8. What is the 'Third side' rule for triangles?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Invert the second fraction (reciprocal) and multiply
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.

9. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A line is a 180-degree angle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

10. Convert to a percentage: 3/5
60%
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)+
An integer is divisible by 2 if its units digit is divisible by 2.
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.

11. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
Not reading the problems carefully enough!
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'.
S²

12. HIGH: What is the Pythagorean theorem?

13. The probability of an event happening and the probability of an event NOT happening must add up to what number?
A triangle in which one of the three interior angles is 90 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.
1. Given event A: A + notA = 1.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

14. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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
It will be a great advantage on test day to have your times table memorized from 1 through 15.
2r

15. 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.
1/1
Probability A * Probability B
An integer is divisible by 2 if its units digit is divisible by 2.

16. HIGH: List the two most common side ratios for right triangles
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
3:4:5 5:12:13
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

17. Convert to a percentage: 1/4
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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

18. HIGH: What is the unfactored version of (x-y)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.
An integer is divisible by 5 if its units digit is either 0 or 5.
The total # of possible outcomes.
x² -2xy + y²

19. v4 =
2
1/1
25%
An integer is divisible by 2 if its units digit is divisible by 2.

20. What is a 'Right' 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
Find a common denominator and make equivalent fractions. Then add or subtract.
The average - mean - median - or mode.
A 90-degree angle.

21. HIGH: What is the median?
An integer is divisible by 2 if its units digit is divisible by 2.
S*v2
A radius
The # falling in the center of an ordered data set

22. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
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.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

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

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

25. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
1/1
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
180 degrees
Probability A + Probability B

26. What is an 'equilateral' triangle?
2pr -or- pd
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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

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

28. What is the equation for a group problem?
2r
360 degrees
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.
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

29. What is the name of a line that extends from the center of a circle to the edge of a circle?
1/x^n For example - 6-² = 1/6² = 1/36
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
A radius
The value that appears most often in a data set.

30. List two odd behaviors of exponents
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.
60%
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

31. Diameter of a circle?
Bh
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.
Example: 1 < x < 10
2r

32. An integer is divisible by 3 if...
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
6

33. HIGH: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Between 0 and 1.
x²-y²

34. The three exterior angles of a triangle add up to...
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
180 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.
360 degrees

35. HIGH: Area of a circle
A=pr²
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.

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

37. How is a range expressed with inequalities?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Example: 1 < x < 10
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

38. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
25%
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.

39. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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

40. HIGH: What is the formula for the diagonal of any square?
A radius
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S*v2

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

42. Does order matter for a permutation? How about for a combination?
'Big' angles and 'Small' angles.
Find the total - or whole - first - and then set up a Ratio Box.
Order does matter for a permutation - but does not matter for a combination.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

43. Explain how to use a 'Rate Pie'
2pr -or- pd
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 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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

44. Explain the special properties of zero.
80%
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.
Percentage Change = Difference/Original * 100
The value that appears most often in a data set.

45. What do combination problems usually ask for?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
Groups - teams - or committees.
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.

46. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
A radius
Between 0 and 1.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

47. Simplify this: v32
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
An integer is divisible by 9 if the sum of its digits is divisible by 9.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

48. Convert to a percentage: 4/5
80%
360 degrees
The value that appears most often in a data set.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

49. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
4 angles are formed. Their sum is 360 degrees

50. How do you add or subtract fractions?
x² + 2xy + y²
Find a common denominator and make equivalent fractions. Then add or subtract.
V=pr²h (This is just the area multiplied by the height)
Bh