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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 and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Probability A * Probability B
Not necessarily. This is a trick question - because x could be either positive or negative.
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
S²

2. What causes 80% of errors on the math section of the GRE?
180 degrees.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Not reading the problems carefully enough!

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

4. HIGH: Simplify this: v75/v27
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
25%
Invert the second fraction (reciprocal) and multiply
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.

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

6. Area of a parallelogram?
The average - mean - median - or mode.
Bh
(x+y)²
Order does matter for a permutation - but does not matter for a combination.

7. 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.
'Big' angles and 'Small' angles.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

8. Define a factorial of a number - and how it is written.
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.
2r
1

9. How do you add or subtract 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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find a common denominator and make equivalent fractions. Then add or subtract.
25%

10. Explain the special properties of zero.
A triangle in which one of the three interior angles is 90 degrees.
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.
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.
(0 -0)

11. List two odd behaviors of exponents
(x-y)²
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
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

12. What degree angle is a line?
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.
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 line is a 180-degree angle.
80%

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

14. Convert to a percentage: 2/5
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.
40%
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.

15. What number goes on the bottom of a probability fraction?
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The total # of possible outcomes.
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.

16. HIGH: How do you calculate the circumference of a circle?
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
Not reading the problems carefully enough!
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
2pr -or- pd

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

18. HIGH: What is the side ratio for a 30:60:90 triangle?
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'.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1
Probability A + Probability B

19. In a coordinate system - what is the origin?
A=pr²
(0 -0)
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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

20. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
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 6 if it'S divisible by BOTH 2 and 3.
A radius

21. HIGH: What is the formula for the diagonal of any square?
S*v2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
4 angles are formed. Their sum is 360 degrees

22. An integer is divisible by 5 if...
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Favorable Outcomes/Total Possible Outcomes
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An integer is divisible by 5 if its units digit is either 0 or 5.

23. The three exterior angles of a triangle add up to...
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
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.
360 degrees

24. The three interior angles of a triangle add up to...
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.
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'.
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.
180 degrees

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

26. Explain the difference between handling a permutation versus a combination.
A radius
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.
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.
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.

27. 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.
The total # of possible outcomes.
4 angles are formed. Their sum is 360 degrees
A triangle in which one of the three interior angles is 90 degrees.

28. HIGH: Rough est. of v3 =
180 degrees.
1.7
An integer is divisible by 2 if its units digit is divisible by 2.
'Big' angles and 'Small' angles.

29. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
2pr -or- pd
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
x² -2xy + y²

30. Area of a square?
S²
360 degrees
1/1
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.

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

32. An integer is divisible by 3 if...
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
25%
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.

33. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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.
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.

34. HIGH: List the two most common side ratios for right triangles
'Big' angles and 'Small' angles.
The # falling in the center of an ordered data set
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.
3:4:5 5:12:13

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

36. HIGH: What is the Pythagorean theorem?

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

38. HIGH: Area of a circle
1
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
A=pr²

39. Does order matter for a permutation? How about for a combination?
x²-y²
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)+
Order does matter for a permutation - but does not matter for a combination.
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.

40. 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 - and greater than the difference between the other two sides.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Example: 1 < x < 10
A 90-degree angle.

41. What is the sum of any 'big' angle and any 'Small' angle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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.

42. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
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'.
1

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

44. Convert to a percentage: 4/5
1. Given event A: A + notA = 1.
80%
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 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

45. HIGH: how do you calculate the surface area of a rectangular box?
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. 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
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.
Order does matter for a permutation - but does not matter for a combination.

46. Explain how to solve for 7/¼
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
3:4:5 5:12:13
2r

47. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
x² + 2xy + y²
Probability A + Probability B
1/x^n For example - 6-² = 1/6² = 1/36
180 degrees

48. How is a range expressed with inequalities?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Example: 1 < x < 10
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x-y)²

49. HIGH: Volume of a cylinder?
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.
V=pr²h (This is just the area multiplied by the height)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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

50. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
S*v2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x² + 2xy + y²