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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. What is the key to dealing with ratio questions?
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.
1.7
Find the total - or whole - first - and then set up a Ratio Box.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

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

3. If x² = 144 - does v144 = x?
Probability A + Probability B
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Not necessarily. This is a trick question - because x could be either positive or negative.

4. HIGH: List the two most common side ratios for right triangles
4 angles are formed. Their sum is 360 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.
3:4:5 5:12:13
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.

5. HIGH: What is the mode?
S*v2
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)+
The value that appears most often in a data set.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

6. Define a factorial of a number - and how it is written.
x² + 2xy + y²
1.7
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.
Invert the second fraction (reciprocal) and multiply

7. Explain the special properties of zero.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
1/1
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.

8. What is the sum of any 'big' angle and any 'Small' angle?
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.
The average - mean - median - or mode.
180 degrees.

9. HIGH: What is the factored version of x² + 2xy + y² ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
90 degrees each.
2r
(x+y)²

10. HIGH: What is the Pythagorean theorem?

11. How do you divide fractions?
(0 -0)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Invert the second fraction (reciprocal) and multiply

12. HIGH: Explain the process to solve '56 is what percent of 80?'

13. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Not reading the problems carefully enough!
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.
A 90-degree angle.

14. Does order matter for a permutation? How about for a combination?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

15. What is the equation for a group problem?
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
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Arrangements - orders - schedules - or lists.

16. HIGH: Define the formula for calculating slope.
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
80%
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.

17. HIGH: What is the unfactored version of (x-y)² ?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
1.7
x² -2xy + y²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

18. Solve this: v6 * -v6 = ?
Probability A + Probability B
An integer is divisible by 5 if its units digit is either 0 or 5.
6
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.

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

20. HIGH: Simplify this: v75/v27
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2
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.

21. What is the 'Third side' rule for triangles?
The total # of possible outcomes.
Multiply numerator times numerator and denominator times denominator.
3:4:5 5:12:13
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. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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
(x+y)²
(x+y)(x-y)

23. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.

24. What degree angle is a line?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Invert the second fraction (reciprocal) and multiply
Probability A + Probability B
A line is a 180-degree angle.

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

26. What is the 'distributive law'?
6
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.
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.
x² -2xy + y²

27. If something is certain to happen - how is the probability of this event expressed mathematically?
(x-y)²
A 90-degree angle.
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.
1/1

28. HIGH: Volume of a cylinder?
The value that appears most often in a data set.
V=pr²h (This is just the area multiplied by the height)
Order does matter for a permutation - but does not matter for a combination.
Probability A + Probability B

29. In a coordinate system - what is the origin?
Groups - teams - or committees.
(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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

30. Explain how to solve for 7/¼
The average - mean - median - or mode.
1/1
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x² -2xy + y²

31. HIGH: What is a 'Right isosceles' triangle?
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.
60%
2
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

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

33. HIGH: What is the unfactored version of x²-y² ?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Probability A * Probability B
(x+y)(x-y)
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

34. HIGH: How do you multiply powers with the same base?
V=s³
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A radius
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.

35. What are 'vertical angles'?
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%.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
Probability A * Probability B

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

37. What do permutation problems often ask for?
90 degrees each.
V=s³
Arrangements - orders - schedules - or lists.
180 degrees.

38. HIGH: x^-n is equal to
x² + 2xy + y²
(a+b)(a-b)
Bh
1/x^n For example - 6-² = 1/6² = 1/36

39. How is a range expressed with inequalities?
(x+y)(x-y)
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Example: 1 < x < 10
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

40. What is a 'Right' triangle?
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
A radius
A triangle in which one of the three interior angles is 90 degrees.
x² -2xy + y²

41. Diameter of a circle?
A=pr²
The total # of possible outcomes.
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.
2r

42. List all the prime numbers that are less than 30:
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
60%
Arrangements - orders - schedules - or lists.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

43. 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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

44. What is an 'equilateral' triangle?
90 degrees each.
V=pr²h (This is just the area multiplied by the height)
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

45. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

46. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
360 degrees
2pr -or- pd
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

47. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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'.
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.
S²

48. HIGH: Volume of a cube?
(a+b)(a-b)
An integer is divisible by 5 if its units digit is either 0 or 5.
V=s³
'Big' angles and 'Small' angles.

49. HIGH: What is the unfactored version of (x+y)² ?
Order does matter for a permutation - but does not matter for a combination.
x² + 2xy + y²
90 degrees each.
2pr -or- pd

50. What do combination problems usually ask for?
Groups - teams - or committees.
180 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Percentage Change = Difference/Original * 100