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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: What is the unfactored version of (x+y)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.
x² + 2xy + y²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

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

3. HIGH: What is the median?
The # falling in the center of an ordered data set
4 angles are formed. Their sum is 360 degrees
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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. Explain the difference between a digit and a number.

5. 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.
S²
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

6. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(x+y)²
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.
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

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

8. The three exterior angles of a triangle add up to...
Multiply numerator times numerator and denominator times denominator.
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.
360 degrees
(x+y)²

9. If something is possible but not certain - what is the numeric range of probability of it happening?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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)+
Between 0 and 1.
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%.

10. HIGH: How do you calculate the circumference of a circle?
A radius
2pr -or- pd
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
S²

11. HIGH: What is the factored version of (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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
x²-y²

12. Probability Formula
Favorable Outcomes/Total Possible Outcomes
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
1/x^n For example - 6-² = 1/6² = 1/36
1/1

13. Explain the special properties of zero.
S*v2
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.
The total # of possible outcomes.
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.

14. Explain how to use an 'Average Pie'
A radius
2
V=pr²h (This is just the area multiplied by the height)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

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

16. HIGH: What is the formula for the diagonal of any square?
S*v2
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/x^n For example - 6-² = 1/6² = 1/36
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.

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

18. Define 'proportionate' values
(x-y)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
Example: 1 < x < 10

19. HIGH: What is the order of math operations - and the mnemonic to remember it?
2r
S²
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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

20. What is the name of a line that extends from the center of a circle to the edge of a circle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.
A radius
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.

21. What is the factored version of x² -2xy + y² ?
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(x-y)²

22. HIGH: Rough est. of v1 =
1
S²
(0 -0)
Example: 1 < x < 10

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

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

25. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Bh
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.
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.

26. Simplify this: v32
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
x² -2xy + y²

27. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

28. On the GRE - should you ever assume that diagrams are truthful?
4 angles are formed. Their sum is 360 degrees
Find a common denominator and make equivalent fractions. Then add or subtract.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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.

29. What is the formula to determine probability?
Probability A * Probability B
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
(x+y)(x-y)

30. What is the 'distributive law'?
(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 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
1.7

31. How do you solve a permutation?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
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
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.

32. How do you multiply fractions?
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.
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.
(0 -0)
Multiply numerator times numerator and denominator times denominator.

33. 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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
360 degrees

34. HIGH: To divide powers with the same base...
2r
Favorable Outcomes/Total Possible Outcomes
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

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

36. Define the mode of a set of numbers.
An integer is divisible by 2 if its units digit is divisible by 2.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.

37. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(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.

38. Diameter of a circle?
2r
1/x^n For example - 6-² = 1/6² = 1/36
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.

39. What is a 'Right' angle?
A 90-degree angle.
1.7
Groups - teams - or committees.
Example: 1 < x < 10

40. HIGH: What is the mode?
A line is a 180-degree angle.
The value that appears most often in a data set.
A triangle in which one of the three interior angles is 90 degrees.
4 angles are formed. Their sum is 360 degrees

41. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
The average - mean - median - or mode.
2pr -or- pd
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.

42. HIGH: How do you multiply and divide square roots?
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.
1. Given event A: A + notA = 1.
2pr -or- pd

43. Convert to a percentage: 3/5
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
60%
Percentage Change = Difference/Original * 100

44. HIGH: Define the formula for calculating slope.
(x+y)²
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.
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.

45. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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'.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
An integer is divisible by 2 if its units digit is divisible by 2.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

46. HIGH: What is the side ratio for a 30:60:90 triangle?
A line is a 180-degree angle.
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.
40%
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

47. What'S the most important thing to remember about charts you'll see on 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.
An integer is divisible by 2 if its units digit is divisible by 2.
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.
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.

48. If something is certain to happen - how is the probability of this event expressed mathematically?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

49. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
2r

50. List all the prime numbers that are less than 30:
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Probability A + Probability B
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3