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GRE High Frequency Math Terms

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 ?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
x² + 2xy + y²
180 degrees.
A=pr²

2. HIGH: how do you calculate the surface area of a rectangular box?
S*v2
Not reading the problems carefully enough!
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.

3. Explain how to calculate an average (arithmetic mean)
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+b)(a-b)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

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

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

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

7. Area of a square?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
S²
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)+
2r

8. In a coordinate system - identify the quadrants and describe their location.
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.
Example: 1 < x < 10
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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)+

9. How do you solve a combination?

10. How do you solve a permutation?
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. 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
A line is a 180-degree angle.
40%

11. a² - b² is equal to
1. Given event A: A + notA = 1.
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 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+b)(a-b)

12. Convert to a percentage: 2/5
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.
40%
1
(x+y)(x-y)

13. What degree angle is a line?
A line is a 180-degree angle.
2r
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x² + 2xy + y²

14. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Between 0 and 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

15. An integer is divisible by 2 if...
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 2 if its units digit is divisible by 2.

16. Define the range of a set of numbers.
Example: 1 < x < 10
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.

17. What is the 'Third side' rule for triangles?
Invert the second fraction (reciprocal) and multiply
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.

18. HIGH: Rough est. of v3 =
1.7
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
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%.
360 degrees

19. What do permutation problems often ask for?
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.
80%
Arrangements - orders - schedules - or lists.
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.

20. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
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.
90 degrees each.

21. Explain how to use a 'Rate Pie'
x² -2xy + y²
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.
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
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.

22. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/x^n For example - 6-² = 1/6² = 1/36
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.

23. Explain how to use an 'Average Pie'
'Big' angles and 'Small' angles.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.

24. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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
Multiply numerator times numerator and denominator times denominator.
The value that appears most often in a data set.

25. Define 'proportionate' values
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.
1.7
360 degrees
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

26. v4 =
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2

27. HIGH: What are the percentages for standard deviation?
80%
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
A triangle in which one of the three interior angles is 90 degrees.

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

29. HIGH: What is the mode?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2pr -or- pd
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
The value that appears most often in a data set.

30. What is a 'Right' triangle?
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.
A triangle in which one of the three interior angles is 90 degrees.
Probability A + Probability B
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

31. List all the prime numbers that are less than 30:
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

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

33. An integer is divisible by 5 if...
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
(0 -0)
An integer is divisible by 5 if its units digit is either 0 or 5.

34. Solve this: v6 * -v6 = ?
The value that appears most often in a data set.
80%
6
An integer is divisible by 2 if its units digit is divisible by 2.

35. Convert to a percentage: 4/5
A=pr²
4 angles are formed. Their sum is 360 degrees
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.
80%

36. In a coordinate system - what is the origin?
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.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(0 -0)

37. Define the mode of a set of numbers.
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.
2pr -or- pd
A 90-degree angle.
80%

38. What are 'vertical angles'?
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
The value that appears most often in a data set.
x² -2xy + y²

39. List two odd behaviors of exponents
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(0 -0)
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.
1. Given event A: A + notA = 1.

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

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

42. Area of a parallelogram?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1
A 90-degree angle.
Bh

43. An integer is divisible by 3 if...
1/1
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.
25%
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

44. HIGH: Volume of a cylinder?
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
2r
V=pr²h (This is just the area multiplied by the height)
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.

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

46. HIGH: Simplify this: v75/v27
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
360 degrees
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

47. What is the sum of any 'big' angle and any 'Small' angle?
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.
6
180 degrees.

48. The three interior angles of a triangle add up to...
(x+y)(x-y)
Invert the second fraction (reciprocal) and multiply
180 degrees
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

49. HIGH: Area of a triangle?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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'.
360 degrees

50. 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
4 angles are formed. Their sum is 360 degrees
(a+b)(a-b)