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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 factored version of x² + 2xy + y² ?
Multiply numerator times numerator and denominator times denominator.
(x+y)²
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

2. 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.
The average - mean - median - or mode.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

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

4. HIGH: What is the Pythagorean theorem?

5. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
90 degrees each.

6. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
(a+b)(a-b)
x²-y²
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.

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

8. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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.
1. Given event A: A + notA = 1.
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
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.

9. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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/x^n For example - 6-² = 1/6² = 1/36
1

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

11. How do you divide fractions?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Invert the second fraction (reciprocal) and multiply
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

12. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
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
Bh
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

13. HIGH: Describe how to deal with 2 sets of parentheses.
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%.
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 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.
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)+

14. HIGH: what is the side ratio for a Right Isosceles triangle?
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 90-degree angle.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
60%

15. Define the range of a set of numbers.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

16. What degree angle is a line?
2
(x+y)²
A line is a 180-degree 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.

17. Explain how to divide fractions.
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.
Groups - teams - or committees.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
The value that appears most often in a data set.

18. What is a 'Right' triangle?
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.
V=pr²h (This is just the area multiplied by the height)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
A triangle in which one of the three interior angles is 90 degrees.

19. In a coordinate system - what is the origin?
(0 -0)
The average - mean - median - or mode.
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 5 if its units digit is either 0 or 5.

20. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Order does matter for a permutation - but does not matter for a combination.
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.

21. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
(x+y)²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.

22. HIGH: To divide powers with the same base...
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Find the total - or whole - first - and then set up a Ratio Box.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

23. Convert to a percentage: 1/4
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
A line is a 180-degree angle.
25%

24. The three exterior angles of a triangle add up to...
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
A radius
x² -2xy + y²
360 degrees

25. Explain the difference between handling a permutation versus a combination.
A=pr²
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+b)(a-b)
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.

26. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
(# 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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

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

28. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
(0 -0)
1
40%

29. HIGH: What is a 'Right isosceles' triangle?
The total # of possible outcomes.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

30. An integer is divisible by 8 if...

31. What causes 80% of errors on the math section of the GRE?
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
Probability A * Probability B
Find a common denominator and make equivalent fractions. Then add or subtract.
Not reading the problems carefully enough!

32. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
(0 -0)
Between 0 and 1.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

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.
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 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

34. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
4 angles are formed. Their sum is 360 degrees
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
x² + 2xy + y²

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

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

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

38. HIGH: how do you calculate the surface area of a rectangular box?
Multiply numerator times numerator and denominator times denominator.
1.7
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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. An integer is divisible by 2 if...
An integer is divisible by 2 if its units digit is divisible by 2.
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.
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.
x² + 2xy + y²

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

41. If something is possible but not certain - what is the numeric range of probability of it happening?
Bh
Between 0 and 1.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

42. HIGH: How do you multiply powers with the same base?
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

43. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
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
1. Given event A: A + notA = 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.

44. HIGH: What are the percentages for standard deviation?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a+b)(a-b)
The total # of possible outcomes.

45. HIGH: What is the mode?
4 angles are formed. Their sum is 360 degrees
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.
Bh
The value that appears most often in a data set.

46. Convert to a percentage: 2/5
1.4
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 6 if it'S divisible by BOTH 2 and 3.
40%

47. Solve this: v6 * -v6 = ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
6
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.

48. HIGH: List the two most common side ratios for right triangles
Multiply numerator times numerator and denominator times denominator.
180 degrees.
3:4:5 5:12:13
(0 -0)

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

50. HIGH: Define the formula for calculating slope.
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.
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.
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.