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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. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
Invert the second fraction (reciprocal) and multiply
Order does matter for a permutation - but does not matter for a combination.
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.

2. What is the 'Third side' rule for triangles?
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.
x² + 2xy + y²
(a+b)(a-b)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

3. HIGH: What is a 'Right isosceles' triangle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

4. HIGH: How much of your times table should you know - for the GRE?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
360 degrees
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
It will be a great advantage on test day to have your times table memorized from 1 through 15.

5. Convert to a percentage: 2/5
Not reading the problems carefully enough!
40%
(a+b)(a-b)
Arrangements - orders - schedules - or lists.

6. Define 'proportionate' values
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'.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
An integer is divisible by 2 if its units digit is divisible by 2.

7. Explain how to solve for 7/¼
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.
2
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

8. List two odd behaviors of exponents
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/x^n For example - 6-² = 1/6² = 1/36
A triangle in which one of the three interior angles is 90 degrees.
Invert the second fraction (reciprocal) and multiply

9. HIGH: Area of a triangle?
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

10. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
Probability A + Probability B
Bh
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

11. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
6
S*v2
Between 0 and 1.

12. HIGH: What is the factored version of x² + 2xy + y² ?
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(x+y)²
1

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

14. HIGH: Simplify this: v75/v27
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
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.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

15. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Bh
A radius
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1. Given event A: A + notA = 1.

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

17. How do you multiply fractions?
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.
Multiply numerator times numerator and denominator times denominator.
A line is a 180-degree angle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

18. HIGH: What is the mode?
Groups - teams - or committees.
90 degrees each.
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.
The value that appears most often in a data set.

19. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
60%
The average - mean - median - or mode.

20. Define a factorial of a number - and how it is written.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A triangle in which one of the three interior angles is 90 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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

21. HIGH: Rough est. of v1 =
'Big' angles and 'Small' angles.
(x-y)²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
1

22. The three interior angles of a triangle add up to...
180 degrees
1. Given event A: A + notA = 1.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

23. What are 'vertical angles'?
Favorable Outcomes/Total Possible Outcomes
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

24. Diameter of a circle?
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.
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.
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.
2r

25. HIGH: What is a '30:60:90' triangle?
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
Invert the second fraction (reciprocal) and multiply
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
2r

26. How many degrees does a circle contain?
Find the total - or whole - first - and then set up a Ratio Box.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
360 degrees

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

28. Area of a parallelogram?
A triangle in which one of the three interior angles is 90 degrees.
60%
Bh
Find the total - or whole - first - and then set up a Ratio Box.

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

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

31. HIGH: What is the unfactored version of (x-y)² ?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Order does matter for a permutation - but does not matter for a combination.
x² -2xy + y²
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.

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

33. What is the sum of any 'big' angle and any 'Small' angle?
Not reading the problems carefully enough!
180 degrees.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

34. In a coordinate system - identify the quadrants and describe their location.
A 90-degree angle.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
1.7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

35. Explain how to use an 'Average Pie'
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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

36. Convert to a percentage: 4/5
80%
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.
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

37. Probability Formula
Favorable Outcomes/Total Possible Outcomes
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

38. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

39. List all the prime numbers that are less than 30:
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.
V=pr²h (This is just the area multiplied by the height)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
S²

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

41. An integer is divisible by 5 if...
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A triangle in which one of the three interior angles is 90 degrees.
Percentage Change = Difference/Original * 100
An integer is divisible by 5 if its units digit is either 0 or 5.

42. a² - b² is equal to
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
(a+b)(a-b)
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.

43. Define the mode of a set of numbers.
25%
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.
The average - mean - median - or mode.
1. Given event A: A + notA = 1.

44. How do you solve a permutation?
2pr -or- pd
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%
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

45. Define the range of a set of numbers.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Find a common denominator and make equivalent fractions. Then add or subtract.
Invert the second fraction (reciprocal) and multiply

46. How do you calculate the probability of two events in a row? (Probability of A and B)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A * Probability 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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

47. How is a range expressed with inequalities?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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
Example: 1 < x < 10

48. What are the side ratios for a 30:60:90 triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Bh

49. Explain the special properties of zero.
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Not reading the problems carefully enough!
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.

50. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A 90-degree angle.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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%.