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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. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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
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.
90 degrees each.
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'.

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

3. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
An integer is divisible by 2 if its units digit is divisible by 2.
V=pr²h (This is just the area multiplied by the height)

4. List all the prime numbers that are less than 30:
The # falling in the center of an ordered data set
(0 -0)
180 degrees.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

5. HIGH: What is the Pythagorean theorem?

6. HIGH: What is the unfactored version of (x-y)² ?
3:4:5 5:12:13
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
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
x² -2xy + y²

7. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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.
A radius
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.

8. What do permutation problems often ask for?
3:4:5 5:12:13
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Arrangements - orders - schedules - or lists.
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.

9. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Favorable Outcomes/Total Possible Outcomes
80%
The average - mean - median - or mode.

10. HIGH: how do you calculate the surface area of a rectangular box?
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
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

11. v4 =
Between 0 and 1.
Groups - teams - or committees.
1.4
2

12. The three interior angles of a triangle add up to...
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
180 degrees
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

13. What is the 'distributive law'?
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
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

14. What is the 'Third side' rule for triangles?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
180 degrees.
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
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.

15. How many degrees does a circle contain?
360 degrees
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)+
Multiply numerator times numerator and denominator times denominator.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

16. List two odd behaviors of exponents
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
The average - mean - median - or mode.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

17. HIGH: Simplify this: v75/v27
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.
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.
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
(x-y)²

18. Probability Formula
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
x²-y²
Favorable Outcomes/Total Possible Outcomes

19. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
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.
(x+y)(x-y)
2

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

21. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
60%
An integer is divisible by 2 if its units digit is divisible by 2.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

22. How do you solve a permutation?
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.
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
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.
1. Given event A: A + notA = 1.

23. Explain the special properties of zero.
360 degrees
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.
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%.
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.

24. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
90 degrees each.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
60%
80%

25. An integer is divisible by 2 if...
Groups - teams - or committees.
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
An integer is divisible by 2 if its units digit is divisible by 2.
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

26. How do you calculate the probability of two events in a row? (Probability of A and B)
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')
V=s³
40%

27. HIGH: To divide powers with the same base...
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
25%
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Invert the second fraction (reciprocal) and multiply

28. Explain how to use an 'Average Pie'
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
(x-y)²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

29. HIGH: Rough est. of v1 =
An integer is divisible by 5 if its units digit is either 0 or 5.
1
180 degrees.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

30. An integer is divisible by 9 if...
(0 -0)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Not reading the problems carefully enough!

31. Explain how to calculate an average (arithmetic mean)
A=pr²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
360 degrees

32. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Probability A + Probability B

33. How do you calculate the percentage of change?
Not necessarily. This is a trick question - because x could be either positive or negative.
S²
x²-y²
Percentage Change = Difference/Original * 100

34. How do you multiply fractions?
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
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.
Example: 1 < x < 10
Multiply numerator times numerator and denominator times denominator.

35. HIGH: Rough est. of v3 =
1.7
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(x+y)(x-y)

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

37. Does order matter for a permutation? How about for a combination?
(0 -0)
Find a common denominator and make equivalent fractions. Then add or subtract.
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

38. Convert to a percentage: 4/5
80%
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.
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
Arrangements - orders - schedules - or lists.

39. What are the side ratios for a 30:60:90 triangle?
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)+
An integer is divisible by 5 if its units digit is either 0 or 5.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The average - mean - median - or mode.

40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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.
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. 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

41. HIGH: What is the median?
Between 0 and 1.
The # falling in the center of an ordered data set
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.

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

43. a² - b² is equal to
A radius
(a+b)(a-b)
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.

44. HIGH: What is a '30:60:90' triangle?
Find a common denominator and make equivalent fractions. Then add or subtract.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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

45. Define 'proportionate' values
The # falling in the center of an ordered data set
An integer is divisible by 9 if the sum of its digits is divisible by 9.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

46. Explain the difference between handling a permutation versus a combination.
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.
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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
x² -2xy + y²

47. HIGH: What is the side ratio for a 30:60:90 triangle?
(x+y)²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

48. HIGH: x^-n is equal to
Groups - teams - or committees.
Invert the second fraction (reciprocal) and multiply
S*v2
1/x^n For example - 6-² = 1/6² = 1/36

49. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
3:4:5 5:12:13
'Big' angles and 'Small' angles.
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.
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'.

50. HIGH: How do you multiply and divide square roots?
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 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.
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2