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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: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Not reading the problems carefully enough!
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.
40%

2. What do combination problems usually ask for?
180 degrees.
6
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Groups - teams - or committees.

3. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
Order does matter for a permutation - but does not matter for a combination.

4. On the GRE - should you ever assume that diagrams are truthful?
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.
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

5. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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%.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x+y)²

6. Explain how to use a 'Rate Pie'
The # falling in the center of an ordered data set
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Not reading the problems carefully enough!
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

7. Convert to a percentage: 3/5
60%
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.
Favorable Outcomes/Total Possible Outcomes
1. Given event A: A + notA = 1.

8. HIGH: What is the formula for the diagonal of any square?
Groups - teams - or committees.
S*v2
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.
3:4:5 5:12:13

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

10. HIGH: How do you multiply and divide square roots?
1/x^n For example - 6-² = 1/6² = 1/36
(x-y)²
x²-y²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

11. Area of a parallelogram?
The value that appears most often in a data set.
180 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Bh

12. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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+b)(a-b)

13. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 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
90 degrees each.
x² -2xy + y²
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.

14. Explain the special properties of zero.
Order does matter for a permutation - but does not matter for a combination.
x² -2xy + y²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

15. What is an 'equilateral' triangle?
90 degrees each.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

16. v4 =
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
2
(x-y)²
A=pr²

17. The three interior angles of a triangle add up to...
(x+y)²
180 degrees
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

18. In a coordinate system - identify the quadrants and describe their location.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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

19. An integer is divisible by 3 if...
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.
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.
Not reading the problems carefully enough!
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.

20. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Find the total - or whole - first - and then set up a Ratio Box.
1

21. List two odd behaviors of exponents
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.
Probability A * Probability B
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.

22. a² - b² is equal to
25%
4 angles are formed. Their sum is 360 degrees
(a+b)(a-b)
Percentage Change = Difference/Original * 100

23. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
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
Between 0 and 1.

24. In a coordinate system - what is the origin?
Find a common denominator and make equivalent fractions. Then add or subtract.
(0 -0)
An integer is divisible by 5 if its units digit is either 0 or 5.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

25. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Probability A * Probability B
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
3:4:5 5:12:13
(x+y)(x-y)

26. Explain how to use an 'Average Pie'
180 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.
A line is a 180-degree angle.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

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

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

29. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
180 degrees.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

30. Define the range of a set of numbers.
An integer is divisible by 2 if its units digit is divisible by 2.
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.
(x+y)²
(a+b)(a-b)

31. An integer is divisible by 5 if...
1
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2pr -or- pd
An integer is divisible by 5 if its units digit is either 0 or 5.

32. How do you divide fractions?
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.
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.
Invert the second fraction (reciprocal) and multiply
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%.

33. Explain how to divide fractions.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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

34. HIGH: What is the Pythagorean theorem?

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

36. HIGH: What is a '30:60:90' triangle?
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.
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.
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

37. HIGH: Rough est. of v1 =
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.
1
360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.

38. HIGH: What are the percentages for standard deviation?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
x²-y²

39. Convert to a percentage: 4/5
80%
(x-y)²
Find the total - or whole - first - and then set up a Ratio Box.
(0 -0)

40. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
V=s³
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

41. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
S*v2
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
Between 0 and 1.
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.

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

43. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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%.

44. HIGH: What is the unfactored version of x²-y² ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x+y)(x-y)
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: Volume of a cylinder?
Bh
V=pr²h (This is just the area multiplied by the height)
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.

46. How do you calculate the percentage of change?
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.
2pr -or- pd
Percentage Change = Difference/Original * 100
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

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

48. HIGH: x^-n is equal to
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
The total # of possible outcomes.
(x+y)²
1/x^n For example - 6-² = 1/6² = 1/36

49. 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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Groups - teams - or committees.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

50. An integer is divisible by 2 if...
25%
2r
An integer is divisible by 2 if its units digit is divisible by 2.
1/1