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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. What degree angle is a line?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
A line is a 180-degree angle.
An integer is divisible by 2 if its units digit is divisible by 2.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

2. HIGH: how do you calculate the surface area of a rectangular box?
'Big' angles and 'Small' angles.
The average - mean - median - or mode.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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. HIGH: What is the factored version of x² + 2xy + y² ?
Not necessarily. This is a trick question - because x could be either positive or negative.
(x+y)²
Find the total - or whole - first - and then set up a Ratio Box.
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.

4. On the GRE - should you ever assume that diagrams are truthful?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Favorable Outcomes/Total Possible Outcomes

5. What do permutation problems often ask for?
An integer is divisible by 5 if its units digit is either 0 or 5.
Arrangements - orders - schedules - or lists.
2pr -or- pd
Multiply numerator times numerator and denominator times denominator.

6. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
The ratio of sides is x:x:xv2 - where xv2 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
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.
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'.

7. HIGH: What is the side ratio for a 30:60:90 triangle?
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.
Bh
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

8. Convert to a percentage: 4/5
Probability A * Probability B
Not reading the problems carefully enough!
6
80%

9. HIGH: Simplify this: v75/v27
Bh
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 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

10. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
60%
360 degrees
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

11. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

12. Explain how to use an 'Average Pie'
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A 90-degree angle.

13. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
A=pr²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
V=s³

14. 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% |
60%
(x-y)²
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.

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

16. Simplify this: v32
Invert the second fraction (reciprocal) and multiply
V=s³
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Probability A * Probability B

17. How do you divide fractions?
40%
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
6
Invert the second fraction (reciprocal) and multiply

18. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
V=s³
1/x^n For example - 6-² = 1/6² = 1/36
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

19. 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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x+y)²

20. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
40%
The average - mean - median - or mode.
'Big' angles and 'Small' angles.

21. HIGH: How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
360 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

22. v4 =
(x+y)²
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 average - mean - median - or mode.
2

23. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
An integer is divisible by 9 if the sum of its digits is divisible by 9.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1.4

24. 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.
Find the total - or whole - first - and then set up a Ratio Box.
2pr -or- pd

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

26. How is a range expressed with inequalities?
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.
Groups - teams - or committees.
Example: 1 < x < 10
The value that appears most often in a data set.

27. Define a factorial of a number - and how it is written.
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.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

28. Convert to a percentage: 3/5
60%
2r
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

29. What is a 'Right' triangle?
Bh
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
x² + 2xy + y²
A triangle in which one of the three interior angles is 90 degrees.

30. HIGH: Rough est. of v2 =
1.4
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.

31. Probability Formula
Order does matter for a permutation - but does not matter for a combination.
Favorable Outcomes/Total Possible Outcomes
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

32. Explain how to solve for 7/¼
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

33. Explain how to divide fractions.
Not reading the problems carefully enough!
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A radius
1/1

34. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
1
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

35. For a bell curve - what three terms might be used to describe the number in the middle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The average - mean - median - or mode.
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
Invert the second fraction (reciprocal) and multiply

36. Diameter of a circle?
2r
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.
1/1
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.

37. HIGH: Volume of a cylinder?
Between 0 and 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A radius
V=pr²h (This is just the area multiplied by the height)

38. What is a 'Right' angle?
360 degrees
x² -2xy + y²
A 90-degree angle.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

39. HIGH: x^-n is equal to
A triangle in which one of the three interior angles is 90 degrees.
360 degrees
1/x^n For example - 6-² = 1/6² = 1/36
3:4:5 5:12:13

40. HIGH: What is a '30:60:90' 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
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
Favorable Outcomes/Total Possible Outcomes
60%

41. HIGH: What is the order of math operations - and the mnemonic to remember it?
Example: 1 < x < 10
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 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.
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

42. An integer is divisible by 2 if...
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
An integer is divisible by 2 if its units digit is divisible by 2.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

43. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
S*v2
The average - mean - median - or mode.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
Multiply numerator times numerator and denominator times denominator.

44. How do you multiply fractions?
Arrangements - orders - schedules - or lists.
Multiply numerator times numerator and denominator times denominator.
1
2r

45. HIGH: Volume of a cube?
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.
V=s³
3:4:5 5:12:13
Example: 1 < x < 10

46. HIGH: Define the formula for calculating slope.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
6
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.

47. List two odd behaviors of exponents
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A radius
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.
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.

48. Solve this: v6 * -v6 = ?
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.
6
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.
1.4

49. How do you calculate the probability of two events in a row? (Probability of A and B)
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'.
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.
Probability A * Probability B
Probability A + Probability B

50. What do combination problems usually ask for?
Groups - teams - or committees.
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.
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 90-degree angle.