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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. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
(a+b)(a-b)
(x+y)²
An integer is divisible by 9 if the sum of its digits is divisible by 9.

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

3. HIGH: what is the side ratio for a Right Isosceles triangle?
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.
V=pr²h (This is just the area multiplied by the height)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² + 2xy + y²

4. HIGH: Rough est. of v3 =
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
1.7
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1.4

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

6. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
(x-y)²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Find the total - or whole - first - and then set up a Ratio Box.

7. HIGH: how do you calculate the surface area of a rectangular box?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
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'.
25%

8. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
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.
1/1

9. Explain how to divide fractions.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

10. Explain how to use an 'Average Pie'
S*v2
2r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

11. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
A triangle in which one of the three interior angles is 90 degrees.
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

12. If something is certain to happen - how is the probability of this event expressed mathematically?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1/1
A line is a 180-degree angle.
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)+

13. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
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.

14. What is the sum of any 'big' angle and any 'Small' angle?
A=pr²
4 angles are formed. Their sum is 360 degrees
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
180 degrees.

15. HIGH: How much of your times table should you know - for the GRE?
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

16. HIGH: Rough est. of v2 =
1.4
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
2r
A=pr²

17. List all the prime numbers that are less than 30:
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
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
Invert the second fraction (reciprocal) and multiply

18. 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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
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

19. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
360 degrees
Invert the second fraction (reciprocal) and multiply
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

20. HIGH: What is the median?
The # falling in the center of an ordered data set
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A radius

21. a² - b² is equal to
(x-y)²
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+b)(a-b)
A radius

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

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

24. What'S the most important thing to remember about charts you'll see on the GRE?
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Order does matter for a permutation - but does not matter for a combination.
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.

25. An integer is divisible by 3 if...
2r
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.
1
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.

26. HIGH: What is the unfactored version of (x-y)² ?
x² -2xy + y²
80%
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
A radius

27. 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
1.4
Bh

28. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/1
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 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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

29. What is the factored version of x² -2xy + y² ?
(x-y)²
The total # of possible outcomes.
Find a common denominator and make equivalent fractions. Then add or subtract.
180 degrees.

30. HIGH: Rough est. of v1 =
1
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.
1/x^n For example - 6-² = 1/6² = 1/36
x² -2xy + y²

31. Explain how to solve for 7/¼
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Favorable Outcomes/Total Possible Outcomes
Find a common denominator and make equivalent fractions. Then add or subtract.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

32. What degree angle is a line?
Not necessarily. This is a trick question - because x could be either positive or negative.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
A line is a 180-degree angle.

33. HIGH: Area of a circle
2
A=pr²
1/1
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%.

34. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

35. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
80%
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.

36. How do you calculate the probability of two events in a row? (Probability of A and B)
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
An integer is divisible by 5 if its units digit is either 0 or 5.
6
Probability A * Probability B

37. HIGH: What is the 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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
The value that appears most often in a data set.
1

38. Define the range of a set of numbers.
V=s³
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
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.
Find a common denominator and make equivalent fractions. Then add or subtract.

39. What is the key to dealing with ratio questions?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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
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.
Find the total - or whole - first - and then set up a Ratio Box.

40. Explain how to calculate an average (arithmetic mean)
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

41. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
S²
An integer is divisible by 5 if its units digit is either 0 or 5.
V=pr²h (This is just the area multiplied by the height)

42. HIGH: Area of a triangle?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
6
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

43. HIGH: Define the formula for calculating slope.
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
V=pr²h (This is just the area multiplied by the height)

44. Convert to a percentage: 1/4
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
25%
Multiply numerator times numerator and denominator times denominator.
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

45. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The value that appears most often in a data set.
V=s³
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

46. HIGH: Simplify this: v75/v27
The average - mean - median - or mode.
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.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

47. HIGH: What is 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)+
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 radius
1.4

48. An integer is divisible by 2 if...
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
The total # of possible outcomes.
An integer is divisible by 2 if its units digit is divisible by 2.
Multiply numerator times numerator and denominator times denominator.

49. What is a 'Right' angle?
Bh
A 90-degree angle.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
2r

50. What is a 'Right' triangle?
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.
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 triangle in which one of the three interior angles is 90 degrees.
1