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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: What is the equation of a line?

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

3. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A line is a 180-degree angle.
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 9 if the sum of its digits is divisible by 9.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

4. How many degrees does a circle contain?
V=pr²h (This is just the area multiplied by the height)
360 degrees
Bh
180 degrees

5. What is the factored version of x² -2xy + y² ?
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 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)²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

6. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
The total # of possible outcomes.
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

7. An integer is divisible by 4 if...

8. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x+y)²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

9. HIGH: What is the median?
Groups - teams - or committees.
1/1
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
The # falling in the center of an ordered data set

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

11. Explain the difference between handling a permutation versus a combination.
6
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.
(0 -0)

12. HIGH: Volume of a cube?
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
A line is a 180-degree angle.
Not necessarily. This is a trick question - because x could be either positive or negative.
V=s³

13. On the GRE - should you ever assume that diagrams are truthful?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
V=pr²h (This is just the area multiplied by the height)

14. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
'Big' angles and 'Small' angles.
(x-y)²
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

15. Convert to a percentage: 4/5
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
80%
The # falling in the center of an ordered data set
360 degrees

16. The three exterior angles of a triangle add up to...
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
360 degrees
V=s³
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

17. HIGH: What is a 'Right isosceles' triangle?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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
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.

18. HIGH: Area of a circle
A=pr²
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
1.4

19. Convert to a percentage: 2/5
40%
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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
x²-y²

20. HIGH: How do you calculate the circumference of a circle?
(a+b)(a-b)
2pr -or- pd
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

21. What are 'vertical angles'?
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'.
'Big' angles and 'Small' angles.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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%.

22. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
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.
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

23. Solve this: v6 * -v6 = ?
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.
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.
6
V=pr²h (This is just the area multiplied by the height)

24. What do combination problems usually ask for?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Groups - teams - or committees.
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.
A radius

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

26. HIGH: What is the mode?
The value that appears most often in a data set.
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

27. Simplify this: v32
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1. Given event A: A + notA = 1.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.

28. What'S the most important thing to remember about charts you'll see on the GRE?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
Invert the second fraction (reciprocal) and multiply
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

29. HIGH: how do you calculate the surface area of a rectangular box?
2
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

30. HIGH: How do you multiply powers with the same base?
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.
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 90-degree angle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

31. What number goes on the bottom of a probability fraction?
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 total # of possible outcomes.
Percentage Change = Difference/Original * 100
A line is a 180-degree angle.

32. 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.
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')
A=pr²

33. The three interior angles of a triangle add up to...
180 degrees
Example: 1 < x < 10
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.
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.

34. Area of a parallelogram?
Bh
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.
180 degrees.
V=pr²h (This is just the area multiplied by the height)

35. What is the sum of any 'big' angle and any 'Small' angle?
1/x^n For example - 6-² = 1/6² = 1/36
Between 0 and 1.
180 degrees.
4 angles are formed. Their sum is 360 degrees

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

37. In a coordinate system - what is the origin?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
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.
(0 -0)

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

39. What is the 'distributive law'?
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

40. HIGH: Rough est. of v1 =
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
1

41. HIGH: Rough est. of v2 =
Order does matter for a permutation - but does not matter for a combination.
An integer is divisible by 5 if its units digit is either 0 or 5.
x² -2xy + y²
1.4

42. An integer is divisible by 5 if...
2r
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.
An integer is divisible by 5 if its units digit is either 0 or 5.

43. HIGH: What is the unfactored version of (x-y)² ?
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.
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.
1.7
x² -2xy + y²

44. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
x²-y²
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.
4 angles are formed. Their sum is 360 degrees
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

45. HIGH: How do you multiply and divide square roots?
(x+y)²
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
360 degrees

46. HIGH: What is the factored version of x² + 2xy + y² ?
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.
(x+y)²
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

47. Diameter of a circle?
2r
Invert the second fraction (reciprocal) and multiply
The average - mean - median - or mode.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

48. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
2pr -or- pd
1.4

49. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

50. Define a factorial of a number - and how it is written.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
The average - mean - median - or mode.
25%