Test your basic knowledge |

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.
6
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
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.

2. HIGH: What is the unfactored version of (x+y)² ?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2pr -or- pd
x² + 2xy + y²
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.

3. 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.
180 degrees
The # falling in the center of an ordered data set
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.

4. How do you divide fractions?
60%
Probability A * Probability B
Invert the second fraction (reciprocal) and multiply
1.4

5. Explain how to use a 'Rate Pie'
80%
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
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.
2

6. Explain the special properties of zero.
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.
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
V=pr²h (This is just the area multiplied by the height)

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

8. How is a range expressed with inequalities?
180 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Example: 1 < x < 10

9. HIGH: Explain the process to solve '56 is what percent of 80?'

10. An integer is divisible by 5 if...
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
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
360 degrees

11. HIGH: Volume of a cylinder?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
V=pr²h (This is just the area multiplied by the height)

12. HIGH: What is the factored version of x² + 2xy + y² ?
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(x+y)²
(x-y)²

13. HIGH: how do you calculate the surface area of a rectangular box?
x²-y²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.

14. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
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
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Multiply numerator times numerator and denominator times denominator.

15. HIGH: How do you multiply and divide square roots?
4 angles are formed. Their sum is 360 degrees
(x-y)²
1.7
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

16. What is the equation for a group problem?
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.
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
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%.

17. What is a 'Right' angle?
A 90-degree angle.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
An integer is divisible by 2 if its units digit is divisible by 2.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

18. Simplify this: v32
Example: 1 < x < 10
6
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

19. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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%.
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

20. HIGH: What is the factored version of (x+y)(x-y) ?
60%
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 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.
x²-y²

21. An integer is divisible by 3 if...
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
Favorable Outcomes/Total Possible Outcomes

22. List all the prime numbers that are less than 30:
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
A line is a 180-degree angle.

23. In a coordinate system - what is the origin?
(0 -0)
180 degrees.
V=s³
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.

24. Diameter of a circle?
Groups - teams - or committees.
Probability A + Probability B
2r
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

25. On the GRE - should you ever assume that diagrams are truthful?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

26. What'S one way to avoid mistakes on algebra questions in the GRE?

27. HIGH: What is a 'Right isosceles' triangle?
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%.
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.
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 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. The three interior angles of a triangle add up to...
x²-y²
1.4
180 degrees
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.

29. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
40%
Probability A + Probability B
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2

30. Explain how to solve for 7/¼
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Find the total - or whole - first - and then set up a Ratio Box.
Multiply numerator times numerator and denominator times denominator.

31. What do combination problems usually ask for?
(a+b)(a-b)
x² -2xy + y²
Groups - teams - or committees.
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

32. The three exterior angles of a triangle add up to...
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
360 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.
1.7

33. HIGH: Area of a circle
V=s³
A=pr²
40%
Favorable Outcomes/Total Possible Outcomes

34. HIGH: Volume of a cube?
V=s³
(x-y)²
Multiply numerator times numerator and denominator times denominator.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

35. 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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

36. HIGH: What is the median?
x² + 2xy + y²
A=pr²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
The # falling in the center of an ordered data set

37. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

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

39. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Probability A * Probability B
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The average - mean - median - or mode.

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

41. HIGH: What is a '30:60:90' triangle?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
Order does matter for a permutation - but does not matter for a combination.
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

42. Probability Formula
Between 0 and 1.
Favorable Outcomes/Total Possible Outcomes
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
x²-y²

43. Explain the difference between handling a permutation versus a combination.
3:4:5 5:12:13
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
The value that appears most often in a data set.

44. An integer is divisible by 8 if...

45. HIGH: What is the formula for the diagonal of any square?
1. Given event A: A + notA = 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(0 -0)
S*v2

46. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
A 90-degree angle.

47. How do you calculate the probability of two events in a row? (Probability of A and B)
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Probability A * Probability B
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.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.

48. If something is certain to happen - how is the probability of this event expressed mathematically?
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 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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
1/1

49. HIGH: What is the mode?
x² -2xy + y²
4 angles are formed. Their sum is 360 degrees
360 degrees
The value that appears most often in a data set.

50. HIGH: what is the side ratio for a Right Isosceles triangle?
The total # of possible outcomes.
40%
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Probability A * Probability B