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. What is the factored version of x² -2xy + y² ?
(x-y)²
An integer is divisible by 5 if its units digit is either 0 or 5.
Invert the second fraction (reciprocal) and multiply
1. Given event A: A + notA = 1.

2. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
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.
2r
Groups - teams - or committees.

3. The three interior angles of a triangle add up to...
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
Arrangements - orders - schedules - or lists.
180 degrees
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

4. What should you do BEFORE you start to solve a GRE math problem?

5. How do you add or subtract fractions?
V=s³
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Find a common denominator and make equivalent fractions. Then add or subtract.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

6. Solve this: v6 * -v6 = ?
Invert the second fraction (reciprocal) and multiply
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
6

7. What causes 80% of errors on the math section of the GRE?
Between 0 and 1.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Not reading the problems carefully enough!
It will be a great advantage on test day to have your times table memorized from 1 through 15.

8. The three exterior angles of a triangle add up to...
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
6
360 degrees

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

10. Diameter of a circle?
Percentage Change = Difference/Original * 100
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
2r
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

11. HIGH: How do you multiply powers with the same base?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
'Big' angles and 'Small' angles.

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

13. HIGH: What is a '30:60:90' triangle?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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
x² + 2xy + y²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

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

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

16. How do you calculate the probability of two events in a row? (Probability of A and B)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Bh
Probability A * Probability B
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

17. HIGH: What is the median?
360 degrees
The # falling in the center of an ordered data set
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.
180 degrees

18. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
'Big' angles and 'Small' angles.
x²-y²
V=pr²h (This is just the area multiplied by the height)

19. Explain how to use an 'Average Pie'
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Invert the second fraction (reciprocal) and multiply

20. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
S*v2
2r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

21. Area of a parallelogram?
Bh
A triangle in which one of the three interior angles is 90 degrees.
A radius
V=pr²h (This is just the area multiplied by the height)

22. An integer is divisible by 3 if...
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.
S*v2
1
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.

23. Probability Formula
Favorable Outcomes/Total Possible Outcomes
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A 90-degree angle.

24. HIGH: Describe how to deal with 2 sets of parentheses.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Probability A + Probability B
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)+
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: How much of your times table should you know - for the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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
1. Given event A: A + notA = 1.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

26. If something is certain to happen - how is the probability of this event expressed mathematically?
S*v2
1/1
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.
3:4:5 5:12:13

27. Explain how to use a 'Rate Pie'
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
x²-y²
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
(x+y)(x-y)

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

29. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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'.
6

30. Explain the special properties of zero.
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.
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.
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.
2pr -or- pd

31. HIGH: Simplify this: v75/v27
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.
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.
Order does matter for a permutation - but does not matter for a combination.
360 degrees

32. HIGH: What is the factored version of (x+y)(x-y) ?
x²-y²
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
V=pr²h (This is just the area multiplied by the height)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

33. What is a 'Right' triangle?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A triangle in which one of the three interior angles is 90 degrees.
Invert the second fraction (reciprocal) and multiply
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.

34. For a bell curve - what three terms might be used to describe the number in the middle?
40%
The average - mean - median - or mode.
Arrangements - orders - schedules - or lists.
Probability A + Probability B

35. What'S the most important thing to remember about charts you'll see on the GRE?
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
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Percentage Change = Difference/Original * 100

36. HIGH: Rough est. of v1 =
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1
A=pr²
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

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

38. How many degrees does a circle contain?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
360 degrees
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. 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.

39. In a coordinate system - what is the origin?
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)
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.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

40. Convert to a percentage: 3/5
60%
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
6

41. What is the equation for a group problem?
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.
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.
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
(x+y)(x-y)

42. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(x+y)(x-y)
Favorable Outcomes/Total Possible Outcomes
180 degrees
Probability A + Probability B

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

44. What degree angle is a line?
Probability A + Probability B
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A line is a 180-degree angle.

45. HIGH: What is the Pythagorean theorem?

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

47. HIGH: What is a 'Right isosceles' triangle?
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Find the total - or whole - first - and then set up a Ratio Box.
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.

48. Define the range of a set of numbers.
Not necessarily. This is a trick question - because x could be either positive or negative.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
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

49. List all the prime numbers that are less than 30:
x² + 2xy + y²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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.

50. What is the 'Third side' rule for triangles?
The total # of possible outcomes.
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.
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.