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: What is the factored version of x² + 2xy + y² ?
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.
S*v2
1/1
(x+y)²

2. HIGH: Rough est. of v1 =
Probability A * Probability B
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
1

3. How precise do you need to be - using p on the GRE?

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

5. How do you add or subtract fractions?
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%.
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
2r

6. If something is possible but not certain - what is the numeric range of probability of it happening?
2r
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)+
Between 0 and 1.
(x+y)²

7. HIGH: Area of a circle
A=pr²
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
1.4
180 degrees

8. HIGH: Volume of a cylinder?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
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.
V=pr²h (This is just the area multiplied by the height)

9. An integer is divisible by 5 if...
(x+y)(x-y)
An integer is divisible by 5 if its units digit is either 0 or 5.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

10. Solve this: v6 * -v6 = ?
360 degrees
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
6
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.

11. HIGH: What is the formula for the diagonal of any square?
S*v2
60%
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
6

12. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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
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.
A line is a 180-degree angle.

13. Explain the special properties of zero.
Probability A * Probability B
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 line is a 180-degree angle.
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

14. HIGH: List the two most common side ratios for right 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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
3:4:5 5:12:13
V=pr²h (This is just the area multiplied by the height)

15. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
60%
1/x^n For example - 6-² = 1/6² = 1/36
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

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

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

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

19. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
An integer is divisible by 2 if its units digit is divisible by 2.
x² -2xy + y²
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

20. Define a factorial of a number - and how it is written.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

21. HIGH: What is the order of math operations - and the mnemonic to remember it?
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
An integer is divisible by 5 if its units digit is either 0 or 5.
Groups - teams - or committees.

22. a² - b² is equal to
(a+b)(a-b)
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

23. HIGH: Rough est. of v2 =
1.4
(x-y)²
S*v2
S²

24. HIGH: Volume of a cube?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=s³
1. Given event A: A + notA = 1.

25. What is the 'Third side' rule for triangles?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Not reading the problems carefully enough!
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.

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

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

28. 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
(0 -0)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

29. How do you solve a permutation?
(x-y)²
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.
Bh
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

30. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
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)+
Percentage Change = Difference/Original * 100
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

31. What is the sum of any 'big' angle and any 'Small' angle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
180 degrees.
80%
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.

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

33. For a bell curve - what three terms might be used to describe the number in the middle?
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.
The average - mean - median - or mode.
1.4
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

34. 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% |
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

35. Define the range of a set of numbers.
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.
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.
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.

36. HIGH: Area of a triangle?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
The average - mean - median - or mode.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

37. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Order does matter for a permutation - but does not matter for a combination.
1/1
Percentage Change = Difference/Original * 100

38. 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
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Arrangements - orders - schedules - or lists.
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

39. Explain how to divide fractions.
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

40. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
(x-y)²
3:4:5 5:12:13
Percentage Change = Difference/Original * 100

41. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Arrangements - orders - schedules - or lists.
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.
A line is a 180-degree angle.

42. HIGH: To divide powers with the same base...
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
It will be a great advantage on test day to have your times table memorized from 1 through 15.

43. An integer is divisible by 3 if...
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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 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.
Between 0 and 1.

44. If x² = 144 - does v144 = x?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
360 degrees
Not necessarily. This is a trick question - because x could be either positive or negative.

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

46. v4 =
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.
Order does matter for a permutation - but does not matter for a combination.
2
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

47. Explain how to calculate an average (arithmetic mean)
2pr -or- pd
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
A radius
Invert the second fraction (reciprocal) and multiply

48. List all the prime numbers that are less than 30:
Not necessarily. This is a trick question - because x could be either positive or negative.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
1.4

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

50. On the GRE - should you ever assume that diagrams are truthful?
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%.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
(a+b)(a-b)
1