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: Rough est. of v1 =
1
A line is a 180-degree angle.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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%.

2. Solve this: v6 * -v6 = ?
80%
6
'Big' angles and 'Small' angles.
x² -2xy + y²

3. HIGH: Area of a triangle?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Groups - teams - or committees.
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'.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

4. The three interior angles of a triangle add up to...
An integer is divisible by 2 if its units digit is divisible by 2.
180 degrees
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.
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%.

5. What number goes on the bottom of a probability fraction?
(0 -0)
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
The 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.

6. HIGH: Simplify this: v75/v27
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'.
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The average - mean - median - or mode.

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

8. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
180 degrees

9. Diameter of a circle?
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.
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
2r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

10. Explain the difference between handling a permutation versus a combination.
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.
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.
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.
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.

11. Explain how to use a 'Rate Pie'
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
180 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

12. Define a factorial of a number - and how it is written.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
Not reading the problems carefully enough!
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.

13. HIGH: What is the median?
Bh
1/x^n For example - 6-² = 1/6² = 1/36
S*v2
The # falling in the center of an ordered data set

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

15. The three exterior angles of a triangle add up to...
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.
25%
360 degrees
(x+y)(x-y)

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

17. Convert to a percentage: 1/4
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
25%
x²-y²

18. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
Not necessarily. This is a trick question - because x could be either positive or negative.
The value that appears most often in a data set.
1.7

19. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
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%.
x² -2xy + y²
Not necessarily. This is a trick question - because x could be either positive or negative.

20. An integer is divisible by 2 if...
x² -2xy + y²
6
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

21. HIGH: how do you calculate the surface area of a rectangular box?
Find the total - or whole - first - and then set up a Ratio Box.
A line is a 180-degree angle.
(x-y)²
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.

22. HIGH: What is the unfactored version of (x+y)² ?
ZONE-F numbers: Zero - One - Negatives - Extreme values - 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.
x² + 2xy + y²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

23. Define the mode of a set of numbers.
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.
25%
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
2pr -or- pd

24. What is the 'Third side' rule for triangles?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.
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.
Groups - teams - or committees.

25. HIGH: How do you multiply powers with the same base?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

26. Probability Formula
(x+y)²
Probability A + Probability B
An integer is divisible by 5 if its units digit is either 0 or 5.
Favorable Outcomes/Total Possible Outcomes

27. Convert to a percentage: 2/5
The value that appears most often in a data set.
40%
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

28. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
90 degrees each.
Probability A * Probability B
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

29. HIGH: How do you calculate the circumference of a circle?
1.4
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
2pr -or- pd
V=s³

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

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

32. HIGH: What is the side ratio 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.
360 degrees
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

33. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

34. How do you solve a combination?

35. How do you add or subtract fractions?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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
Find a common denominator and make equivalent fractions. Then add or subtract.
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.

36. How is a range expressed with inequalities?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Multiply numerator times numerator and denominator times denominator.
90 degrees each.
Example: 1 < x < 10

37. HIGH: What is the mode?
The value that appears most often in a data set.
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
Not necessarily. This is a trick question - because x could be either positive or negative.
1.4

38. Explain how to solve for 7/¼
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
(0 -0)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

39. What is the key to dealing with ratio questions?
Example: 1 < x < 10
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.
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.
Find the total - or whole - first - and then set up a Ratio Box.

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

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

42. Explain how to calculate an average (arithmetic mean)
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1

43. Explain how to use an 'Average Pie'
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2

44. An integer is divisible by 3 if...
S*v2
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

45. Area of a square?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
S²
90 degrees each.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

46. HIGH: What is the order of math operations - and the mnemonic to remember it?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
80%
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.

47. List two odd behaviors of exponents
1
An integer is divisible by 2 if its units digit is divisible by 2.
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
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.

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

49. HIGH: Volume of a cylinder?
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.
1/x^n For example - 6-² = 1/6² = 1/36
V=pr²h (This is just the area multiplied by the height)
A 90-degree angle.

50. How do you divide fractions?
The value that appears most often in a data set.
(x+y)(x-y)
Invert the second fraction (reciprocal) and multiply
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.