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: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

2. HIGH: What is a '30:60:90' triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
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.
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

3. HIGH: What is the formula for the diagonal of any square?
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'.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
S*v2
2pr -or- pd

4. What degree angle is a line?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
A line is a 180-degree angle.

5. What is the key to dealing with ratio questions?
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.
Not reading the problems carefully enough!
360 degrees
Find the total - or whole - first - and then set up a Ratio Box.

6. 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.
A 90-degree angle.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
1/x^n For example - 6-² = 1/6² = 1/36

7. HIGH: Rough est. of v3 =
Between 0 and 1.
1.7
A line is a 180-degree angle.
An integer is divisible by 2 if its units digit is divisible by 2.

8. Explain how to use a 'Rate Pie'
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%.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
Bh

9. What is the formula to determine probability?
(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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

10. An integer is divisible by 3 if...
4 angles are formed. Their sum is 360 degrees
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.
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.
x² -2xy + y²

11. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
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.
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
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

12. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
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.
360 degrees
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

13. HIGH: What is the factored version of x² + 2xy + y² ?
A line is a 180-degree angle.
(x+y)²
3:4:5 5:12:13
1.4

14. 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.
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
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.
An integer is divisible by 5 if its units digit is either 0 or 5.

15. Define a factorial of a number - and how it is written.
1/x^n For example - 6-² = 1/6² = 1/36
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.
180 degrees
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

16. Define 'proportionate' values
2r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
80%
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.

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

18. HIGH: Area of a circle
A=pr²
Find a common denominator and make equivalent fractions. Then add or subtract.
Probability A * Probability B
40%

19. HIGH: Volume of a cube?
(x+y)(x-y)
V=s³
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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'.

20. The three exterior angles of a triangle add up to...
Groups - teams - or committees.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
360 degrees
The # falling in the center of an ordered data set

21. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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'.
1. Given event A: A + notA = 1.
(x+y)²
3:4:5 5:12:13

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

23. Diameter of a circle?
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
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
2r
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

24. a² - b² is equal to
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.
(a+b)(a-b)
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

25. 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 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
3:4:5 5:12:13
180 degrees

26. If x² = 144 - does v144 = x?
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 average - mean - median - or 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.
Not necessarily. This is a trick question - because x could be either positive or negative.

27. HIGH: What is the unfactored version of x²-y² ?
V=s³
360 degrees
(x+y)(x-y)
A radius

28. In a coordinate system - identify the quadrants and describe their location.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
x² + 2xy + y²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.

29. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
(x+y)²
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
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

30. HIGH: Volume of a cylinder?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The # falling in the center of an ordered data set
V=pr²h (This is just the area multiplied by the height)
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.

31. Area of a square?
A 90-degree angle.
S²
Not necessarily. This is a trick question - because x could be either positive or negative.
2pr -or- pd

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

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

34. Explain the special properties of zero.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
90 degrees each.
(x+y)(x-y)

35. What are 'vertical angles'?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
360 degrees
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

36. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Between 0 and 1.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

37. Convert to a percentage: 1/4
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.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
25%

38. What is the equation for a group problem?
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
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

39. 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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A radius
Favorable Outcomes/Total Possible Outcomes

40. 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.
2
Find a common denominator and make equivalent fractions. Then add or subtract.
360 degrees

41. How do you add or subtract 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.
Find a common denominator and make equivalent fractions. Then add or subtract.
(x-y)²
A=pr²

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

43. How many degrees does a circle contain?
80%
360 degrees
A 90-degree angle.
The average - mean - median - or mode.

44. Does order matter for a permutation? How about for a combination?
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.
2r
Order does matter for a permutation - but does not matter for a combination.

45. How do you calculate the percentage of change?
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'.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
Percentage Change = Difference/Original * 100

46. Explain how to solve for 7/¼
(x-y)²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
V=pr²h (This is just the area multiplied by the height)
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.

47. What is the factored version of x² -2xy + y² ?
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 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.
(x-y)²
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

48. HIGH: How much of your times table should you know - for the GRE?
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.
S²
It will be a great advantage on test day to have your times table memorized from 1 through 15.
An integer is divisible by 9 if the sum of its digits is divisible by 9.

49. The three interior angles of a triangle add up to...
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.
2
180 degrees

50. Explain how to divide fractions.
The value that appears most often in a data set.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
An integer is divisible by 9 if the sum of its digits is divisible by 9.