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Test your basic knowledge |
GRE High Frequency Math Terms
Start Test
Study First
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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
2. On the GRE - should you ever assume that diagrams are truthful?
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.
(0 -0)
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
3. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
4. In a coordinate system - what is the origin?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
40%
(0 -0)
2pr -or- pd
5. How many degrees does a circle contain?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1. Given event A: A + notA = 1.
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.
360 degrees
6. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
4 angles are formed. Their sum is 360 degrees
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
7. HIGH: What is the unfactored version of (x-y)² ?
An integer is divisible by 5 if its units digit is either 0 or 5.
x² -2xy + y²
(x+y)(x-y)
25%
8. HIGH: What is the unfactored version of (x+y)² ?
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
The value that appears most often in a data set.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² + 2xy + y²
9. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
x²-y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 5 if its units digit is either 0 or 5.
10. Does order matter for a permutation? How about for a combination?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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. Given event A: A + notA = 1.
Order does matter for a permutation - but does not matter for a combination.
11. HIGH: What is the factored version of (x+y)(x-y) ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
An integer is divisible by 9 if the sum of its digits is divisible by 9.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
x²-y²
12. HIGH: What are the percentages for standard deviation?
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
A line is a 180-degree angle.
Find a common denominator and make equivalent fractions. Then add or subtract.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
13. An integer is divisible by 5 if...
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.
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 5 if its units digit is either 0 or 5.
Multiply numerator times numerator and denominator times denominator.
14. Define the mode of a set of numbers.
'Big' angles and 'Small' angles.
Multiply numerator times numerator and denominator times denominator.
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.
80%
15. Convert to a percentage: 3/5
60%
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
4 angles are formed. Their sum is 360 degrees
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.
16. HIGH: x^-n is equal to
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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
17. v4 =
Find a common denominator and make equivalent fractions. Then add or subtract.
2
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
3:4:5 5:12:13
18. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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.
Order does matter for a permutation - but does not matter for a combination.
19. HIGH: What is the mode?
V=s³
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The value that appears most often in a 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.
20. What do permutation problems often ask for?
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.
60%
(x-y)²
Arrangements - orders - schedules - or lists.
21. What should you do BEFORE you start to solve a GRE math problem?
22. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
23. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
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.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
24. HIGH: What is the formula for the diagonal of any square?
Order does matter for a permutation - but does not matter for a combination.
25%
1.4
S*v2
25. Explain how to solve for 7/¼
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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)+
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
26. HIGH: To divide powers with the same base...
180 degrees
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
27. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?
28. a² - b² is equal to
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.
360 degrees
(a+b)(a-b)
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.
29. How do you multiply fractions?
Multiply numerator times numerator and denominator times denominator.
Find a common denominator and make equivalent fractions. Then add or subtract.
The # falling in the center of an ordered data set
A line is a 180-degree angle.
30. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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
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
31. Explain how to calculate an average (arithmetic mean)
Favorable Outcomes/Total Possible Outcomes
(a+b)(a-b)
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
'Big' angles and 'Small' angles.
32. HIGH: What is the factored version of x² + 2xy + y² ?
Multiply numerator times numerator and denominator times denominator.
(x+y)²
360 degrees
The value that appears most often in a data set.
33. HIGH: Define the formula for calculating slope.
Probability A * Probability B
Bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
34. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
1
25%
35. An integer is divisible by 9 if...
1/x^n For example - 6-² = 1/6² = 1/36
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Bh
Probability A * Probability B
36. What degree angle is a line?
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 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.
A line is a 180-degree angle.
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.
37. HIGH: Explain the process to solve '56 is what percent of 80?'
38. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
39. What are 'vertical angles'?
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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
90 degrees each.
S²
40. HIGH: How much of your times table should you know - for the GRE?
Favorable Outcomes/Total Possible Outcomes
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
2
It will be a great advantage on test day to have your times table memorized from 1 through 15.
41. HIGH: List the two most common side ratios for right triangles
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a-b)
3:4:5 5:12:13
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.
42. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
43. An integer is divisible by 2 if...
(x+y)²
Probability A * Probability B
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
An integer is divisible by 2 if its units digit is divisible by 2.
44. HIGH: Define the 'Third side' rule for triangles
45. Explain the difference between a digit and a number.
46. Explain the special properties of zero.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
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.
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
47. HIGH: Volume of a cube?
Between 0 and 1.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
V=s³
48. Convert to a percentage: 4/5
80%
The average - mean - median - or mode.
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.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
49. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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
An integer is divisible by 5 if its units digit is either 0 or 5.
50. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
(0 -0)
90 degrees each.
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 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.