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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. a² - b² is equal to
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.
(a+b)(a-b)
'Big' angles and 'Small' angles.
2. Does order matter for a permutation? How about for a combination?
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Not reading the problems carefully enough!
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Order does matter for a permutation - but does not matter for a combination.
3. 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.
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
1/1
4. HIGH: Area of a triangle?
1.4
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
5. HIGH: Rough est. of v3 =
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.
1.7
1
3:4:5 5:12:13
6. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
7. Define 'proportionate' values
40%
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Arrangements - orders - schedules - or lists.
Find a common denominator and make equivalent fractions. Then add or subtract.
8. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?
9. In a coordinate system - what is the origin?
Groups - teams - or committees.
Favorable Outcomes/Total Possible Outcomes
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%.
(0 -0)
10. Define the range of a set of numbers.
An integer is divisible by 2 if its units digit is divisible by 2.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Favorable Outcomes/Total Possible Outcomes
11. How do you solve a permutation?
(x+y)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
Bh
x² + 2xy + y²
12. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1.7
Groups - teams - or committees.
4 angles are formed. Their sum is 360 degrees
13. How do you solve a combination?
14. HIGH: What must be true before a quadratic equation can be solved?
15. Convert to a percentage: 3/5
(0 -0)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
60%
16. An integer is divisible by 5 if...
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Example: 1 < x < 10
17. What is the 'Third side' rule for triangles?
The average - mean - median - or mode.
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.
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.
25%
18. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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
Probability A * Probability B
19. How do you multiply fractions?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Multiply numerator times numerator and denominator times denominator.
Not reading the problems carefully enough!
4 angles are formed. Their sum is 360 degrees
20. HIGH: What is the median?
The # falling in the center of an ordered data set
(0 -0)
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Order does matter for a permutation - but does not matter for a combination.
21. How precise do you need to be - using p on the GRE?
22. HIGH: What is the equation of a line?
23. Area of a square?
S²
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
3:4:5 5:12:13
24. HIGH: how do you calculate the surface area of a rectangular box?
A line is a 180-degree angle.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Not reading the problems carefully enough!
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.
25. Solve this: v6 * -v6 = ?
6
1/x^n For example - 6-² = 1/6² = 1/36
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.
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.
26. What is the 'distributive law'?
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.
Between 0 and 1.
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.
360 degrees
27. For a bell curve - what three terms might be used to describe the number in the middle?
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.
The average - mean - median - or mode.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
'Big' angles and 'Small' angles.
28. List two odd behaviors of exponents
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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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
29. HIGH: How do you calculate the length of an arc?
30. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Order does matter for a permutation - but does not matter for a combination.
Favorable Outcomes/Total Possible Outcomes
31. Convert to a percentage: 4/5
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
80%
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
32. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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
2
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
33. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or 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.
Probability A + Probability B
60%
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
34. HIGH: What is the unfactored version of (x-y)² ?
Favorable Outcomes/Total Possible Outcomes
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1.7
x² -2xy + y²
35. What number goes on the bottom of a probability fraction?
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The total # of possible outcomes.
Not reading the problems carefully enough!
36. What is the formula to determine probability?
A 90-degree angle.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
V=pr²h (This is just the area multiplied by the height)
37. How is a range expressed with inequalities?
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.
2
Order does matter for a permutation - but does not matter for a combination.
Example: 1 < x < 10
38. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
39. What should you do BEFORE you start to solve a GRE math problem?
40. HIGH: What is a 'Right isosceles' triangle?
1/x^n For example - 6-² = 1/6² = 1/36
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.
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.
41. HIGH: Area of a circle
A=pr²
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
An integer is divisible by 9 if the sum of its digits is divisible by 9.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
42. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
Invert the second fraction (reciprocal) and multiply
'Big' angles and 'Small' angles.
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
43. HIGH: Explain the process to solve '56 is what percent of 80?'
44. Define a factorial of a number - and how it is written.
2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
45. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
2r
Between 0 and 1.
Not necessarily. This is a trick question - because x could be either positive or negative.
46. What do combination problems usually ask for?
Groups - teams - or committees.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Percentage Change = Difference/Original * 100
Bh
47. HIGH: How do you multiply powers with the same base?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
48. 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.
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
Example: 1 < x < 10
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.
49. HIGH: How do you multiply and divide square roots?
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'.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
50. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
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
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.
A line is a 180-degree angle.