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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: What is the mode?
The value that appears most often in a data set.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
An integer is divisible by 2 if its units digit is divisible by 2.
V=pr²h (This is just the area multiplied by the height)
2. Diameter of a circle?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A radius
Order does matter for a permutation - but does not matter for a combination.
2r
3. HIGH: What is a 'Right isosceles' triangle?
Order does matter for a permutation - but does not matter for a combination.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Find the total - or whole - first - and then set up a Ratio Box.
4. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
The value that appears most often in a data set.
A triangle in which one of the three interior angles is 90 degrees.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
5. HIGH: What is the equation of a line?
6. HIGH: What is the median?
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.
The # falling in the center of an ordered data set
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
7. Explain how to solve for 7/¼
(x+y)²
Multiply numerator times numerator and denominator times denominator.
(x-y)²
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
8. An integer is divisible by 8 if...
9. What degree angle is a line?
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
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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 line is a 180-degree angle.
10. HIGH: What is 'absolute value' - and how is it represented?
11. What is the 'Third side' rule for triangles?
A radius
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
12. What should you do BEFORE you start to solve a GRE math problem?
13. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
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/x^n For example - 6-² = 1/6² = 1/36
25%
14. What number goes on the bottom of a probability fraction?
2r
The total # of possible outcomes.
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.
90 degrees each.
15. How do you calculate the probability of two events in a row? (Probability of A and B)
A triangle in which one of the three interior angles is 90 degrees.
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.
Multiply numerator times numerator and denominator times denominator.
Probability A * Probability B
16. HIGH: x^-n is equal to
Probability A + Probability B
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)+
Order does matter for a permutation - but does not matter for a combination.
1/x^n For example - 6-² = 1/6² = 1/36
17. HIGH: Area of a triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
18. In a coordinate system - what is the origin?
Invert the second fraction (reciprocal) and multiply
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.
(0 -0)
19. HIGH: Define the formula for calculating slope.
Multiply numerator times numerator and denominator times denominator.
360 degrees
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
20. HIGH: How do you calculate the circumference of a circle?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
180 degrees.
2pr -or- pd
21. What is the 'distributive law'?
6
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.
x² + 2xy + y²
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
22. HIGH: Rough est. of v3 =
80%
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%.
1.7
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.
23. How do you solve a permutation?
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x+y)²
24. An integer is divisible by 5 if...
25%
The # falling in the center of an ordered data set
An integer is divisible by 5 if its units digit is either 0 or 5.
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%.
25. HIGH: What are the percentages for standard deviation?
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.
40%
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
26. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
80%
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.
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.
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.
27. What is a 'Right' 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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A triangle in which one of the three interior angles is 90 degrees.
28. If x² = 144 - does v144 = x?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Example: 1 < x < 10
(x-y)²
Not necessarily. This is a trick question - because x could be either positive or negative.
29. Define 'proportionate' values
Invert the second fraction (reciprocal) and multiply
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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 value that appears most often in a data set.
30. HIGH: Volume of a cylinder?
Percentage Change = Difference/Original * 100
Favorable Outcomes/Total Possible Outcomes
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
V=pr²h (This is just the area multiplied by the height)
31. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
32. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
A triangle in which one of the three interior angles is 90 degrees.
Probability A + Probability B
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.
3:4:5 5:12:13
33. Explain how to divide fractions.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Arrangements - orders - schedules - or lists.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A line is a 180-degree angle.
34. How many degrees does a circle contain?
Between 0 and 1.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
360 degrees
A 90-degree angle.
35. The three exterior angles of a triangle add up to...
40%
360 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
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.
36. What is the sum of any 'big' angle and any 'Small' angle?
80%
4 angles are formed. Their sum is 360 degrees
x² -2xy + y²
180 degrees.
37. How do you divide fractions?
(0 -0)
Invert the second fraction (reciprocal) and multiply
x²-y²
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.
38. In a coordinate system - identify the quadrants and describe their location.
60%
360 degrees
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
39. 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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Order does matter for a permutation - but does not matter for a combination.
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.
40. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
25%
Find the total - or whole - first - and then set up a Ratio Box.
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 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.
41. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
4 angles are formed. Their sum is 360 degrees
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
42. What is the name of a line that extends from the center of a circle to the edge of a circle?
(0 -0)
A radius
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
43. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Groups - teams - or committees.
1. Given event A: A + notA = 1.
44. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
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
Arrangements - orders - schedules - or lists.
45. HIGH: how do you calculate the surface area of a rectangular box?
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
1/1
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.
46. HIGH: Define the 'Third side' rule for triangles
47. What is the formula to determine probability?
The value that appears most often in a data set.
Not reading the problems carefully enough!
(# 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.
48. HIGH: List the two most common side ratios for right triangles
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 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.
3:4:5 5:12:13
The total # of possible outcomes.
49. How is a range expressed with inequalities?
Example: 1 < x < 10
Probability A * Probability B
180 degrees
180 degrees.
50. Convert to a percentage: 1/4
25%
1. Given event A: A + notA = 1.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |