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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 side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
x² + 2xy + y²
2. 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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
3. HIGH: How do you calculate the circumference of a circle?
x² + 2xy + y²
A 90-degree angle.
Percentage Change = Difference/Original * 100
2pr -or- pd
4. 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.
The total # of possible outcomes.
Multiply numerator times numerator and denominator times denominator.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
5. How precise do you need to be - using p on the GRE?
6. The probability of an event happening and the probability of an event NOT happening must add up to what number?
The average - mean - median - or mode.
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. Given event A: A + notA = 1.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
7. HIGH: Explain the process to solve '56 is what percent of 80?'
8. HIGH: Rough est. of v3 =
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1.7
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 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.
9. What is a 'Right' angle?
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
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
A 90-degree angle.
Invert the second fraction (reciprocal) and multiply
10. What should you do BEFORE you start to solve a GRE math problem?
11. HIGH: Simplify this: v75/v27
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x+y)(x-y)
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.
3:4:5 5:12:13
12. What is a 'Right' triangle?
A triangle in which one of the three interior angles is 90 degrees.
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.
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
2pr -or- pd
13. What'S one way to avoid mistakes on algebra questions in the GRE?
14. HIGH: What is the formula for the diagonal of any square?
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
S*v2
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 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.
15. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4 angles are formed. Their sum is 360 degrees
40%
16. Area of a square?
An integer is divisible by 2 if its units digit is divisible by 2.
x² -2xy + y²
S²
An integer is divisible by 5 if its units digit is either 0 or 5.
17. HIGH: How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A line is a 180-degree angle.
Arrangements - orders - schedules - or lists.
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
18. Convert to a percentage: 3/5
Not reading the problems carefully enough!
Between 0 and 1.
60%
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.
19. 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.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The total # of possible outcomes.
20. Probability Formula
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2r
Favorable Outcomes/Total Possible Outcomes
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.
21. An integer is divisible by 8 if...
22. An integer is divisible by 6 if...
23. If something is certain to happen - how is the probability of this event expressed mathematically?
25%
2r
1/1
(x-y)²
24. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1. Given event A: A + notA = 1.
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.
Invert the second fraction (reciprocal) and multiply
25. If something is possible but not certain - what is the numeric range of probability of it happening?
(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.
Between 0 and 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
26. The three interior angles of a triangle add up to...
180 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.
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.
Example: 1 < x < 10
27. Solve this: v6 * -v6 = ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The average - mean - median - or mode.
6
1.7
28. What causes 80% of errors on the math section of the GRE?
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)+
Example: 1 < x < 10
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 reading the problems carefully enough!
29. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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.
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
30. HIGH: Area of a circle
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.
2r
An integer is divisible by 5 if its units digit is either 0 or 5.
A=pr²
31. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
Probability A + Probability B
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
32. An integer is divisible by 2 if...
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
An integer is divisible by 2 if its units digit is divisible by 2.
(x+y)²
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
33. What is the sum of any 'big' angle and any 'Small' angle?
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.
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.
(a+b)(a-b)
34. 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.
Invert the second fraction (reciprocal) and multiply
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
35. Convert to a percentage: 2/5
40%
Arrangements - orders - schedules - or lists.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
36. What is the 'Third side' rule for triangles?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Order does matter for a permutation - but does not matter for a combination.
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.
x² + 2xy + y²
37. HIGH: What is the unfactored version of x²-y² ?
The average - mean - median - or mode.
(x+y)(x-y)
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.
360 degrees
38. Explain how to use a 'Rate Pie'
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
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 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
A line is a 180-degree angle.
39. How do you solve a combination?
40. What is the name of a line that extends from the center of a circle to the edge of a circle?
1
A radius
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
41. HIGH: Define the 'Third side' rule for triangles
42. Explain the special properties of zero.
360 degrees
A line is a 180-degree angle.
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.
43. HIGH: What must be true before a quadratic equation can be solved?
44. Explain how to calculate an average (arithmetic mean)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
An integer is divisible by 9 if the sum of its digits is divisible by 9.
(x+y)²
45. HIGH: What are the percentages for standard deviation?
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.
180 degrees
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
46. HIGH: What is the median?
1/x^n For example - 6-² = 1/6² = 1/36
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
The # falling in the center of an ordered data set
x² -2xy + y²
47. How do you multiply fractions?
(x+y)(x-y)
(x+y)²
Multiply numerator times numerator and denominator times denominator.
Probability A + Probability B
48. HIGH: how do you calculate the surface area of a rectangular box?
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Favorable Outcomes/Total Possible Outcomes
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.
49. Area of a parallelogram?
Bh
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
360 degrees
50. 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.
1
1.4
80%