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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 Pythagorean theorem?
2. HIGH: Explain the process to solve '56 is what percent of 80?'
3. HIGH: How do you calculate the length of an arc?
4. HIGH: Area of a circle
1/x^n For example - 6-² = 1/6² = 1/36
Between 0 and 1.
Not reading the problems carefully enough!
A=pr²
5. Diameter of a circle?
2r
A 90-degree angle.
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%.
1.4
6. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
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
90 degrees each.
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.
7. Does order matter for a permutation? How about for a combination?
180 degrees
Order does matter for a permutation - but does not matter for a combination.
1. Given event A: A + notA = 1.
80%
8. Convert to a percentage: 1/4
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'.
40%
'Big' angles and 'Small' angles.
25%
9. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
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
A 90-degree angle.
Not reading the problems carefully enough!
10. a² - b² is equal to
60%
(x-y)²
(a+b)(a-b)
Multiply numerator times numerator and denominator times denominator.
11. HIGH: Volume of a cube?
V=s³
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
12. HIGH: how do you calculate the surface area of a rectangular box?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
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%.
Order does matter for a permutation - but does not matter for a combination.
13. Explain how to calculate an average (arithmetic mean)
Bh
(x-y)²
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
14. HIGH: What is a '30:60:90' triangle?
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
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.
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
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.
15. HIGH: What is a 'Right isosceles' triangle?
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.
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.
80%
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
16. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
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)+
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.
17. Area of a square?
Not reading the problems carefully enough!
40%
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
S²
18. What should you do BEFORE you start to solve a GRE math problem?
19. How do you solve a permutation?
Not reading the problems carefully enough!
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
1.7
Groups - teams - or committees.
20. HIGH: What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Find the total - or whole - first - and then set up a Ratio Box.
1.7
An integer is divisible by 5 if its units digit is either 0 or 5.
21. Explain the difference between a digit and a number.
22. An integer is divisible by 4 if...
23. HIGH: What is the median?
x² + 2xy + y²
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 # falling in the center of an ordered data set
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
24. In a coordinate system - identify the quadrants and describe their location.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Find a common denominator and make equivalent fractions. Then add or subtract.
25. HIGH: Rough est. of v1 =
1
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |
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)+
60%
26. An integer is divisible by 2 if...
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
Bh
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 2 if its units digit is divisible by 2.
27. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
28. Explain how to use a 'Rate Pie'
A=pr²
1.4
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
The value that appears most often in a data set.
29. HIGH: What is 'absolute value' - and how is it represented?
30. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
25%
31. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
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.
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Groups - teams - or committees.
32. An integer is divisible by 3 if...
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 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.
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.
1.7
33. The three interior angles of a triangle add up 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.
180 degrees
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S²
34. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The # falling in the center of an ordered data set
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.
Arrangements - orders - schedules - or lists.
35. HIGH: What is the unfactored version of (x-y)² ?
A radius
Find a common denominator and make equivalent fractions. Then add or subtract.
x² -2xy + y²
A=pr²
36. How do you calculate the probability of two events in a row? (Probability of A and B)
6
Probability A * Probability B
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
90 degrees each.
37. Convert to a percentage: 4/5
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
80%
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Arrangements - orders - schedules - or lists.
38. Area of a parallelogram?
Bh
Invert the second fraction (reciprocal) and multiply
(0 -0)
360 degrees
39. An integer is divisible by 6 if...
40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(a+b)(a-b)
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
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
41. What'S the most important thing to remember about charts you'll see on the GRE?
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.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.
42. HIGH: what is the side ratio for a Right Isosceles triangle?
A 90-degree angle.
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.
A=pr²
43. 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
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
The total # of possible outcomes.
44. How do you calculate the percentage of change?
V=pr²h (This is just the area multiplied by the height)
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
Percentage Change = Difference/Original * 100
90 degrees each.
45. HIGH: What must be true before a quadratic equation can be solved?
46. Explain the special properties of zero.
An integer is divisible by 5 if its units digit is either 0 or 5.
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
Bh
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.
47. How is a range expressed with inequalities?
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
Example: 1 < x < 10
The average - mean - median - or mode.
48. HIGH: x^-n is equal to
1/x^n For example - 6-² = 1/6² = 1/36
4 angles are formed. Their sum is 360 degrees
360 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.
49. 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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S*v2
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.
50. What is the equation for a group problem?
The average - mean - median - or mode.
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 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 radius