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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. Convert to a percentage: 4/5
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.
80%
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.
2. How do you add or subtract fractions?
60%
An integer is divisible by 2 if its units digit is divisible by 2.
Find a common denominator and make equivalent fractions. Then add or subtract.
3:4:5 5:12:13
3. What is the key to dealing with ratio questions?
Find the total - or whole - first - and then set up a Ratio Box.
x² + 2xy + y²
'Big' angles and 'Small' angles.
360 degrees
4. What number goes on the bottom of a probability fraction?
The average - mean - median - or mode.
Between 0 and 1.
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.
The total # of possible outcomes.
5. What is the sum of any 'big' angle and any 'Small' angle?
The total # of possible outcomes.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
180 degrees.
Probability A * Probability B
6. v4 =
2
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Not reading the problems carefully enough!
7. How do you calculate the percentage of change?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
S²
Percentage Change = Difference/Original * 100
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
8. What do combination problems usually ask for?
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%.
Multiply numerator times numerator and denominator times denominator.
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
Groups - teams - or committees.
9. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
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.
10. Probability Formula
Probability A * Probability B
Percentage Change = Difference/Original * 100
2r
Favorable Outcomes/Total Possible Outcomes
11. What is the factored version of x² -2xy + y² ?
x² -2xy + y²
(x-y)²
25%
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
12. HIGH: What are the percentages for standard deviation?
x² + 2xy + y²
Multiply numerator times numerator and denominator times denominator.
Groups - teams - or committees.
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. What is the 'Third side' rule for triangles?
A 90-degree angle.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
180 degrees
14. HIGH: To divide powers with the same base...
3:4:5 5:12:13
Invert the second fraction (reciprocal) and multiply
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The # falling in the center of an ordered data set
15. An integer is divisible by 2 if...
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.
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
An integer is divisible by 2 if its units digit is divisible by 2.
16. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3
1/x^n For example - 6-² = 1/6² = 1/36
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
17. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Between 0 and 1.
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
360 degrees
18. HIGH: what is the side ratio for a Right Isosceles triangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
19. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
x² + 2xy + y²
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x² -2xy + y²
20. An integer is divisible by 6 if...
21. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
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.
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
22. HIGH: Simplify this: v75/v27
(0 -0)
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.
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.
23. Explain the special properties of zero.
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.
(0 -0)
A=pr²
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)+
24. What are the side ratios for a 30:60:90 triangle?
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.
The value that appears most often in a data set.
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
25. a² - b² is equal to
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
4 angles are formed. Their sum is 360 degrees
(a+b)(a-b)
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
26. HIGH: Define the 'Third side' rule for triangles
27. HIGH: What is the mode?
The value that appears most often in a data set.
(x-y)²
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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
28. How do you solve a combination?
29. How precise do you need to be - using p on the GRE?
30. On the GRE - should you ever assume that diagrams are truthful?
The # falling in the center of an ordered data set
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
x²-y²
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
31. HIGH: Area of a circle
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%.
Multiply numerator times numerator and denominator times denominator.
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=pr²
32. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
33. HIGH: What is a '30:60:90' triangle?
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.
180 degrees.
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+b)(a-b)
34. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?
35. HIGH: What is the unfactored version of (x+y)² ?
40%
x² + 2xy + y²
V=pr²h (This is just the area multiplied by the height)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
36. How is a range expressed with inequalities?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
60%
Example: 1 < x < 10
A triangle in which one of the three interior angles is 90 degrees.
37. How do you divide fractions?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Invert the second fraction (reciprocal) and multiply
38. What should you do BEFORE you start to solve a GRE math problem?
39. HIGH: List the two most common side ratios for right triangles
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
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
3:4:5 5:12:13
40. What is a 'Right' angle?
60%
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
A 90-degree angle.
41. HIGH: What is the median?
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
An integer is divisible by 2 if its units digit is divisible by 2.
Invert the second fraction (reciprocal) and multiply
The # falling in the center of an ordered data set
42. 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.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
43. Explain how to use a 'Rate Pie'
(x+y)²
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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
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
44. HIGH: What must be true before a quadratic equation can be solved?
45. HIGH: Explain the process to solve '56 is what percent of 80?'
46. The three exterior angles of a triangle add up to...
x²-y²
360 degrees
Example: 1 < x < 10
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.
47. The three interior angles of a triangle add up to...
360 degrees
180 degrees
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.
An integer is divisible by 5 if its units digit is either 0 or 5.
48. An integer is divisible by 9 if...
An integer is divisible by 9 if the sum of its digits is divisible by 9.
80%
360 degrees
(0 -0)
49. HIGH: What is 'absolute value' - and how is it represented?
50. What is the equation for a group problem?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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.
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