Test your basic knowledge |

GRE High Frequency Math Terms

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. For a bell curve - what three terms might be used to describe the number in the middle?
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 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.
The average - mean - median - or mode.
Find a common denominator and make equivalent fractions. Then add or subtract.

2. What is an 'equilateral' triangle?
6
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Favorable Outcomes/Total Possible Outcomes
90 degrees each.

3. What is the 'Third side' rule for triangles?
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.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')

4. HIGH: Area of a circle
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
(x+y)²
A=pr²
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.

5. What do permutation problems often ask for?
The average - mean - median - or mode.
25%
Arrangements - orders - schedules - or lists.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

6. What are 'vertical angles'?
1.7
90 degrees each.
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.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

7. HIGH: Define the formula for calculating slope.
Find a common denominator and make equivalent fractions. Then add or subtract.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

8. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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 9 if the sum of its digits is divisible by 9.
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
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.

9. HIGH: Rough est. of v3 =
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
1.7
4 angles are formed. Their sum is 360 degrees

10. When a pair of parallel lines is intersected by another line - two types of angles are formed. What are they?

11. Convert to a percentage: 2/5
1. Given event A: A + notA = 1.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
40%
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

12. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Probability A + Probability B
Total of the elements divided by the number of elements. Example: (4 -6 -7) -- add 4+6+7 = 17 and divide by 3

13. The three interior angles of a triangle add up to...
Example: 1 < x < 10
Percentage Change = Difference/Original * 100
180 degrees
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'.

14. What are the side ratios for a 30:60:90 triangle?
360 degrees
1.4
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A + Probability B

15. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 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.
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)+
Probability A * Probability B

16. How do you divide fractions?
2pr -or- pd
V=s³
Invert the second fraction (reciprocal) and multiply
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

17. Area of a parallelogram?
The # falling in the center of an ordered data set
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4 angles are formed. Their sum is 360 degrees
Bh

18. a² - b² is equal to
A line is a 180-degree angle.
x² -2xy + y²
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+b)(a-b)

19. HIGH: Rough est. of 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.
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
Probability A + Probability B
1.4

20. HIGH: What is a '30:60:90' triangle?
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
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
3:4:5 5:12:13
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

21. HIGH: how do you calculate the surface area of a rectangular box?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Arrangements - orders - schedules - or lists.

22. Area of a square?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x+y)(x-y)
S²
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

23. An integer is divisible by 4 if...

24. Simplify this: v32
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

25. HIGH: What is the unfactored version of x²-y² ?
(x+y)(x-y)
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.
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)+
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

26. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
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)+
V=pr²h (This is just the area multiplied by the height)
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

27. An integer is divisible by 6 if...

28. HIGH: Simplify this: v75/v27
(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.
S*v2
It will be a great advantage on test day to have your times table memorized from 1 through 15.

29. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
Not necessarily. This is a trick question - because x could be either positive or negative.

30. HIGH: Rough est. of v1 =
Bh
1
The average - mean - median - or mode.
V=s³

31. Explain how to solve for 7/¼
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Not necessarily. This is a trick question - because x could be either positive or negative.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

32. HIGH: What are the percentages for standard deviation?
Groups - teams - or committees.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
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.
2 - 14 - and 34. So - a Bell - standard deviation - or normal distribution curve would be segmented: | 2% | 14% | 34% |average score| 34% | 14% | 2% |

33. What is the name of a line that extends from the center of a circle to the edge of a circle?
A radius
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
180 degrees
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)+

34. Explain how to use a 'Rate Pie'
Invert the second fraction (reciprocal) and multiply
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

35. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

36. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
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.
Invert the second fraction (reciprocal) and multiply
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'.

37. Convert to a percentage: 1/4
Groups - teams - or committees.
The value that appears most often in a data set.
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
25%

38. How do you solve a combination?

39. HIGH: Define the 'Third side' rule for triangles

40. What is the 'distributive law'?
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
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.
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.

41. What is the formula to determine probability?
The total # of possible outcomes.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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 30:60:90 triangle?
S²
60%
6
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

43. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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.
1. Given event A: A + notA = 1.
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
Find a common denominator and make equivalent fractions. Then add or subtract.

44. What'S the most important thing to remember about charts you'll see on the GRE?
x²-y²
A line is a 180-degree angle.
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.
Find the total - or whole - first - and then set up a Ratio Box.

45. On the GRE - should you ever assume that diagrams are truthful?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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
2r

46. How do you add or subtract fractions?
Find a common denominator and make equivalent fractions. Then add or subtract.
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.
2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

47. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
An integer is divisible by 2 if its units digit is divisible by 2.
A=pr²
Between 0 and 1.

48. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
40%
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%.
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.
1.4

49. HIGH: What is the factored version of x² + 2xy + y² ?
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
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.
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
(x+y)²

50. Explain how to use an 'Average Pie'
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
90 degrees each.
x² + 2xy + y²