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. HIGH: What is the equation of a line?

2. HIGH: What is the factored version of x² + 2xy + y² ?
6
1/1
(x+y)²
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.

3. Diameter of a circle?
2r
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

4. HIGH: List the two most common side ratios for right triangles
Invert the second fraction (reciprocal) and multiply
An integer is divisible by 9 if the sum of its digits is divisible by 9.
3:4:5 5:12:13
Order does matter for a permutation - but does not matter for a combination.

5. What is the sum of any 'big' angle and any 'Small' angle?
Order does matter for a permutation - but does not matter for a combination.
180 degrees.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Invert the second fraction (reciprocal) and multiply

6. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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.
A line is a 180-degree angle.
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.

7. HIGH: Describe how to deal with 2 sets of parentheses.
1.4
Not reading the problems carefully enough!
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)+
A triangle in which one of the three interior angles is 90 degrees.

8. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

9. Simplify this: v32
25%
Probability A * Probability B
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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.

10. The three interior angles of a triangle add up to...
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
Find the total - or whole - first - and then set up a Ratio Box.

11. 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.
2r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The average - mean - median - or mode.

12. Explain how to divide fractions.
(x+y)(x-y)
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
2
Find the total - or whole - first - and then set up a Ratio Box.

13. Explain how to use an 'Average Pie'
Not necessarily. This is a trick question - because x could be either positive or negative.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
3:4:5 5:12:13
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

14. What do combination problems usually ask for?
(x+y)²
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'.
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
Groups - teams - or committees.

15. How do you calculate the probability of two events in a row? (Probability of A and B)
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
360 degrees
Find a common denominator and make equivalent fractions. Then add or subtract.
Probability A * Probability B

16. HIGH: what is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
Find the total - or whole - first - and then set up a Ratio Box.
60%

17. HIGH: What is the order of math operations - and the mnemonic to remember it?
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%.
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
Find the total - or whole - first - and then set up a Ratio Box.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions

18. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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

19. Convert to a percentage: 2/5
40%
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
x² -2xy + y²
60%

20. Define a factorial of a number - and how it is written.
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.
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.
360 degrees
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

21. On the GRE - should you ever assume that diagrams are truthful?
Groups - teams - or committees.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
(x+y)(x-y)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

22. An integer is divisible by 9 if...
(x-y)²
180 degrees
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

23. a² - b² is equal to
40%
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.
(a+b)(a-b)
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

24. How do you solve a permutation?
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.
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.
2r
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

25. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

26. HIGH: What is the median?
The # falling in the center of an ordered data set
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
x² -2xy + y²
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)+

27. What is the 'Third side' rule for triangles?
2r
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
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.
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

28. Explain the special properties of zero.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
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%.
3:4:5 5:12:13
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.

29. HIGH: To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1. Given event A: A + notA = 1.
2r
180 degrees.

30. List two odd behaviors of exponents
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
A 90-degree angle.
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.
(x-y)²

31. HIGH: Area of a circle
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
Not reading the problems carefully enough!
A=pr²
1/x^n For example - 6-² = 1/6² = 1/36

32. HIGH: How much of your times table should you know - for the GRE?
4 angles are formed. Their sum is 360 degrees
The average - mean - median - or mode.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

33. 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.
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Probability A * Probability B

34. HIGH: What is a 'Right isosceles' triangle?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
S*v2
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.
An integer is divisible by 2 if its units digit is divisible by 2.

35. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
Bh
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
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%.

36. HIGH: What must be true before a quadratic equation can be solved?

37. Explain how to use a 'Rate Pie'
4 angles are formed. Their sum is 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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

38. HIGH: How do you multiply powers with the same base?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
360 degrees
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

39. HIGH: How do you calculate the circumference of a circle?
2pr -or- pd
A line is a 180-degree angle.
4 angles are formed. Their sum is 360 degrees
An integer is divisible by 5 if its units digit is either 0 or 5.

40. How many angles are formed when 2 lines intersect? and what is the sum of these angles?
4 angles are formed. Their sum is 360 degrees
Not reading the problems carefully enough!
(0 -0)
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.

41. HIGH: What is a '30:60:90' triangle?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
60%
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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

42. HIGH: What is the unfactored version of (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
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. 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
x² -2xy + y²

43. What is a 'Right' triangle?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Order does matter for a permutation - but does not matter for a combination.
A triangle in which one of the three interior angles is 90 degrees.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

44. What degree angle is a line?
A line is a 180-degree angle.
Between 0 and 1.
(x+y)(x-y)
80%

45. The three exterior angles of a triangle add up to...
360 degrees
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
(a+b)(a-b)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

46. What are 'vertical angles'?
'Big' angles and 'Small' angles.
25%
The value that appears most often in a data set.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.

47. An integer is divisible by 3 if...
25%
A line is a 180-degree angle.
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.
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.

48. An integer is divisible by 8 if...

49. HIGH: Volume of a cube?
1/1
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
V=s³
3:4:5 5:12:13

50. 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
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%.
360 degrees