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. If x² = 144 - does v144 = x?
6
Not necessarily. This is a trick question - because x could be either positive or negative.
A triangle in which one of the three interior angles is 90 degrees.
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.

2. An integer is divisible by 2 if...
60%
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.
An integer is divisible by 2 if its units digit is divisible by 2.
2r

3. An integer is divisible by 9 if...
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%.
Percentage Change = Difference/Original * 100
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Find a common denominator and make equivalent fractions. Then add or subtract.

4. The three exterior angles of a triangle add up to...
The total # of possible outcomes.
180 degrees
Find the total - or whole - first - and then set up a Ratio Box.
360 degrees

5. HIGH: Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

6. Convert to a percentage: 2/5
40%
'Big' angles and 'Small' angles.
V=s³
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%.

7. Explain how to solve for 7/¼
A radius
(a+b)(a-b)
(x+y)(x-y)
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

8. HIGH: What is the factored version of (x+y)(x-y) ?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
An integer is divisible by 6 if it'S divisible by BOTH 2 and 3.
x²-y²

9. Convert to a percentage: 3/5
An integer is divisible by 2 if its units digit is divisible by 2.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
Between 0 and 1.
60%

10. 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.
(0 -0)
S*v2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

11. HIGH: Describe how to deal with 2 sets of parentheses.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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)+
Invert the second fraction (reciprocal) and multiply
A radius

12. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
V=pr²h (This is just the area multiplied by the height)
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

13. What are the side ratios for a 30:60:90 triangle?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
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.

14. HIGH: x^-n is equal to
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
1/x^n For example - 6-² = 1/6² = 1/36
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%.
(a+b)(a-b)

15. How many degrees does a circle contain?
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.
Multiply numerator times numerator and denominator times denominator.
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
360 degrees

16. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
A=pr²
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.

17. An integer is divisible by 3 if...
V=pr²h (This is just the area multiplied by the height)
4 angles are formed. Their sum is 360 degrees
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.
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.

18. HIGH: How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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
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.

19. HIGH: What is the Pythagorean theorem?

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

21. Convert to a percentage: 1/4
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.
25%
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
1/1

22. An integer is divisible by 5 if...
An integer is divisible by 5 if its units digit is either 0 or 5.
A line is a 180-degree angle.
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.
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.

23. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
A radius
Bh
40%

24. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Find a common denominator and make equivalent fractions. Then add or subtract.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

25. What should you do BEFORE you start to solve a GRE math problem?

26. HIGH: List the two most common side ratios for right triangles
6
3:4:5 5:12:13
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Favorable Outcomes/Total Possible Outcomes

27. How do you solve a permutation?
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.
(x+y)²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

28. a² - b² is equal to
180 degrees
80%
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
(a+b)(a-b)

29. Area of a square?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
S²
A line is a 180-degree angle.

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

31. Define the mode of a set of numbers.
An integer is divisible by 5 if its units digit is either 0 or 5.
A radius
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

32. HIGH: What is the unfactored version of x²-y² ?
180 degrees
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.
(x+y)(x-y)
Groups - teams - or committees.

33. List two odd behaviors of exponents
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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
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.
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.

34. How do you solve a combination?

35. HIGH: What is 'absolute value' - and how is it represented?

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

37. What'S one way to avoid mistakes on algebra questions in the GRE?

38. If something is possible but not certain - what is the numeric range of probability of it happening?
V=pr²h (This is just the area multiplied by the height)
Between 0 and 1.
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.
(x+y)(x-y)

39. Explain the difference between handling a permutation versus a combination.
A line is a 180-degree angle.
(x+y)(x-y)
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.
360 degrees

40. Explain the special properties of zero.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
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. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

42. What is the sum of any 'big' angle and any 'Small' angle?
180 degrees.
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.
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.
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%.

43. Explain how to use a 'Rate Pie'
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
90 degrees each.
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.

44. Does order matter for a permutation? How about for a combination?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Order does matter for a permutation - but does not matter for a combination.
(x-y)²
1/x^n For example - 6-² = 1/6² = 1/36

45. HIGH: What is the factored version of x² + 2xy + y² ?
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(x+y)²
Find the total - or whole - first - and then set up a Ratio Box.

46. In a coordinate system - what is the origin?
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.
(0 -0)
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.

47. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
180 degrees.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Groups - teams - or committees.

48. HIGH: What is the mode?
x²-y²
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.
The value that appears most often in a data set.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

49. HIGH: How do you multiply and divide square roots?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
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
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.

50. Define 'proportionate' values
x² + 2xy + y²
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.