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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: Rough est. of v2 =
The value that appears most often in a data set.
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.
1.4
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. HIGH: Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
2r
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

3. The three interior angles of a triangle add up to...
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.
6
180 degrees
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.

4. What is the factored version of x² -2xy + y² ?
S²
(x-y)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)

5. HIGH: Explain the process to solve '56 is what percent of 80?'

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

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

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

9. HIGH: What is the formula for the diagonal of any square?
1/x^n For example - 6-² = 1/6² = 1/36
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
'Big' angles and 'Small' angles.
S*v2

10. The three exterior angles of a triangle add up to...
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
1/x^n For example - 6-² = 1/6² = 1/36
360 degrees

11. HIGH: What numbers does ETS hope you'll forget to consider - for quant comp questions?
An integer is divisible by 5 if its units digit is either 0 or 5.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
2pr -or- pd
Favorable Outcomes/Total Possible Outcomes

12. In a coordinate system - identify the quadrants and describe their location.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
Groups - teams - or committees.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

13. HIGH: Volume of a cylinder?
V=pr²h (This is just the area multiplied by the height)
Not reading the problems carefully enough!
x²-y²
Order does matter for a permutation - but does not matter for a combination.

14. How precise do you need to be - using p on the GRE?

15. How do you add or subtract fractions?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
(x+y)²
Find a common denominator and make equivalent fractions. Then add or subtract.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

16. What are the side ratios 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.
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 total # of possible outcomes.

17. Diameter of a circle?
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.
4 angles are formed. Their sum is 360 degrees
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2r

18. HIGH: Rough est. of v3 =
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.
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
V=s³

19. On the GRE - should you ever assume that diagrams are truthful?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
The # falling in the center of an ordered data set
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

20. a² - b² is equal to
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.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(a+b)(a-b)

21. What is a 'Right' 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.
1
A triangle in which one of the three interior angles is 90 degrees.
The total # of possible outcomes.

22. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Invert the second fraction (reciprocal) and multiply
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.
Favorable Outcomes/Total Possible Outcomes
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.

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

24. Define the range of a set of numbers.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Find the total - or whole - first - and then set up a Ratio Box.
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
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.

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

26. HIGH: What is the mode?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The value that appears most often in a data set.
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
25%

27. Explain how to solve for 7/¼
90 degrees each.
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1. Given event A: A + notA = 1.

28. HIGH: What is a 'Right isosceles' triangle?
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)+
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
An integer is divisible by 9 if the sum of its digits is divisible by 9.
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.

29. Explain the difference between a digit and a number.

30. HIGH: Volume of a cube?
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.
Probability A * Probability B
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
V=s³

31. How do you solve a combination?

32. Explain how to divide fractions.
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.
1/x^n For example - 6-² = 1/6² = 1/36
Probability A * Probability B
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4

33. 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
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.
2pr -or- pd
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

34. HIGH: Area of a circle
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.
4 angles are formed. Their sum is 360 degrees
A=pr²
An integer is divisible by 5 if its units digit is either 0 or 5.

35. Explain how to use an 'Average Pie'
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
Percentage Change = Difference/Original * 100
Draw a circle. The top half holds the Total. The bottom left quadrant holds Number of Things. Bottom right holds Average.
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

36. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
90 degrees each.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.

37. What is the 'Third side' rule for triangles?
A line is a 180-degree angle.
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.
3:4:5 5:12:13
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.

38. HIGH: What is the Pythagorean theorem?

39. Explain the difference between handling a permutation versus a combination.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.
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.

40. How is a range expressed with inequalities?
Not necessarily. This is a trick question - because x could be either positive or negative.
The total # of possible outcomes.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Example: 1 < x < 10

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

42. Convert to a percentage: 2/5
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.
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%.
Example: 1 < x < 10

43. HIGH: Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Bh
60%
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

44. An integer is divisible by 2 if...
60%
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.
An integer is divisible by 2 if its units digit is divisible by 2.
4 angles are formed. Their sum is 360 degrees

45. An integer is divisible by 9 if...
1
An integer is divisible by 9 if the sum of its digits is divisible by 9.
360 degrees
S*v2

46. What is the 'distributive law'?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
2r
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.
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.

47. HIGH: How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Favorable Outcomes/Total Possible Outcomes
(x-y)²
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

48. What do combination problems usually ask for?
Not necessarily. This is a trick question - because x could be either positive or negative.
Invert the second fraction (reciprocal) and multiply
Groups - teams - or committees.
25%

49. What is the name of a line that extends from the center of a circle to the edge of a circle?
1.4
6
A radius
(x-y)²

50. Solve this: v6 * -v6 = ?
V=s³
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
6