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. Explain the special properties of zero.
Invert the second fraction (reciprocal) and multiply
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.
S²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

2. Define the range of a set of numbers.
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 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.
Bh
Probability A + Probability B

3. The three exterior angles of a triangle add up to...
360 degrees
An integer is divisible by 9 if the sum of its digits is divisible by 9.
Multiply numerator times numerator and denominator times denominator.
Probability A * Probability B

4. HIGH: Rough est. of v2 =
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
1.4
A line is a 180-degree angle.
(x-y)²

5. HIGH: What is the factored version of x² + 2xy + y² ?
Order does matter for a permutation - but does not matter for a combination.
(x+y)²
1.4
180 degrees

6. HIGH: Volume of a cube?
An integer is divisible by 5 if its units digit is either 0 or 5.
(0 -0)
V=s³
60%

7. In a coordinate system - identify the quadrants and describe their location.
2pr -or- pd
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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

8. How do you solve a permutation?
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.
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 average - mean - median - or mode.
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

9. How do you multiply fractions?
90 degrees each.
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.
Multiply numerator times numerator and denominator times denominator.
360 degrees

10. What is the formula to determine probability?
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
6
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 line is a 180-degree angle.

11. How many degrees does a circle contain?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
360 degrees
(0 -0)
Multiply numerator times numerator and denominator times denominator.

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

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

14. What causes 80% of errors on the math section of the GRE?
Not reading the problems carefully enough!
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
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'.

15. Convert to a percentage: 4/5
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
80%
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.
360 degrees

16. Diameter of a circle?
It will be a great advantage on test day to have your times table memorized from 1 through 15.
2r
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.

17. HIGH: How do you multiply powers with the same base?
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Find the total - or whole - first - and then set up a Ratio Box.
1.7

18. In a coordinate system - what is the origin?
'Big' angles and 'Small' angles.
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(0 -0)
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.

19. HIGH: Simplify this: v75/v27
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.
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Vertical angles are the angles that are across from each other when 2 lines intersect. Vertical angles are always equal.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.

20. HIGH: What is a 'Right isosceles' triangle?
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.
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.
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
180 degrees.

21. Solve this: v6 * -v6 = ?
1.4
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
Bh

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

23. HIGH: what is the side ratio for a Right Isosceles triangle?
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
V=s³
V=pr²h (This is just the area multiplied by the height)

24. How is a range expressed with inequalities?
Percentage Change = Difference/Original * 100
Example: 1 < x < 10
4 angles are formed. Their sum is 360 degrees
2r

25. When 2 lines are perpendicular to each other - their intersection forms 4 angles. What degree are these 4 angles?
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
90 degrees each.
Arrangements - orders - schedules - or lists.
The # falling in the center of an ordered data set

26. Explain how to solve for 7/¼
A 90-degree angle.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
This equals 7 ÷¼ - or 7/1 ÷ 1/4 = 7/1 * 4/1 = 28/1 = 28

27. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Probability A + Probability B
80%
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'.
1. Given event A: A + notA = 1.

28. For a bell curve - what three terms might be used to describe the number in the middle?
1/x^n For example - 6-² = 1/6² = 1/36
For RIGHT triangles only: c² = a² + b² 'c' is the length of the hypotenuse; 'a' and 'b' are the other two sides ('legs')
'Big' angles and 'Small' angles.
The average - mean - median - or mode.

29. What is the 'Third side' rule for triangles?
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'.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
'Big' angles and 'Small' angles.

30. HIGH: What is the side ratio for a 30:60:90 triangle?
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
(x+y)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

31. 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.
A=pr²
V32 = v16*2. We can take the square root of 16 and move it outside the square root symbol - = 4v2.
Probability A + Probability B

32. HIGH: How do you calculate the circumference of a circle?
3:4:5 5:12:13
Not reading the problems carefully enough!
Turn the second fraction upside down (find its reciprocal) and multiply. Example: 2/3 ÷ 4/5 = 2/3 * 5/4
2pr -or- pd

33. Convert to a percentage: 3/5
60%
A=1/2bh. The height of the triangle must be measured by a line perpendicular to the base.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.

34. HIGH: What is the unfactored version of (x+y)² ?
2pr -or- pd
(0 -0)
x² + 2xy + y²
An integer is divisible by 8 if its last three digits form a number that'S divisible by 8. For example - 11 -640.

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

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

37. HIGH: how do you calculate a diagonal inside a 3-dimensional rectangular box?
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1.4

38. How do you solve a combination?

39. HIGH: List the two most common side ratios for right triangles
3:4:5 5:12:13
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 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.
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.

40. What is the name of a line that extends from the center of a circle to the edge of a circle?
An integer is divisible by 9 if the sum of its digits is divisible by 9.
A radius
(# of possible outcomes that satisfy the condition) ÷ (total # of possible outcomes)
A line is a 180-degree angle.

41. What is a 'Right' angle?
180 degrees.
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.
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
A 90-degree angle.

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

43. HIGH: What is the median?
Probability A * Probability B
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 # falling in the center of an ordered data set
A radius

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

45. HIGH: Describe how to deal with 2 sets of parentheses.
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)+
360 degrees
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.
1.4

46. HIGH: how do you calculate the surface area of a rectangular box?
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.
It will be a great advantage on test day to have your times table memorized from 1 through 15.
Not reading the problems carefully enough!

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

48. HIGH: What is the order of math operations - and the mnemonic to remember it?
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.
No. Never believe what you see - only what you read. GRE diagrams are often deliberately designed to be misleading or confusing.
ZONE-F numbers: Zero - One - Negatives - Extreme values - Fractions
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

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

50. List all the prime numbers that are less than 30:
2 -3 -5 -7 -11 -13 -17 -19 -23 -29. Note that 0 and 1 are not prime numbers.
The average - mean - median - or mode.
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.
Using a simple '3' is usually close enough. Just remember that p is slightly more than 3 - if a comparison is called for.