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GRE Math: Facts

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. What is p?
A = bh
(Circumference/diameter) of a circle - or approximately 3.14.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = [(s^2*v3)/4]

2. What is a prime number?
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

3. What is a divisor and a factor of an integer?
Their sum is 180°.
Area = (x°/360)(pr^2) where x is the central angle.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
They are both the same. A divisor or factor of an integer leaves no remainder.

4. Law of exponents 2
B^m/b^n = b^m-n
(x + y)(x - y) = x^2 - y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any integer n: 1^n = 1.

5. What are the properties of a rectangle?
A = 6(l^2)
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

6. What is the formula for the volume of a rectangular solid?
V = lwh
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
D = 2r
1 is the smallest positive odd integer.

7. What important property do similar triangles have?
Shifted down 2 units.
Cannot is 0 - must is 1 - all others are in between.
Corresponding sides of similar triangles are in proportion.
They are both the same. A divisor or factor of an integer leaves no remainder.

8. What is true about the areas of similar triangles?
Write the percent over 100 and reduce.
Set x = 0 - and solve.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
V = lwh

9. What formula is used for an average?
For any number b: b = -b if and only if b = 0.
Shifted left 2 units.
The product of their slopes is -1 (negative reciprocal).
Avg = sum of n numbers/n

10. What is an even and an odd number?
Write the percent as a decimal - and multiply.
0 is the only number that is neither positive nor negative.
Then the quotient y/x is a constant.
Even numbers are divisible by 2 and odd numbers are not.

11. Important binomial 3
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

12. Properties of zero 1
Their sum is 90°.
A = lw
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
0 is the only number that is neither positive nor negative.

13. What is a negative exponent?
A^m/b^m = (a/b)^m
Write the percent as a decimal - and multiply.
For any number n: x^-n means 1/x^n.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.

14. What is a percent?
M = (y2 - y1)/(x2 - x1)
Arc = (x°/360)(2pr) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A fraction whose denominator is 100 i.e. 17% = 17/100

15. What is the triangle inequality?
Set x = 0 - and solve.
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
No matter how many angles there are - the sum around the point is 360°.
(Circumference/diameter) of a circle - or approximately 3.14.

16. What is the graph of a function?
(x + y)(x - y) = x^2 - y^2
0 is the only number that is neither positive nor negative.
The set of all ordered pairs (x -y) such that y = f(x).
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.

17. Properties of square roots
V = pr^2h
Shifted left 2 units.
Avg = sum of n numbers/n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

18. What is a fractional exponent?
V = pr^2h
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

19. What is true about the measures of the three angles in a triangle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Their sum is 180°.
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
A^m/b^m = (a/b)^m

20. How do we write the equation of a line?
Equal slopes.
M = (y2 - y1)/(x2 - x1)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted down 2 units.

21. What is the sum of the measures of the n angles of a polygon with n sides?
Their sum is 90°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(n - 2)(180°)
V = l^3

22. What is the formula for the volume of a cylinder?
A = (1/2)bh.
V = pr^2h
(b^m)^n = b^mn
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

23. Law of exponents 5
Corresponding sides of similar triangles are in proportion.
For any number b: b = -b if and only if b = 0.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A^m/b^m = (a/b)^m

24. What is the formula for the area of a parallelogram?
A = bh
In the expression x^b - x is the base and b is the exponent.
If a is negative and b is positive - then a < 0 < b.
Then the product xy is a constant.

25. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted left 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
No matter how many angles there are - the sum around the point is 360°.

26. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The set of all ordered pairs (x -y) such that y = f(x).
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
V = pr^2h

27. What is the formula for the area of a triangle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Is a right triangle with a ratio of sides x:xv3:2x.
The product of their slopes is -1 (negative reciprocal).
A = (1/2)bh.

28. What is an exterior angle of a triangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The ratio of corresponding sides of similar triangles.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
V = pr^2h

29. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted up 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.

30. Properties of zero 3
0 is a multiple of every integer.
The product of their slopes is -1 (negative reciprocal).
Then the product xy is a constant.
The two pairs of opposite angles formed are equal to each other.

31. In a circle of radius r - what is the formula for the area?
A = (1/2)bh.
At least one of the factors is 0.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = pr^2

32. Law of exponents 4
A^m*b^m = (ab)^m
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Their sum is 180°.
D = 2r

33. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = lw

34. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
A^m*b^m = (ab)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
360°

35. If the product of two or more numbers is 0 - what do you know about the numbers?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The set of all ordered pairs (x -y) such that y = f(x).
At least one of the factors is 0.
Set y = 0 - and solve.

36. In a circle of radius r - what is the formula for the circumference?
0 is a multiple of every integer.
C = p2r
Shifted up 2 units.
An angle formed by extending the side of the polygon.

37. What is the midpoint formula?
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
How steep the line is. Horizontal line = 0 - vertical has no slope.
[(x1 + x2)/2] -[(y1 + y2)/2]
Area = (x°/360)(pr^2) where x is the central angle.

38. What are the quotient and the remainder?

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39. Properties of one 4
A = s^2 or A =d^2/2 where d is the diagonal
1 is the smallest positive odd integer.
A = lw
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

40. What is a Venn diagram?
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A^m*b^m = (ab)^m

41. What is a ratio?

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42. How do you find the probability that an event will occur?
A fraction whose denominator is 100 i.e. 17% = 17/100
Set y = 0 - and solve.
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

43. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
V = l^3
360°
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

44. What is an exterior angle of a polygon?
For any right triangle - a^2 + b^2 = c^2.
[(x1 + x2)/2] -[(y1 + y2)/2]
An angle formed by extending the side of the polygon.
180°. If two or more angles form a straight angle - their sum is 180°.

45. How do you find the area of a sector of a circle?
V = lwh
Area = (x°/360)(pr^2) where x is the central angle.
A = pr^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

46. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
No matter how many angles there are - the sum around the point is 360°.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

47. Properties of one 2
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the quotient y/x is a constant.
For any integer n: 1^n = 1.

48. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
For any integer n: 1^n = 1.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

49. Important binomial 1
For any number n: x^-n means 1/x^n.
(x + y)(x - y) = x^2 - y^2
1 is a divisor (or factor) of every integer.
All positive and negative whole numbers - and zero.

50. Law of exponents 3
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
(b^m)^n = b^mn
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.