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GRE Math: Facts

Subjects : gre, math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Then the quotient y/x is a constant.
A = 6(l^2)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

2. What is the formula for the area of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
They are both the same. A divisor or factor of an integer leaves no remainder.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = bh

3. Important binomial 1
(Circumference/diameter) of a circle - or approximately 3.14.
(n - 2)(180°)
(x + y)(x - y) = x^2 - y^2
At least one of the factors is 0.

4. Law of exponents 5
V = lwh
0 is the only number that is neither positive nor negative.
A^m/b^m = (a/b)^m
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

5. What is a Venn diagram?
Then the product xy is a constant.
(Circumference/diameter) of a circle - or approximately 3.14.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The set of all ordered pairs (x -y) such that y = f(x).

6. If the product of two or more numbers is 0 - what do you know about the numbers?
Corresponding sides of similar triangles are in proportion.
The product of their slopes is -1 (negative reciprocal).
At least one of the factors is 0.
For any number a: a * 1 = a and a / 1 = a.

7. How do you calculate percent increases and decreases?
Avg = sum of n numbers/n
A = 6(l^2)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number a: a * 1 = a and a / 1 = a.

8. What formula is used for an average?
Avg = sum of n numbers/n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

9. Properties of zero 1
A = lw
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 number a: a * 1 = a and a / 1 = a.
0 is the only number that is neither positive nor negative.

10. What is a percent?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The set of all ordered pairs (x -y) such that y = f(x).
A fraction whose denominator is 100 i.e. 17% = 17/100
For any integer n: 1^n = 1.

11. What is the formula for the volume of a cylinder?
(x + y)(x - y) = x^2 - y^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.
V = pr^2h

12. In a circle of radius r - what is the formula for the diameter?
For any number b: b = -b if and only if b = 0.
D = 2r
Their sum is 90°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

13. What is the measure of a straight angle?
Set x = 0 - and solve.
180°. If two or more angles form a straight angle - their sum is 180°.
0 is a multiple of every integer.
1 is the smallest positive odd integer.

14. What is the sum of the measures of the n angles of a polygon with n sides?
A = pr^2
(n - 2)(180°)
A = 2(lw + lh + hw)
1 is a divisor (or factor) of every integer.

15. What is a ratio?

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16. For what values of a function is the function undefined?
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°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

17. In a circle of radius r - what is the formula for the area?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = pr^2
A = 6(l^2)

18. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
M = (y2 - y1)/(x2 - x1)

19. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
C = p2r
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.
M = (y2 - y1)/(x2 - x1)

20. What are the quotient and the remainder?

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21. What are similar triangles?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
They are both the same. A divisor or factor of an integer leaves no remainder.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If a is negative and b is positive - then a < 0 < b.

22. What is a composite number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
M = (y2 - y1)/(x2 - x1)
An integer greater than one that is not prime.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

23. Properties of zero 3
0 is a multiple of every integer.
No matter how many angles there are - the sum around the point is 360°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

24. How do we write the equation of a line?
They are both the same. A divisor or factor of an integer leaves no remainder.
(Circumference/diameter) of a circle - or approximately 3.14.
Arc = (x°/360)(2pr) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

25. Important binomial 3
A = [(s^2*v3)/4]
An angle formed by extending the side of the polygon.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
360°

26. What is the formula for the area of a triangle?
Shifted left 2 units.
An angle formed by extending the side of the polygon.
A = (1/2)bh.
V = lwh

27. What is the formula for the volume of a rectangular solid?
V = lwh
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
They are both the same. A divisor or factor of an integer leaves no remainder.
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.

28. Properties of zero 5
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted down 2 units.
Arc = (x°/360)(2pr) where x is the central angle.
For any number b: b = -b if and only if b = 0.

29. How do you find the probability that an event will occur?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Then the quotient y/x is a constant.

30. What is true about the areas of similar triangles?
B^m/b^n = b^m-n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
V = lwh
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

31. What is the formula for the surface area of a cube?
Then the quotient y/x is a constant.
A = lw
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = 6(l^2)

32. What is the graph of a function?
Then the product xy is a constant.
The set of all ordered pairs (x -y) such that y = f(x).
[(x1 + x2)/2] -[(y1 + y2)/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.

33. What is the midpoint formula?
Then the product xy is a constant.
[(x1 + x2)/2] -[(y1 + y2)/2]
D = 2r
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.

34. What does it mean if y is directly proportional to x?
(Circumference/diameter) of a circle - or approximately 3.14.
A = 6(l^2)
A = [(s^2*v3)/4]
Then the quotient y/x is a constant.

35. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted left 2 units.

36. How do you find the y-intercept of a graph?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
M = (y2 - y1)/(x2 - x1)
Then the product xy is a constant.
Set x = 0 - and solve.

37. In a circle of radius r - what is the formula for the circumference?
For any number a: a * 1 = a and a / 1 = a.
Set x = 0 - and solve.
C = p2r
For any number b: b = -b if and only if b = 0.

38. What are the properties of a rectangle?
A = lw
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m/b^m = (a/b)^m
Cannot is 0 - must is 1 - all others are in between.

39. What is true about the measures of the four angles formed by two intersecting lines?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The two pairs of opposite angles formed are equal to each other.
360°
Set y = 0 - and solve.

40. What is an exterior angle of a polygon?
At least one of the factors is 0.
Shifted left 2 units.
An angle formed by extending the side of the polygon.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

41. What is the formula for the area of a rectangle?
360°
0 is a multiple of every integer.
Their sum is 180°.
A = lw

42. What are the important properties of 30-60-90 triangle?
Avg = sum of n numbers/n
Is a right triangle with a ratio of sides x:xv3:2x.
They are both the same. A divisor or factor of an integer leaves no remainder.
All positive and negative whole numbers - and zero.

43. What is true about the measures of the two acute angles in a right triangle?
A = bh
Their sum is 90°.
A = s^2 or A =d^2/2 where d is the diagonal
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

44. Properties of one 2
In the expression x^b - x is the base and b is the exponent.
For any integer n: 1^n = 1.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
0 is a multiple of every integer.

45. How do you find a percent of a number?
A = s^2 or A =d^2/2 where d is the diagonal
Write the percent as a decimal - and multiply.
Corresponding sides of similar triangles are in proportion.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

46. Properties of zero 4
D = 2r
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
1 is a divisor (or factor) of every integer.
A^m/b^m = (a/b)^m

47. What is the square root of a number?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m*b^n = b^m+n
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

48. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
A = [(s^2*v3)/4]
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

49. Properties of square roots
Area = (x°/360)(pr^2) where x is the central angle.
An integer greater than one that is not prime.
Their sum is 180°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

50. Properties of one 4
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°.
1 is the smallest positive odd integer.
V = l^3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

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