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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 the formula for the volume of a cylinder?
V = l^3
M = (y2 - y1)/(x2 - x1)
V = pr^2h
For any right triangle - a^2 + b^2 = c^2.

2. What is a ratio?

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3. What do we mean by the slope of the line?
Arc = (x°/360)(2pr) where x is the central angle.
Their sum is 90°.
Set y = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.

4. How do you find the probability that an event will occur?
A^m*b^m = (ab)^m
In the expression x^b - x is the base and b is the exponent.
0 is a multiple of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

5. Important binomial 1
360°
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Equal slopes.
(x + y)(x - y) = x^2 - y^2

6. Properties of zero 5
At least one of the factors is 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
C = p2r
For any number b: b = -b if and only if b = 0.

7. What is true about the slopes of perpendicular lines?
(x + y)(x - y) = x^2 - y^2
The product of their slopes is -1 (negative reciprocal).
In the expression x^b - x is the base and b is the exponent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

8. In a circle of radius r - what is the formula for the area?
A = pr^2
The ratio of corresponding sides of similar triangles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

9. Properties of zero 3
Even numbers are divisible by 2 and odd numbers are not.
Shifted right 2 units.
0 is a multiple of every integer.
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.

10. How do you convert a percent to a fraction or a decimal?
For any number n: x^-n means 1/x^n.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Is a right triangle with a ratio of sides x:xv3:2x.
Write the percent over 100 and reduce.

11. What is an exterior angle of a polygon?
V = pr^2h
An angle formed by extending the side of the polygon.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

12. If the product of two or more numbers is 0 - what do you know about the numbers?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
At least one of the factors is 0.
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.

13. What is a percent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m
A = (1/2)bh.

14. What is a composite number?
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.
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.

15. What is true about the measures of the four angles formed by two intersecting lines?
A = lw
A = 6(l^2)
The two pairs of opposite angles formed are equal to each other.
B^m*b^n = b^m+n

16. How you convert a fraction or a decimal to a percent?
The two pairs of opposite angles formed are equal to each other.
Divide - then multiply by 100.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

17. What is true about the areas of similar triangles?
1 is a divisor (or factor) of every integer.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Cannot is 0 - must is 1 - all others are in between.
If a is negative and b is positive - then a < 0 < b.

18. What is the sum of the measures of all angles around a point?
1 is a divisor (or factor) of every integer.
No matter how many angles there are - the sum around the point is 360°.
0 is the only number that is neither positive nor negative.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

19. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
180°. If two or more angles form a straight angle - their sum is 180°.
For any number a: a * 1 = a and a / 1 = a.
B^m*b^n = b^m+n

20. What is the Pythagorean theorem?
Corresponding sides of similar triangles are in proportion.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any right triangle - a^2 + b^2 = c^2.

21. What is a multiple of an integer?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An angle formed by extending the side of the polygon.

22. What are the properties of a parallelogram?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Cannot is 0 - must is 1 - all others are in between.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = pr^2h

23. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set y = 0 - and solve.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

24. What is the distributive law?
The ratio of corresponding sides of similar triangles.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
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.

25. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
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.
Shifted right 2 units.
Their sum is 180°.
180°. If two or more angles form a straight angle - their sum is 180°.

26. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
Shifted left 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = 6(l^2)

27. What are the properties of a rectangle?
An angle formed by extending the side of the polygon.
A = s^2 or A =d^2/2 where d is the diagonal
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
0 is a multiple of every integer.

28. Properties of one 1
The ratio of corresponding sides of similar triangles.
For any number a: a * 1 = a and a / 1 = a.
[(x1 + x2)/2] -[(y1 + y2)/2]
(n - 2)(180°)

29. What is the measure of a straight angle?
A = (1/2)bh.
180°. If two or more angles form a straight angle - their sum is 180°.
Even numbers are divisible by 2 and odd numbers are not.
Divide - then multiply by 100.

30. What is true about the slopes of parallel lines?
In the expression x^b - x is the base and b is the exponent.
Equal slopes.
A = s^2 or A =d^2/2 where d is the diagonal
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

31. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m/b^n = b^m-n
360°
Set y = 0 - and solve.

32. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted down 2 units.
A = pr^2
V = pr^2h

33. How do you calculate percent increases and decreases?
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.
For any number n: x^-n means 1/x^n.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A^m*b^m = (ab)^m

34. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Shifted up 2 units.
B^m*b^n = b^m+n
180°. If two or more angles form a straight angle - their sum is 180°.

35. How do you find the x-intercept of a graph?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Even numbers are divisible by 2 and odd numbers are not.
Set y = 0 - and solve.
A = bh

36. What is the distance formula?
The product of their slopes is -1 (negative reciprocal).
(Circumference/diameter) of a circle - or approximately 3.14.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any right triangle - a^2 + b^2 = c^2.

37. What is the sum of the measures of the four angles in a quadrilateral?
Write the percent as a decimal - and multiply.
A^m/b^m = (a/b)^m
360°
Their sum is 180°.

38. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
[(x1 + x2)/2] -[(y1 + y2)/2]

39. What are the quotient and the remainder?

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40. What is a divisor and a factor of an integer?
A^m/b^m = (a/b)^m
They are both the same. A divisor or factor of an integer leaves no remainder.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number n: x^-n means 1/x^n.

41. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
D = 2r
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The product of their slopes is -1 (negative reciprocal).

42. What is the volume of a cube?
For any right triangle - a^2 + b^2 = c^2.
Is a right triangle with a ratio of sides x:xv3:2x.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
V = l^3

43. How do we write the equation of a line?
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.
The product of their slopes is -1 (negative reciprocal).
1 is a divisor (or factor) of every integer.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

44. Properties of one 3
Shifted right 2 units.
1 is a divisor (or factor) of every integer.
At least one of the factors is 0.
Shifted left 2 units.

45. What is the formula for the area of a triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
A = (1/2)bh.
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 any number n: x^-n means 1/x^n.

46. Properties of one 2
Cannot is 0 - must is 1 - all others are in between.
For any integer n: 1^n = 1.
1 is a divisor (or factor) of every integer.
A = pr^2

47. What is the sum of the measures of the n angles of a polygon with n sides?
360°
(n - 2)(180°)
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.
A = s^2 or A =d^2/2 where d is the diagonal

48. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 180°.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

49. What are the important properties of a 45-45 - 90 triangle?
A^m*b^m = (ab)^m
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A fraction whose denominator is 100 i.e. 17% = 17/100
V = lwh

50. What important property do similar triangles have?
Shifted right 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Corresponding sides of similar triangles are in proportion.
They are both the same. A divisor or factor of an integer leaves no remainder.