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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 the graph of a function?
Is a right triangle with a ratio of sides x:xv3:2x.
The product of their slopes is -1 (negative reciprocal).
A = lw
The set of all ordered pairs (x -y) such that y = f(x).

2. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
0 is the only number that is neither positive nor negative.
360°
(x + y)(x - y) = x^2 - y^2
At least one of the factors is 0.

3. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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.
For any number n: x^-n means 1/x^n.

4. What is a ratio?

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5. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
V = l^3
1 is the smallest positive odd integer.
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.

6. 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.
V = l^3
An equation that states that two ratios are equivalent. 4/6 = 10/15
(n - 2)(180°)

7. Properties of one 4
In the expression x^b - x is the base and b is the exponent.
A = [(s^2*v3)/4]
The set of all ordered pairs (x -y) such that y = f(x).
1 is the smallest positive odd integer.

8. What is the formula for the area of a triangle?
Then the quotient y/x is a constant.
A = (1/2)bh.
Even numbers are divisible by 2 and odd numbers are not.
If a is negative and b is positive - then a < 0 < b.

9. What is the Pythagorean theorem?
180°. If two or more angles form a straight angle - their sum is 180°.
A fraction whose denominator is 100 i.e. 17% = 17/100
For any right triangle - a^2 + b^2 = c^2.
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.

10. What is a divisor and a factor of an integer?
A = bh
They are both the same. A divisor or factor of an integer leaves no remainder.
Even numbers are divisible by 2 and odd numbers are not.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

11. What important property do similar triangles have?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Corresponding sides of similar triangles are in proportion.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

12. What is a Venn diagram?
Shifted down 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If a is negative and b is positive - then a < 0 < b.
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.

13. What are the properties of a parallelogram?
For any number b: b = -b if and only if b = 0.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
360°
0 is a multiple of every integer.

14. What is an exponent?
A = 2(lw + lh + hw)
Even numbers are divisible by 2 and odd numbers are not.
A = 6(l^2)
In the expression x^b - x is the base and b is the exponent.

15. In a circle of radius r - what is the formula for the area?
For any number b: b = -b if and only if b = 0.
Their sum is 90°.
A = pr^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

16. What is true about the slopes of parallel lines?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
All positive and negative whole numbers - and zero.
An integer greater than one that is not prime.
Equal slopes.

17. What is the triangle inequality?
360°
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.
The ratio of corresponding sides of similar triangles.
M = (y2 - y1)/(x2 - x1)

18. What is an exterior angle of a triangle?
Cannot is 0 - must is 1 - all others are in between.
180°. If two or more angles form a straight angle - their sum is 180°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Equal slopes.

19. Law of exponents 1
For any integer n: 1^n = 1.
B^m*b^n = b^m+n
360°
An integer greater than one that is not prime.

20. What do we mean by the slope of the line?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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)
How steep the line is. Horizontal line = 0 - vertical has no slope.

21. What is a prime number?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Equal slopes.
The set of all ordered pairs (x -y) such that y = f(x).
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.

22. What is the volume of a cube?
A fraction whose denominator is 100 i.e. 17% = 17/100
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Equal slopes.
V = l^3

23. What is the distance formula?
Is a right triangle with a ratio of sides x:xv3:2x.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted down 2 units.
V = lwh

24. Properties of zero 1
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.
0 is the only number that is neither positive nor negative.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted down 2 units.

25. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
1 is a divisor (or factor) of every integer.
V = l^3
Divide - then multiply by 100.

26. Law of exponents 3
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(b^m)^n = b^mn
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

27. What is the distributive law?
(n - 2)(180°)
Equal slopes.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

28. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
0 is the only number that is neither positive nor negative.
V = l^3
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

29. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
In the expression x^b - x is the base and b is the exponent.
No matter how many angles there are - the sum around the point is 360°.
Shifted down 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

30. What is the measure of a straight angle?
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
They are both the same. A divisor or factor of an integer leaves no remainder.
180°. If two or more angles form a straight angle - their sum is 180°.

31. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
If a is negative and b is positive - then a < 0 < b.
Corresponding sides of similar triangles are in proportion.
A = 2(lw + lh + hw)

32. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
An angle formed by extending the side of the polygon.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Avg = sum of n numbers/n
Shifted up 2 units.

33. Properties of zero 3
Their sum is 180°.
Set x = 0 - and solve.
0 is a multiple of every integer.
The ratio of corresponding sides of similar triangles.

34. Properties of zero 4
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted down 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = 2(lw + lh + hw)

35. What is a proportion?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An equation that states that two ratios are equivalent. 4/6 = 10/15
All positive and negative whole numbers - and zero.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

36. What formula is used for an average?
Shifted left 2 units.
Avg = sum of n numbers/n
(Circumference/diameter) of a circle - or approximately 3.14.
0 is the only number that is neither positive nor negative.

37. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
A^m*b^m = (ab)^m

38. What is a negative exponent?
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 = l^3
For any number n: x^-n means 1/x^n.
All positive and negative whole numbers - and zero.

39. In a circle of radius r - what is the formula for the diameter?
360°
D = 2r
Even numbers are divisible by 2 and odd numbers are not.
B^m/b^n = b^m-n

40. What is true about the areas of similar triangles?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A fraction whose denominator is 100 i.e. 17% = 17/100
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

41. What is an integer?
M = (y2 - y1)/(x2 - x1)
A = 2(lw + lh + hw)
360°
All positive and negative whole numbers - and zero.

42. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
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.
If a is negative and b is positive - then a < 0 < b.
For any number n: x^-n means 1/x^n.

43. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
They are both the same. A divisor or factor of an integer leaves no remainder.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted up 2 units.

44. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted down 2 units.
A = bh
D = 2r

45. What does it mean if y is directly proportional to x?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Divide - then multiply by 100.
A = s^2 or A =d^2/2 where d is the diagonal
Then the quotient y/x is a constant.

46. What is the formula for the area of a rectangle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = lw
An angle formed by extending the side of the polygon.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

47. What are the properties of a rectangle?
Cannot is 0 - must is 1 - all others are in between.
A^m*b^m = (ab)^m
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = 2(lw + lh + hw)

48. Properties of zero 2
A = s^2 or A =d^2/2 where d is the diagonal
Is a right triangle with a ratio of sides x:xv3:2x.
C = p2r
If a is negative and b is positive - then a < 0 < b.

49. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
For any integer n: 1^n = 1.
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°.
180°. If two or more angles form a straight angle - their sum is 180°.
(x + y)(x - y) = x^2 - y^2

50. Important binomial 2
A = s^2 or A =d^2/2 where d is the diagonal
Set x = 0 - and solve.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The set of all ordered pairs (x -y) such that y = f(x).