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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 formula for the surface area of a cube?
A = (1/2)bh.
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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = 6(l^2)

2. How do you find the length of an arc of a circle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
V = lwh
Arc = (x°/360)(2pr) where x is the central angle.
M = (y2 - y1)/(x2 - x1)

3. What is the sum of the measures of the four angles in a quadrilateral?
B^m/b^n = b^m-n
M = (y2 - y1)/(x2 - x1)
In the expression x^b - x is the base and b is the exponent.
360°

4. What is a multiple of an integer?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

5. Properties of zero 3
C = p2r
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

6. What is a negative exponent?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number n: x^-n means 1/x^n.
C = p2r
Write the percent as a decimal - and multiply.

7. What is the formula for the area of a triangle?
A = (1/2)bh.
Then the quotient y/x is a constant.
Their sum is 90°.
For any right triangle - a^2 + b^2 = c^2.

8. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
In the expression x^b - x is the base and b is the exponent.
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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

9. What is the sum of the measures of the n angles of a polygon with n sides?
For any integer n: 1^n = 1.
1 is a divisor (or factor) of every integer.
(n - 2)(180°)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

10. What are similar triangles?
Even numbers are divisible by 2 and odd numbers are not.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = pr^2h

11. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
A = 6(l^2)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

12. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any integer n: 1^n = 1.
All positive and negative whole numbers - and zero.
Then the quotient y/x is a constant.

13. What is the volume of a cube?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
C = p2r
V = l^3

14. What is the graph of a function?
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.
Their sum is 90°.
The set of all ordered pairs (x -y) such that y = f(x).
No matter how many angles there are - the sum around the point is 360°.

15. What is the square root of a number?
A fraction whose denominator is 100 i.e. 17% = 17/100
(Circumference/diameter) of a circle - or approximately 3.14.
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)

16. If the product of two or more numbers is 0 - what do you know about the numbers?
An equation that states that two ratios are equivalent. 4/6 = 10/15
At least one of the factors is 0.
The set of all ordered pairs (x -y) such that y = f(x).
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

17. How do you calculate a weighted average?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
No matter how many angles there are - the sum around the point is 360°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
For any integer n: 1^n = 1.

18. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
180°. If two or more angles form a straight angle - their sum is 180°.
V = pr^2h
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

19. What is a Venn diagram?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted up 2 units.
0 is the only number that is neither positive nor negative.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

20. What is the probability of an event that cannot occur? That must occur?
Equal slopes.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Cannot is 0 - must is 1 - all others are in between.
Corresponding sides of similar triangles are in proportion.

21. What is true about the measures of the two acute angles in a right triangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 90°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted down 2 units.

22. Properties of zero 2
360°
Write the percent over 100 and reduce.
180°. If two or more angles form a straight angle - their sum is 180°.
If a is negative and b is positive - then a < 0 < b.

23. 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°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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°.

24. For what values of a function is the function undefined?
Area = (x°/360)(pr^2) where x is the central angle.
No matter how many angles there are - the sum around the point is 360°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

25. What is the sum of the measures of all angles around a point?
At least one of the factors is 0.
The ratio of corresponding sides of similar triangles.
The product of their slopes is -1 (negative reciprocal).
No matter how many angles there are - the sum around the point is 360°.

26. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
A = 6(l^2)
If a is negative and b is positive - then a < 0 < b.
(b^m)^n = b^mn

27. Important binomial 3
V = pr^2h
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Divide - then multiply by 100.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

28. How do you calculate percent increases and decreases?
0 is the only number that is neither positive nor negative.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

29. What is the ratio of similitude?
Shifted down 2 units.
B^m*b^n = b^m+n
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The ratio of corresponding sides of similar triangles.

30. What is an exponent?
(n - 2)(180°)
In the expression x^b - x is the base and b is the exponent.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is 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°.

31. What is a function?
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = bh
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

32. What is the formula for the area of a rectangle?
A = lw
Then the product xy is a constant.
M = (y2 - y1)/(x2 - x1)
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

33. What are the properties of a parallelogram?
Then the product xy is a constant.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

34. What is a composite number?
(x + y)(x - y) = x^2 - y^2
Corresponding sides of similar triangles are in proportion.
An integer greater than one that is not prime.
Set y = 0 - and solve.

35. What is the formula for the volume of a rectangular solid?
0 is a multiple of every integer.
V = lwh
Shifted down 2 units.
A = 6(l^2)

36. Law of exponents 1
A = 6(l^2)
B^m*b^n = b^m+n
A = pr^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

37. Properties of zero 5
Set x = 0 - and solve.
Then the product xy is a constant.
For any number b: b = -b if and only if b = 0.
The two pairs of opposite angles formed are equal to each other.

38. What is the area of a square?
Equal slopes.
V = l^3
A = s^2 or A =d^2/2 where d is the diagonal
(Circumference/diameter) of a circle - or approximately 3.14.

39. Properties of one 1
Avg = sum of n numbers/n
For any number a: a * 1 = a and a / 1 = a.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
1 is the smallest positive odd integer.

40. 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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.

41. What is an exterior angle of a polygon?
Is a right triangle with a ratio of sides x:xv3:2x.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An angle formed by extending the side of the polygon.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

42. What does it mean if y is directly proportional to x?
In the expression x^b - x is the base and b is the exponent.
Then the quotient y/x is a constant.
Corresponding sides of similar triangles are in proportion.
Even numbers are divisible by 2 and odd numbers are not.

43. How do you find the slope of a line?
Shifted down 2 units.
M = (y2 - y1)/(x2 - x1)
Write the percent over 100 and reduce.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

44. What is the formula for the surface area of a rectangular solid?
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 = 2(lw + lh + hw)
If a is negative and b is positive - then a < 0 < b.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

45. Law of exponents 3
1 is a divisor (or factor) of every integer.
(b^m)^n = b^mn
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Area = (x°/360)(pr^2) where x is the central angle.

46. What are the properties of a square?
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.
The two pairs of opposite angles formed are equal to each other.
Shifted up 2 units.
0 is the only number that is neither positive nor negative.

47. What is a proportion?
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any integer n: 1^n = 1.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

48. Properties of zero 4
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
No matter how many angles there are - the sum around the point is 360°.

49. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
For any number n: x^-n means 1/x^n.
An equation that states that two ratios are equivalent. 4/6 = 10/15
At least one of the factors is 0.
Shifted down 2 units.

50. In a circle of radius r - what is the formula for the area?
A = pr^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^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.
(n - 2)(180°)