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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. In a circle of radius r - what is the formula for the area?
A = pr^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Cannot is 0 - must is 1 - all others are in between.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

2. What does it mean if y is directly proportional to x?
A = [(s^2*v3)/4]
Then the quotient y/x is a constant.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

3. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
At least one of the factors is 0.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = pr^2

4. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
The set of all ordered pairs (x -y) such that y = f(x).
(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.

5. What is the formula for the surface area of a cube?
Shifted left 2 units.
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.
No matter how many angles there are - the sum around the point is 360°.
A = 6(l^2)

6. What is a percent?
Their sum is 90°.
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
A fraction whose denominator is 100 i.e. 17% = 17/100

7. What is the triangle inequality?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Shifted left 2 units.
Shifted down 2 units.
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.

8. What is a ratio?

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9. How do you calculate percent increases and decreases?
If a is negative and b is positive - then a < 0 < b.
V = l^3
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

10. What is a negative exponent?
For any right triangle - a^2 + b^2 = c^2.
For any number n: x^-n means 1/x^n.
1 is the smallest positive odd integer.
1 is a divisor (or factor) of every integer.

11. How do you convert a percent to a fraction or a decimal?
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted down 2 units.
Write the percent over 100 and reduce.
Set y = 0 - and solve.

12. How do you find the probability that an event will occur?
Shifted down 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Is a right triangle with a ratio of sides x:xv3:2x.
How steep the line is. Horizontal line = 0 - vertical has no slope.

13. What important property do similar triangles have?
Then the quotient y/x is a constant.
For any right triangle - a^2 + b^2 = c^2.
V = lwh
Corresponding sides of similar triangles are in proportion.

14. What is the formula for the volume of a rectangular solid?
(Circumference/diameter) of a circle - or approximately 3.14.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
V = lwh
They are both the same. A divisor or factor of an integer leaves no remainder.

15. What are the properties of a rectangle?
360°
The two pairs of opposite angles formed are equal to each other.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(b^m)^n = b^mn

16. What is true about the slopes of parallel lines?
Arc = (x°/360)(2pr) where x is the central angle.
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.
Their sum is 90°.
Equal slopes.

17. Properties of one 1
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number a: a * 1 = a and a / 1 = a.
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).

18. What is an even and an odd number?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Even numbers are divisible by 2 and odd numbers are not.
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.

19. Properties of zero 5
B^m*b^n = b^m+n
For any number b: b = -b if and only if b = 0.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
360°

20. What is p?
Cannot is 0 - must is 1 - all others are in between.
(Circumference/diameter) of a circle - or approximately 3.14.
(n - 2)(180°)
An equation that states that two ratios are equivalent. 4/6 = 10/15

21. What is the distance formula?
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.
1 is a divisor (or factor) of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Shifted left 2 units.

22. What are the sum - difference - products - and quotient of two numbers?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

23. Important binomial 1
(x + y)(x - y) = x^2 - y^2
Arc = (x°/360)(2pr) where x is the central angle.
Cannot is 0 - must is 1 - all others are in between.
They are both the same. A divisor or factor of an integer leaves no remainder.

24. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
For any integer n: 1^n = 1.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted right 2 units.
(x + y)(x - y) = x^2 - y^2

25. Important binomial 3
In the expression x^b - x is the base and b is the exponent.
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = l^3

26. What is the ratio of similitude?
Corresponding sides of similar triangles are in proportion.
The ratio of corresponding sides of similar triangles.
A = s^2 or A =d^2/2 where d is the diagonal
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

27. Law of exponents 4
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A^m*b^m = (ab)^m
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

28. In a circle of radius r - what is the formula for the diameter?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
D = 2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(Circumference/diameter) of a circle - or approximately 3.14.

29. 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.
C = p2r
D = 2r
Equal slopes.

30. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Equal slopes.
All positive and negative whole numbers - and zero.
360°

31. What is the measure of a straight angle?
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.
0 is a multiple of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

32. Properties of one 2
For any integer n: 1^n = 1.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Is a right triangle with a ratio of sides x:xv3:2x.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

33. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = pr^2
Shifted right 2 units.
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°.
(b^m)^n = b^mn

34. What is the volume of a cube?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(b^m)^n = b^mn
Equal slopes.
V = l^3

35. What is a Venn diagram?
360°
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
B^m/b^n = b^m-n
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

36. What is a multiple of an integer?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
In the expression x^b - x is the base and b is the exponent.
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.
Their sum is 180°.

37. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = s^2 or A =d^2/2 where d is the diagonal
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.

38. 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.
B^m/b^n = b^m-n
1 is the smallest positive odd integer.
Avg = sum of n numbers/n

39. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
180°. If two or more angles form a straight angle - their sum is 180°.
C = p2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

40. Properties of zero 3
Area = (x°/360)(pr^2) where x is the central angle.
0 is a multiple of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

41. Law of exponents 2
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.
B^m/b^n = b^m-n
Shifted right 2 units.

42. What is the sum of the measures of the n angles of a polygon with n sides?
A = s^2 or A =d^2/2 where d is the diagonal
(n - 2)(180°)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
1 is a divisor (or factor) of every integer.

43. 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.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Even numbers are divisible by 2 and odd numbers are not.

44. Properties of one 4
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.
1 is the smallest positive odd integer.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

45. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
0 is a multiple of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A fraction whose denominator is 100 i.e. 17% = 17/100

46. 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.
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).

47. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 180°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Avg = sum of n numbers/n

48. What is an exterior angle of a polygon?
The two pairs of opposite angles formed are equal to each other.
(n - 2)(180°)
Write the percent over 100 and reduce.
An angle formed by extending the side of the polygon.

49. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
How steep the line is. Horizontal line = 0 - vertical has no slope.
(Circumference/diameter) of a circle - or approximately 3.14.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Shifted up 2 units.

50. What is an integer?
All positive and negative whole numbers - and zero.
Arc = (x°/360)(2pr) where x is the central angle.
For any number a: a * 1 = a and a / 1 = a.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]