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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. Properties of one 4
Arc = (x°/360)(2pr) where x is the central angle.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
1 is the smallest positive odd integer.
An angle formed by extending the side of the polygon.

2. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Shifted left 2 units.
360°
A = bh
1 is a divisor (or factor) of every integer.

3. In a circle of radius r - what is the formula for the diameter?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
1 is the smallest positive odd integer.
D = 2r
A = 6(l^2)

4. Law of exponents 1
Then the quotient y/x is a constant.
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.
B^m*b^n = b^m+n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

5. How do you find the x-intercept of a graph?
All positive and negative whole numbers - and zero.
Set y = 0 - and solve.
M = (y2 - y1)/(x2 - x1)
C = p2r

6. For what values of a function is the function undefined?
For any right triangle - a^2 + b^2 = c^2.
A = bh
[(x1 + x2)/2] -[(y1 + y2)/2]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

7. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
180°. If two or more angles form a straight angle - their sum is 180°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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°.

8. What is true about the measures of the three angles in a triangle?
(b^m)^n = b^mn
M = (y2 - y1)/(x2 - x1)
Their sum is 90°.
Their sum is 180°.

9. What is the relationship between a radius of a circle and a line that is tangent to the circle?
For any number n: x^-n means 1/x^n.
0 is a multiple of every integer.
C = p2r
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

10. What are the quotient and the remainder?

11. What is the volume of a cube?
V = l^3
An integer greater than one that is not prime.
If a is negative and b is positive - then a < 0 < b.
A fraction whose denominator is 100 i.e. 17% = 17/100

12. How do you find the probability that an event will occur?
1 is a divisor (or factor) of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Avg = sum of n numbers/n
Then the quotient y/x is a constant.

13. What is the triangle inequality?
The ratio of corresponding sides of similar triangles.
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.
A = lw
B^m*b^n = b^m+n

14. How do you find the y-intercept of a graph?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Set x = 0 - and solve.
Arc = (x°/360)(2pr) where x is the central angle.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

15. In a circle of radius r - what is the formula for the area?
Shifted down 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = pr^2
Write the percent over 100 and reduce.

16. What is the distributive law?
The ratio of corresponding sides of similar triangles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Arc = (x°/360)(2pr) where x is the central angle.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

17. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
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.
B^m/b^n = b^m-n
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.

18. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted right 2 units.

19. What formula is used for an average?
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n
(Circumference/diameter) of a circle - or approximately 3.14.
An integer greater than one that is not prime.

20. How do you convert a percent to a fraction or a decimal?
Divide - then multiply by 100.
B^m/b^n = b^m-n
Write the percent over 100 and reduce.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

21. How do you find the length of an arc of a circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Arc = (x°/360)(2pr) where x is the central angle.
Divide - then multiply by 100.
They are both the same. A divisor or factor of an integer leaves no remainder.

22. Important binomial 1
(x + y)(x - y) = x^2 - y^2
1 is a divisor (or factor) of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Their sum is 180°.

23. What is the formula for the surface area of a cube?
A = 6(l^2)
1 is the smallest positive odd integer.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted right 2 units.

24. What is a function?
B^m/b^n = b^m-n
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
V = l^3
Cannot is 0 - must is 1 - all others are in between.

25. 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.
Shifted down 2 units.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Even numbers are divisible by 2 and odd numbers are not.

26. What are the properties of a rectangle?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = pr^2h
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.

27. What is the area of a square?
Their sum is 180°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = s^2 or A =d^2/2 where d is the diagonal
360°

28. Law of exponents 3
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.
(b^m)^n = b^mn
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

29. What does it mean if y is directly proportional to x?
All positive and negative whole numbers - and zero.
Then the quotient y/x is a constant.
Set x = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

30. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.
Area = (x°/360)(pr^2) where x is the central angle.

31. Properties of zero 5
Write the percent as a decimal - and multiply.
Area = (x°/360)(pr^2) where x is the central angle.
1 is a divisor (or factor) of every integer.
For any number b: b = -b if and only if b = 0.

32. Law of exponents 2
In the expression x^b - x is the base and b is the exponent.
A = (1/2)bh.
B^m/b^n = b^m-n
V = l^3

33. What is a composite number?
An integer greater than one that is not prime.
Write the percent as a decimal - and multiply.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

34. What is the distance formula?
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = 6(l^2)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

35. Properties of zero 4
Divide - then multiply by 100.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Equal slopes.

36. Properties of square roots
Arc = (x°/360)(2pr) where x is the central angle.
For any right triangle - a^2 + b^2 = c^2.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
In the expression x^b - x is the base and b is the exponent.

37. What is true about the slopes of parallel lines?
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.
Equal slopes.
A = pr^2
(n - 2)(180°)

38. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
V = pr^2h
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
0 is the only number that is neither positive nor negative.

39. What is the sum of the measures of the four angles in a quadrilateral?
Then the product xy is a constant.
A = s^2 or A =d^2/2 where d is the diagonal
An equation that states that two ratios are equivalent. 4/6 = 10/15
360°

40. What is the measure of a straight angle?
Equal slopes.
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.
180°. If two or more angles form a straight angle - their sum is 180°.
A = (1/2)bh.

41. What is the formula for the volume of a cylinder?
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°.
All positive and negative whole numbers - and zero.
Area = (x°/360)(pr^2) where x is the central angle.
V = pr^2h

42. Properties of zero 3
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 a multiple of every integer.
At least one of the factors is 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

43. What is the formula for the area of a parallelogram?
1 is the smallest positive odd integer.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = bh

44. What are the median and the mode of a set of data?
A^m*b^m = (ab)^m
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.
(Circumference/diameter) of a circle - or approximately 3.14.
Write the percent over 100 and reduce.

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

46. 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.
Write the percent as a decimal - and multiply.
Their sum is 90°.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

47. What is a Venn diagram?
Set y = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

48. Law of exponents 5
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A^m/b^m = (a/b)^m
A = lw
Corresponding sides of similar triangles are in proportion.

49. Law of exponents 4
Write the percent as a decimal - and multiply.
Equal slopes.
A^m*b^m = (ab)^m
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.

50. What are the properties of a parallelogram?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3