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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 a percent?
Even numbers are divisible by 2 and odd numbers are not.
360°
A fraction whose denominator is 100 i.e. 17% = 17/100
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

2. Properties of one 2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Then the product xy is a constant.
For any integer n: 1^n = 1.
Shifted up 2 units.

3. Properties of zero 1
0 is the only number that is neither positive nor negative.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Area = (x°/360)(pr^2) where x is the central angle.

4. What is true about the measures of the two acute angles in a right triangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
B^m*b^n = b^m+n
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Their sum is 90°.

5. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
For any integer n: 1^n = 1.
Shifted left 2 units.
A = (1/2)bh.
0 is the only number that is neither positive nor negative.

6. What are the properties of a square?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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°.
Their sum is 180°.

7. What is the distributive law?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

8. What are similar triangles?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

9. What is a prime number?
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*b^n = b^m+n
(b^m)^n = b^mn
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.

10. In a circle of radius r - what is the formula for the diameter?
D = 2r
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted left 2 units.

11. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An integer greater than one that is not prime.
Then the product xy is a constant.
All positive and negative whole numbers - and zero.

12. What is the formula for the surface area of a cube?
A = 6(l^2)
The ratio of corresponding sides of similar triangles.
A^m*b^m = (ab)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

13. If the product of two or more numbers is 0 - what do you know about the numbers?
V = lwh
(x + y)(x - y) = x^2 - y^2
At least one of the factors is 0.
360°

14. What is a ratio?

15. What is an even and an odd number?
For any number n: x^-n means 1/x^n.
Is a right triangle with a ratio of sides x:xv3:2x.
Even numbers are divisible by 2 and odd numbers are not.
0 is the only number that is neither positive nor negative.

16. If you were given the graph of y = f(x) - what does f(a) represent?
Set y = 0 - and solve.
Shifted right 2 units.
Set x = 0 - and solve.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

17. What does it mean if y is inversely proportional to x?
B^m/b^n = b^m-n
Then the product xy is a constant.
M = (y2 - y1)/(x2 - x1)
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

18. What is a function?
D = 2r
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = [(s^2*v3)/4]
A = s^2 or A =d^2/2 where d is the diagonal

19. How do we write the equation of a line?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted right 2 units.
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.

20. What is true about the areas of similar triangles?
Arc = (x°/360)(2pr) where x is the central angle.
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

21. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Divide - then multiply by 100.
Set x = 0 - and solve.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

22. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Write the percent over 100 and reduce.
For any number b: b = -b if and only if b = 0.
A = pr^2
Shifted up 2 units.

23. What is p?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
(Circumference/diameter) of a circle - or approximately 3.14.
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/b^n = b^m-n

24. Law of exponents 1
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m*b^n = b^m+n
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

25. Law of exponents 5
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.
A^m/b^m = (a/b)^m
For any number n: x^-n means 1/x^n.
In the expression x^b - x is the base and b is the exponent.

26. What is the sum of the measures of all angles around a point?
A = 2(lw + lh + hw)
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
No matter how many angles there are - the sum around the point is 360°.

27. What is special formula for the area of an equilateral triangle?
Then the product xy is a constant.
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.
A = [(s^2*v3)/4]
For any number n: x^-n means 1/x^n.

28. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
At least one of the factors is 0.
Shifted down 2 units.
(b^m)^n = b^mn

29. Law of exponents 2
(x + y)(x - y) = x^2 - y^2
B^m/b^n = b^m-n
Write the percent as a decimal - and multiply.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

30. How do you find the area of a sector of a circle?
0 is the only number that is neither positive nor negative.
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.
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.
Area = (x°/360)(pr^2) where x is the central angle.

31. Properties of zero 3
The product of their slopes is -1 (negative reciprocal).
A = 6(l^2)
0 is a multiple of every integer.
Equal slopes.

32. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A^m/b^m = (a/b)^m
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If a is negative and b is positive - then a < 0 < b.
360°

33. What is the sum of the measures of the n angles of a polygon with n sides?
A fraction whose denominator is 100 i.e. 17% = 17/100
For any integer n: 1^n = 1.
(b^m)^n = b^mn
(n - 2)(180°)

34. In a circle of radius r - what is the formula for the area?
Set y = 0 - and solve.
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°.
Then the quotient y/x is a constant.
A = pr^2

35. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

36. Important binomial 3
(x + y)(x - y) = x^2 - y^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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted left 2 units.

37. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(Circumference/diameter) of a circle - or approximately 3.14.
Write the percent as a decimal - and multiply.
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°.

38. How do you find the y-intercept of a graph?
No matter how many angles there are - the sum around the point is 360°.
Arc = (x°/360)(2pr) where x is the central angle.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set x = 0 - and solve.

39. What is the formula for the volume of a cylinder?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Set x = 0 - and solve.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
V = pr^2h

40. What are the median and the mode of a set of data?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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 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.
Is a right triangle with a ratio of sides x:xv3:2x.

41. How do you find the slope of a line?
[(x1 + x2)/2] -[(y1 + y2)/2]
180°. If two or more angles form a straight angle - their sum is 180°.
V = l^3
M = (y2 - y1)/(x2 - x1)

42. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
B^m*b^n = b^m+n
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

43. How do you convert a percent to a fraction or a decimal?
180°. If two or more angles form a straight angle - their sum is 180°.
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent over 100 and reduce.

44. How do you find the probability that an event will occur?
An angle formed by extending the side of the polygon.
An equation that states that two ratios are equivalent. 4/6 = 10/15
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

45. Properties of zero 5
For any number b: b = -b if and only if b = 0.
An angle formed by extending the side of the polygon.
Their sum is 180°.
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.

46. Important binomial 2
A = s^2 or A =d^2/2 where d is the diagonal
The product of their slopes is -1 (negative reciprocal).
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A^m*b^m = (ab)^m

47. What is a proportion?
0 is a multiple of every integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A^m/b^m = (a/b)^m
(Circumference/diameter) of a circle - or approximately 3.14.

48. Law of exponents 4
A^m*b^m = (ab)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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°.
(Circumference/diameter) of a circle - or approximately 3.14.

49. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
0 is the only number that is neither positive nor negative.
They are both the same. A divisor or factor of an integer leaves no remainder.
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°.

50. What is true about the measures of the three angles in a triangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 180°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The two pairs of opposite angles formed are equal to each other.