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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 1
V = l^3
Set x = 0 - and solve.
For any number a: a * 1 = a and a / 1 = a.
A = pr^2

2. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Is a right triangle with a ratio of sides x:xv3:2x.
For any number a: a * 1 = a and a / 1 = a.
Equal slopes.

3. What is the formula for the volume of a cylinder?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Equal slopes.
For any integer n: 1^n = 1.
V = pr^2h

4. What is a percent?
Write the percent as a decimal - and multiply.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A fraction whose denominator is 100 i.e. 17% = 17/100
(b^m)^n = b^mn

5. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
1 is a divisor (or factor) of every integer.
Write the percent over 100 and reduce.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

6. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)

7. What is a Venn diagram?
V = l^3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any integer n: 1^n = 1.

8. What are the important properties of a 45-45 - 90 triangle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
Shifted left 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

9. What important property do similar triangles have?
0 is the only number that is neither positive nor negative.
Corresponding sides of similar triangles are in proportion.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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 multiple of an integer?
(n - 2)(180°)
Even numbers are divisible by 2 and odd numbers are not.
An integer greater than one that is not prime.
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.

11. How do you calculate a weighted average?
A = lw
No matter how many angles there are - the sum around the point is 360°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

12. What is a negative exponent?
V = lwh
Set y = 0 - and solve.
For any number n: x^-n means 1/x^n.
Avg = sum of n numbers/n

13. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any integer n: 1^n = 1.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(Circumference/diameter) of a circle - or approximately 3.14.

14. What is an integer?
If a is negative and b is positive - then a < 0 < b.
The product of their slopes is -1 (negative reciprocal).
V = pr^2h
All positive and negative whole numbers - and zero.

15. Properties of zero 3
A = bh
0 is a multiple of every integer.
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.

16. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Set y = 0 - and solve.

17. How do you find the area of a sector of a circle?
A = s^2 or A =d^2/2 where d is the diagonal
Area = (x°/360)(pr^2) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

18. Properties of zero 5
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number b: b = -b if and only if b = 0.
A = 2(lw + lh + hw)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

19. What is a composite number?
The two pairs of opposite angles formed are equal to each other.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
An integer greater than one that is not prime.
0 is a multiple of every integer.

20. Law of exponents 2
0 is the only number that is neither positive nor negative.
The product of their slopes is -1 (negative reciprocal).
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
B^m/b^n = b^m-n

21. 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.
Then the product xy is a constant.
Their sum is 90°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

22. Properties of zero 1
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 longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
0 is the only number that is neither positive nor negative.

23. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
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.
Shifted right 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = s^2 or A =d^2/2 where d is the diagonal

24. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
For any number b: b = -b if and only if b = 0.
The two pairs of opposite angles formed are equal to each other.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

25. What is true about the measures of the four angles formed by two intersecting lines?
For any number n: x^-n means 1/x^n.
The two pairs of opposite angles formed are equal to each other.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
360°

26. What are the quotient and the remainder?

27. What is the formula for the area of a parallelogram?
A = pr^2
A = bh
Shifted left 2 units.
In the expression x^b - x is the base and b is the exponent.

28. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
A = (1/2)bh.
Then the quotient y/x is a constant.
B^m/b^n = b^m-n

29. What is a divisor and a factor of an integer?
V = l^3
They are both the same. A divisor or factor of an integer leaves no remainder.
M = (y2 - y1)/(x2 - x1)
(n - 2)(180°)

30. How do we write the equation of a line?
B^m/b^n = b^m-n
At least one of the factors is 0.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

31. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
A^m*b^m = (ab)^m
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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°.

32. What is the sum of the measures of the four angles in a quadrilateral?
360°
A fraction whose denominator is 100 i.e. 17% = 17/100
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

33. What is a proportion?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The product of their slopes is -1 (negative reciprocal).
1 is a divisor (or factor) of every integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15

34. In a circle of radius r - what is the formula for the area?
A = pr^2
Arc = (x°/360)(2pr) where x is the central angle.
(x + y)(x - y) = x^2 - y^2
For any number b: b = -b if and only if b = 0.

35. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Cannot is 0 - must is 1 - all others are in between.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

36. What is the formula for the volume of a rectangular solid?
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = lw
V = lwh

37. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
For any right triangle - a^2 + b^2 = c^2.
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.
Divide - then multiply by 100.

38. What is the Pythagorean theorem?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = lw
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°.
For any right triangle - a^2 + b^2 = c^2.

39. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
V = lwh
Shifted left 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
Arc = (x°/360)(2pr) where x is the central angle.

40. What formula is used for an average?
Divide - then multiply by 100.
360°
1 is the smallest positive odd integer.
Avg = sum of n numbers/n

41. What is the distributive law?
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.
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.

42. What is true about the measures of the three angles in a triangle?
(x + y)(x - y) = x^2 - y^2
Their sum is 180°.
V = pr^2h
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

43. What is p?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
M = (y2 - y1)/(x2 - x1)
V = lwh
(Circumference/diameter) of a circle - or approximately 3.14.

44. What is the sum of the measures of all angles around a point?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
No matter how many angles there are - the sum around the point is 360°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

45. What are the properties of a square?
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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.

46. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
Area = (x°/360)(pr^2) where x is the central angle.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If a is negative and b is positive - then a < 0 < b.

47. What are the important properties of 30-60-90 triangle?
(n - 2)(180°)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Is a right triangle with a ratio of sides x:xv3:2x.
Then the quotient y/x is a constant.

48. How do you calculate percent increases and decreases?
The two pairs of opposite angles formed are equal to each other.
Then the quotient y/x is a constant.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

49. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Even numbers are divisible by 2 and odd numbers are not.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(n - 2)(180°)

50. How do you find the slope of a line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Set x = 0 - and solve.
M = (y2 - y1)/(x2 - x1)
Corresponding sides of similar triangles are in proportion.