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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 square roots
For any number b: b = -b if and only if b = 0.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Their sum is 180°.
(Circumference/diameter) of a circle - or approximately 3.14.

2. Law of exponents 2
An equation that states that two ratios are equivalent. 4/6 = 10/15
A^m*b^m = (ab)^m
B^m/b^n = b^m-n
Arc = (x°/360)(2pr) where x is the central angle.

3. What is the formula for the area of a triangle?
A = (1/2)bh.
Even numbers are divisible by 2 and odd numbers are not.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
D = 2r

4. What is true about the slopes of perpendicular 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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The product of their slopes is -1 (negative reciprocal).

5. Properties of zero 2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If a is negative and b is positive - then a < 0 < b.
Shifted right 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

6. Important binomial 1
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.
(x + y)(x - y) = x^2 - y^2
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

7. What is an integer?
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/b^n = b^m-n
All positive and negative whole numbers - and zero.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

8. How do you find the length of an arc of a circle?
0 is a multiple of every integer.
A^m/b^m = (a/b)^m
V = lwh
Arc = (x°/360)(2pr) where x is the central angle.

9. What is a divisor and a factor of an integer?
Write the percent as a decimal - and multiply.
They are both the same. A divisor or factor of an integer leaves no remainder.
A = 6(l^2)
[(x1 + x2)/2] -[(y1 + y2)/2]

10. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
V = pr^2h

11. What is a Venn diagram?
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.
The two pairs of opposite angles formed are equal to each other.
C = p2r

12. What is true about the measures of the four angles formed by two intersecting lines?
(Circumference/diameter) of a circle - or approximately 3.14.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The two pairs of opposite angles formed are equal to each other.
A fraction whose denominator is 100 i.e. 17% = 17/100

13. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted left 2 units.
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.

14. 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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

15. What does it mean if y is inversely proportional to x?
If a is negative and b is positive - then a < 0 < b.
Then the product xy is a constant.
A = 6(l^2)
An integer greater than one that is not prime.

16. Properties of zero 1
360°
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
0 is the only number that is neither positive nor negative.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

17. 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.
B^m/b^n = b^m-n
Shifted left 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

18. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

19. Important binomial 3
C = p2r
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

20. What is the sum of the measures of the n angles of a polygon with n sides?
A = [(s^2*v3)/4]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(n - 2)(180°)

21. How do you find the slope of a line?
A = s^2 or A =d^2/2 where d is the diagonal
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
M = (y2 - y1)/(x2 - x1)
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.

22. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Cannot is 0 - must is 1 - all others are in between.
Even numbers are divisible by 2 and odd numbers are not.
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.

23. How do you find a percent of a number?
Set y = 0 - and solve.
Write the percent as a decimal - and multiply.
A = s^2 or A =d^2/2 where d is the diagonal
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

24. What are the properties of a rectangle?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Then the product xy is a constant.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

25. What is the distributive law?
Divide - then multiply by 100.
A = s^2 or A =d^2/2 where d is the diagonal
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.

26. Properties of one 3
B^m*b^n = b^m+n
If a is negative and b is positive - then a < 0 < b.
The two pairs of opposite angles formed are equal to each other.
1 is a divisor (or factor) of every integer.

27. What are the median and the mode of a set of data?
D = 2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
Set y = 0 - and solve.

28. What is a composite number?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
No matter how many angles there are - the sum around the point is 360°.
An integer greater than one that is not prime.

29. What is a percent?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A fraction whose denominator is 100 i.e. 17% = 17/100
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = pr^2h

30. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Set x = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = s^2 or A =d^2/2 where d is the diagonal
360°

31. If the product of two or more numbers is 0 - what do you know about the numbers?
The two pairs of opposite angles formed are equal to each other.
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.
At least one of the factors is 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

32. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Is a right triangle with a ratio of sides x:xv3:2x.
Avg = sum of n numbers/n
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.

33. What is the sum of the measures of all angles around a point?
(x + y)(x - y) = x^2 - y^2
M = (y2 - y1)/(x2 - x1)
No matter how many angles there are - the sum around the point is 360°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

34. What is the ratio of similitude?
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 any right triangle - a^2 + b^2 = c^2.
The ratio of corresponding sides of similar triangles.
Cannot is 0 - must is 1 - all others are in between.

35. What is the square root of a number?
M = (y2 - y1)/(x2 - x1)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted left 2 units.
V = pr^2h

36. 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.
An integer greater than one that is not prime.
A = 6(l^2)
0 is a multiple of every integer.

37. How do we write the equation of a line?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = s^2 or A =d^2/2 where d is the diagonal
A^m*b^m = (ab)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

38. How do you find the probability that an event will occur?
Set y = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(n - 2)(180°)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

39. What is true about the slopes of parallel lines?
Equal slopes.
An equation that states that two ratios are equivalent. 4/6 = 10/15
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

40. What is a ratio?

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41. What is the Pythagorean theorem?
A = (1/2)bh.
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.
A = bh

42. Properties of one 1
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any number a: a * 1 = a and a / 1 = a.

43. What is the formula for the area of a rectangle?
A = lw
At least one of the factors is 0.
B^m/b^n = b^m-n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

44. Properties of one 4
The two pairs of opposite angles formed are equal to each other.
An integer greater than one that is not prime.
1 is the smallest positive odd integer.
The set of all ordered pairs (x -y) such that y = f(x).

45. What are the quotient and the remainder?

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46. What is a proportion?
V = l^3
The product of their slopes is -1 (negative reciprocal).
V = lwh
An equation that states that two ratios are equivalent. 4/6 = 10/15

47. What is the formula for the surface area of a cube?
V = pr^2h
A = 6(l^2)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(x + y)(x - y) = x^2 - y^2

48. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
D = 2r
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.
A^m/b^m = (a/b)^m

49. What is an exterior angle of a triangle?
Set x = 0 - and solve.
A = lw
For any number n: x^-n means 1/x^n.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

50. What is the midpoint formula?
In the expression x^b - x is the base and b is the exponent.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number n: x^-n means 1/x^n.
Write the percent as a decimal - and multiply.