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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 the relationship between the graph of f(x) the graph of y = f(x) - 2?
M = (y2 - y1)/(x2 - x1)
Set x = 0 - and solve.
V = l^3
Shifted down 2 units.

2. What are the sum - difference - products - and quotient of two numbers?
M = (y2 - y1)/(x2 - x1)
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted right 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

3. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Shifted right 2 units.
A^m/b^m = (a/b)^m
360°
D = 2r

4. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
The ratio of corresponding sides of similar triangles.
For any right triangle - a^2 + b^2 = c^2.
B^m/b^n = b^m-n

5. What do we mean by the slope of the line?
Even numbers are divisible by 2 and odd numbers are not.
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.

6. How do you find the y-intercept of a graph?
C = p2r
(x + y)(x - y) = x^2 - y^2
Area = (x°/360)(pr^2) where x is the central angle.
Set x = 0 - and solve.

7. What is p?
Equal slopes.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(Circumference/diameter) of a circle - or approximately 3.14.

8. Law of exponents 4
A^m*b^m = (ab)^m
0 is a multiple of every integer.
The product of their slopes is -1 (negative reciprocal).
(b^m)^n = b^mn

9. Properties of square roots
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any integer n: 1^n = 1.
A^m/b^m = (a/b)^m
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

10. What is an integer?
Equal slopes.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
All positive and negative whole numbers - and zero.
For any integer n: 1^n = 1.

11. Properties of zero 3
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
Cannot is 0 - must is 1 - all others are in between.
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.

12. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
B^m/b^n = b^m-n
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°.
Their sum is 180°.

13. Properties of zero 1
B^m/b^n = b^m-n
For any number b: b = -b if and only if b = 0.
0 is the only number that is neither positive nor negative.
Shifted right 2 units.

14. What is the probability of an event that cannot occur? That must occur?
Set y = 0 - and solve.
The ratio of corresponding sides of similar triangles.
Cannot is 0 - must is 1 - all others are in between.
D = 2r

15. What are the properties of a rectangle?
Their sum is 90°.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set y = 0 - and solve.
All positive and negative whole numbers - and zero.

16. What is an even and an odd number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Even numbers are divisible by 2 and odd numbers are not.
Write the percent as a decimal - and multiply.

17. In a circle of radius r - what is the formula for the diameter?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
D = 2r

18. What is the formula for the area of a parallelogram?
A = bh
A fraction whose denominator is 100 i.e. 17% = 17/100
180°. If two or more angles form a straight angle - their sum is 180°.
360°

19. What is true about the slopes of perpendicular lines?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = pr^2
Then the quotient y/x is a constant.
The product of their slopes is -1 (negative reciprocal).

20. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
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.
Shifted right 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Then the quotient y/x is a constant.

21. Important binomial 3
The set of all ordered pairs (x -y) such that y = f(x).
If a is negative and b is positive - then a < 0 < b.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

22. What is the formula for the volume of a cylinder?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Write the percent as a decimal - and multiply.
Avg = sum of n numbers/n
V = pr^2h

23. What is an exponent?
D = 2r
In the expression x^b - x is the base and b is the exponent.
A^m*b^m = (ab)^m
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

24. How do we write the equation of a line?
Write the percent as a decimal - and multiply.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x + y)(x - y) = x^2 - y^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)

25. What is a multiple of an integer?
Shifted left 2 units.
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.
In the expression x^b - x is the base and b is the exponent.
Shifted up 2 units.

26. What are the median and the mode of a set of data?
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 longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure 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.
Equal slopes.

27. 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.
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]

28. What is true about the slopes of parallel lines?
B^m/b^n = b^m-n
Equal slopes.
An integer greater than one that is not prime.
C = p2r

29. What is an exterior angle of a polygon?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An angle formed by extending the side of the polygon.
A = (1/2)bh.
A^m/b^m = (a/b)^m

30. What is a divisor and a factor of an integer?
A^m/b^m = (a/b)^m
They are both the same. A divisor or factor of an integer leaves no remainder.
Even numbers are divisible by 2 and odd numbers are not.
A = bh

31. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.
Their sum is 90°.
In the expression x^b - x is the base and b is the exponent.

32. 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.
A = 6(l^2)
Divide - then multiply by 100.
In the expression x^b - x is the base and b is the exponent.

33. Properties of one 2
No matter how many angles there are - the sum around the point is 360°.
V = pr^2h
For any integer n: 1^n = 1.
For any number b: b = -b if and only if b = 0.

34. Law of exponents 2
If a is negative and b is positive - then a < 0 < b.
B^m/b^n = b^m-n
For any integer n: 1^n = 1.
For any number a: a * 1 = a and a / 1 = a.

35. What is the sum of the measures of the four angles in a quadrilateral?
Write the percent over 100 and reduce.
360°
A = s^2 or A =d^2/2 where d is the diagonal
A^m/b^m = (a/b)^m

36. What is a proportion?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
An equation that states that two ratios are equivalent. 4/6 = 10/15
(Circumference/diameter) of a circle - or approximately 3.14.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

37. What is a negative exponent?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.
(Circumference/diameter) of a circle - or approximately 3.14.

38. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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°.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Even numbers are divisible by 2 and odd numbers are not.

39. What is a fractional exponent?
V = lwh
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.

40. How do you calculate percent increases and decreases?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = 6(l^2)
D = 2r

41. What is the formula for the area of a triangle?
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°.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Set y = 0 - and solve.
A = (1/2)bh.

42. What is the graph of a function?
Equal slopes.
The set of all ordered pairs (x -y) such that y = f(x).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(b^m)^n = b^mn

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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
C = p2r
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

44. How do you find the length of an arc of a circle?
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Arc = (x°/360)(2pr) where x is the central angle.
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.

45. What is a percent?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A fraction whose denominator is 100 i.e. 17% = 17/100
M = (y2 - y1)/(x2 - x1)
Then the quotient y/x is a constant.

46. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn
Shifted up 2 units.
Shifted down 2 units.

47. What is true about the measures of the three angles in a triangle?
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.
Their sum is 90°.
Their sum is 180°.

48. What is the formula for the surface area of a cube?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = 6(l^2)
(Circumference/diameter) of a circle - or approximately 3.14.
Equal slopes.

49. Important binomial 1
A = (1/2)bh.
(x + y)(x - y) = x^2 - y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
B^m/b^n = b^m-n

50. What is true about the measures of the four angles formed by two intersecting lines?
Then the quotient y/x is a constant.
Cannot is 0 - must is 1 - all others are in between.
(x + y)(x - y) = x^2 - y^2
The two pairs of opposite angles formed are equal to each other.