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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. How do you find the probability that an event will occur?
A^m/b^m = (a/b)^m
V = pr^2h
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

2. What formula is used for an average?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The product of their slopes is -1 (negative reciprocal).
Avg = sum of n numbers/n
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

3. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
They are both the same. A divisor or factor of an integer leaves no remainder.
Then the product xy is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

4. How do you find the y-intercept of a graph?
Shifted down 2 units.
Their sum is 180°.
Write the percent as a decimal - and multiply.
Set x = 0 - and solve.

5. What is the ratio of similitude?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The ratio of corresponding sides of similar triangles.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Write the percent as a decimal - and multiply.

6. How do you find the area of a sector of a circle?
A = (1/2)bh.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Area = (x°/360)(pr^2) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

7. What is a multiple of an integer?
No matter how many angles there are - the sum around the point is 360°.
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°.
Is a right triangle with a ratio of sides x:xv3:2x.
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.

8. What is an exterior angle of a polygon?
A = 6(l^2)
An angle formed by extending the side of the polygon.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The two pairs of opposite angles formed are equal to each other.

9. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
Shifted down 2 units.
For any right triangle - a^2 + b^2 = c^2.
360°

10. Law of exponents 4
A^m*b^m = (ab)^m
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = pr^2
If a is negative and b is positive - then a < 0 < b.

11. What is the formula for the volume of a rectangular solid?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
V = lwh
A^m*b^m = (ab)^m

12. What do we mean by the slope of the line?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
How steep the line is. Horizontal line = 0 - vertical has no slope.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
1 is a divisor (or factor) of every integer.

13. How do we write the equation of a line?
A = lw
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 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.

14. What is the formula for the surface area of a cube?
Set x = 0 - and solve.
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.
In the expression x^b - x is the base and b is the exponent.
A = 6(l^2)

15. Law of exponents 1
Their sum is 90°.
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
(n - 2)(180°)

16. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = 2(lw + lh + hw)
Arc = (x°/360)(2pr) where x is the central angle.

17. What is the graph of a function?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
The set of all ordered pairs (x -y) such that y = f(x).

18. What is a function?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = pr^2
A = 2(lw + lh + hw)

19. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
The ratio of corresponding sides of similar triangles.
C = p2r
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Shifted right 2 units.

20. Properties of one 2
P(e) = (# of favorable outcomes)/(# of possible outcomes)
An angle formed by extending the side of the polygon.
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.
For any integer n: 1^n = 1.

21. What is an even and an odd number?
A = 6(l^2)
Even numbers are divisible by 2 and odd numbers are not.
The set of all ordered pairs (x -y) such that y = f(x).
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

22. What is true about the measures of the three angles in a triangle?
Arc = (x°/360)(2pr) where x is the central angle.
A = [(s^2*v3)/4]
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Their sum is 180°.

23. What are the quotient and the remainder?

24. What is a percent?
B^m/b^n = b^m-n
Divide - then multiply by 100.
A fraction whose denominator is 100 i.e. 17% = 17/100
D = 2r

25. What are the sum - difference - products - and quotient of two numbers?
Shifted up 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
360°

26. What is a Venn diagram?
For any right triangle - a^2 + b^2 = c^2.
Equal slopes.
Their sum is 90°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

27. What is true about the measures of the four angles formed by two intersecting lines?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = lw
The two pairs of opposite angles formed are equal to each other.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

28. Properties of square roots
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any number a: a * 1 = a and a / 1 = a.

29. What is the distributive law?
Divide - then multiply by 100.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
All positive and negative whole numbers - and zero.
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.

30. What is the measure of a straight angle?
For any number b: b = -b if and only if b = 0.
180°. If two or more angles form a straight angle - their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Is a right triangle with a ratio of sides x:xv3:2x.

31. How do you find the slope of a line?
A = 6(l^2)
M = (y2 - y1)/(x2 - x1)
[(x1 + x2)/2] -[(y1 + y2)/2]
Their sum is 180°.

32. What is the sum of the measures of the four angles in a quadrilateral?
360°
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.
C = p2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

33. If you were given the graph of y = f(x) - what does f(a) represent?
In the expression x^b - x is the base and b is the exponent.
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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

34. What is an integer?
Then the product xy is a constant.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Equal slopes.
All positive and negative whole numbers - and zero.

35. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
A = 6(l^2)
For any number n: x^-n means 1/x^n.
D = 2r

36. What is a prime number?
All positive and negative whole numbers - and zero.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

37. What is the formula for the area of a triangle?
The ratio of corresponding sides of similar triangles.
No matter how many angles there are - the sum around the point is 360°.
A = (1/2)bh.
Their sum is 180°.

38. How do you calculate percent increases and decreases?
Their sum is 90°.
A = 2(lw + lh + hw)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

39. How do you calculate a weighted average?
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.
The ratio of corresponding sides of similar triangles.
Write the percent as a decimal - and multiply.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

40. What are the properties of a parallelogram?
Area = (x°/360)(pr^2) where x is the central angle.
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.
Then the quotient y/x is a constant.

41. What is the formula for the surface area of a rectangular solid?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A = 2(lw + lh + hw)
All positive and negative whole numbers - and zero.
For any integer n: 1^n = 1.

42. Properties of zero 5
Cannot is 0 - must is 1 - all others are in between.
For any number b: b = -b if and only if b = 0.
At least one of the factors is 0.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

43. What are the important properties of a 45-45 - 90 triangle?
A = s^2 or A =d^2/2 where d is the diagonal
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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 = 2(lw + lh + hw)

44. In a circle of radius r - what is the formula for the circumference?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
C = p2r
Area = (x°/360)(pr^2) where x is the central angle.

45. 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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
In the expression x^b - x is the base and b is the exponent.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

46. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
0 is the only number that is neither positive nor negative.
Arc = (x°/360)(2pr) where x is the central angle.
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.

47. What is a composite number?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m*b^n = b^m+n
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.

48. How do you convert a percent to a fraction or a decimal?
At least one of the factors is 0.
A = 2(lw + lh + hw)
0 is a multiple of every integer.
Write the percent over 100 and reduce.

49. What is a fractional exponent?
The two pairs of opposite angles formed are equal to each other.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = 2(lw + lh + hw)
P(e) = (# of favorable outcomes)/(# of possible outcomes)

50. Important binomial 3
Shifted up 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
1 is the smallest positive odd integer.
The ratio of corresponding sides of similar triangles.