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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 calculate a weighted average?
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Equal slopes.
A = [(s^2*v3)/4]

2. What is the sum of the measures of the four angles in a quadrilateral?
Corresponding sides of similar triangles are in proportion.
360°
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
For any integer n: 1^n = 1.

3. Properties of one 1
V = pr^2h
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number a: a * 1 = a and a / 1 = a.
An angle formed by extending the side of the polygon.

4. How do you find the slope of a line?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
M = (y2 - y1)/(x2 - x1)
The product of their slopes is -1 (negative reciprocal).
Set x = 0 - and solve.

5. What are the quotient and the remainder?

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6. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = 2(lw + lh + hw)
A = [(s^2*v3)/4]
Shifted up 2 units.

7. Properties of one 4
How steep the line is. Horizontal line = 0 - vertical has no slope.
1 is the smallest positive odd 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.
A = 6(l^2)

8. Properties of one 3
(x + y)(x - y) = x^2 - y^2
A fraction whose denominator is 100 i.e. 17% = 17/100
1 is a divisor (or factor) of every integer.
Divide - then multiply by 100.

9. Law of exponents 4
For any number b: b = -b if and only if b = 0.
For any integer n: 1^n = 1.
A^m*b^m = (ab)^m
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

10. What does it mean if y is directly proportional to x?
An angle formed by extending the side of the polygon.
Then the quotient y/x is a constant.
V = pr^2h
Set y = 0 - and solve.

11. What is the triangle inequality?
A^m/b^m = (a/b)^m
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
M = (y2 - y1)/(x2 - x1)

12. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
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.
1 is the smallest positive odd integer.
Write the percent as a decimal - and multiply.

13. What is an integer?
For any number b: b = -b if and only if b = 0.
All positive and negative whole numbers - and zero.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Divide - then multiply by 100.

14. Important binomial 1
(x + y)(x - y) = x^2 - y^2
B^m*b^n = b^m+n
Equal slopes.
An equation that states that two ratios are equivalent. 4/6 = 10/15

15. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
180°. If two or more angles form a straight angle - their sum is 180°.
A = (1/2)bh.
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.

16. What is a percent?
Equal slopes.
The product of their slopes is -1 (negative reciprocal).
A fraction whose denominator is 100 i.e. 17% = 17/100
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

17. 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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Set x = 0 - and solve.
An equation that states that two ratios are equivalent. 4/6 = 10/15

18. What is the Pythagorean theorem?
(x + y)(x - y) = x^2 - y^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
V = l^3
For any right triangle - a^2 + b^2 = c^2.

19. What is a composite number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = bh
An integer greater than one that is not prime.
How steep the line is. Horizontal line = 0 - vertical has no slope.

20. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Even numbers are divisible by 2 and odd numbers are not.
A = s^2 or A =d^2/2 where d is the diagonal
B^m*b^n = b^m+n

21. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = (1/2)bh.
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°.
Shifted right 2 units.
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.

22. What is the volume of a cube?
Shifted down 2 units.
At least one of the factors is 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = l^3

23. For what values of a function is the function undefined?
The two pairs of opposite angles formed are equal to each other.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

24. What is the sum of the measures of the n angles of a polygon with n sides?
A = bh
(n - 2)(180°)
The two pairs of opposite angles formed are equal to each other.
Set x = 0 - and solve.

25. What is an even and an odd number?
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.
Even numbers are divisible by 2 and odd numbers are not.
For any number a: a * 1 = a and a / 1 = a.
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°.

26. How do you find the probability that an event will occur?
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

27. Properties of zero 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
M = (y2 - y1)/(x2 - x1)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If a is negative and b is positive - then a < 0 < b.

28. What are the important properties of 30-60-90 triangle?
Shifted right 2 units.
For any integer n: 1^n = 1.
Is a right triangle with a ratio of sides x:xv3:2x.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

29. 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.
180°. If two or more angles form a straight angle - their sum is 180°.
Then the quotient y/x is a constant.
Set y = 0 - and solve.

30. Properties of zero 5
An equation that states that two ratios are equivalent. 4/6 = 10/15
Divide - then multiply by 100.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number b: b = -b if and only if b = 0.

31. What is a ratio?

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32. What is true about the areas of similar triangles?
Their sum is 90°.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Divide - then multiply by 100.
180°. If two or more angles form a straight angle - their sum is 180°.

33. 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.
V = l^3
For any number a: a * 1 = a and a / 1 = a.
D = 2r

34. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
The ratio of corresponding sides of similar triangles.
1 is the smallest positive odd integer.
Write the percent over 100 and reduce.

35. What are the important properties of a 45-45 - 90 triangle?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
1 is a divisor (or factor) of every integer.

36. What is true about the measures of the four angles formed by two intersecting lines?
Cannot is 0 - must is 1 - all others are in between.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The two pairs of opposite angles formed are equal to each other.
0 is the only number that is neither positive nor negative.

37. Law of exponents 3
(b^m)^n = b^mn
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.
0 is a multiple of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

38. Law of exponents 1
B^m*b^n = b^m+n
A^m*b^m = (ab)^m
[(x1 + x2)/2] -[(y1 + y2)/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.

39. Law of exponents 5
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°.
360°
A^m/b^m = (a/b)^m
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

40. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Is a right triangle with a ratio of sides x:xv3:2x.
The product of their slopes is -1 (negative reciprocal).
Shifted down 2 units.

41. What formula is used for an average?
Avg = sum of n numbers/n
The ratio of corresponding sides of similar triangles.
No matter how many angles there are - the sum around the point is 360°.
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.

42. Important binomial 3
(b^m)^n = b^mn
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The two pairs of opposite angles formed are equal to each other.
Divide - then multiply by 100.

43. Properties of one 2
For any right triangle - a^2 + b^2 = c^2.
Shifted right 2 units.
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.
For any integer n: 1^n = 1.

44. What are the properties of a parallelogram?
Their sum is 90°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

45. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
(n - 2)(180°)
A = [(s^2*v3)/4]
Then the product xy is a constant.

46. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = 2(lw + lh + hw)
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.

47. Properties of zero 3
An angle formed by extending the side of the polygon.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
0 is a multiple of every integer.

48. What is the graph of a function?
1 is the smallest positive odd integer.
Avg = sum of n numbers/n
The set of all ordered pairs (x -y) such that y = f(x).
In the expression x^b - x is the base and b is the exponent.

49. What is the distance formula?
The two pairs of opposite angles formed are equal to each other.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Write the percent over 100 and reduce.

50. How do you convert a percent to a fraction or a decimal?
V = l^3
0 is the only number that is neither positive nor negative.
Write the percent over 100 and reduce.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.