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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.
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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 formula for the area of a triangle?
A = (1/2)bh.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

2. Properties of one 3
Area = (x/360)(pr^2) where x is the central angle.
1 is the smallest positive odd integer.
If a is negative and b is positive - then a < 0 < b.
1 is a divisor (or factor) of every integer.

3. What is true about the measures of the three angles in a triangle?
All positive and negative whole numbers - and zero.
Their sum is 180.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
180. If two or more angles form a straight angle - their sum is 180.

4. Properties of zero 1
A = (1/2)bh.
The set of all ordered pairs (x -y) such that y = f(x).
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.
0 is the only number that is neither positive nor negative.

5. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Equal slopes.

6. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
No matter how many angles there are - the sum around the point is 360.
Write the percent over 100 and reduce.
The product of their slopes is -1 (negative reciprocal).

7. How do you find the length of an arc of a circle?
Arc = (x/360)(2pr) where x is the central angle.
In the expression x^b - x is the base and b is the exponent.
All positive and negative whole numbers - and zero.
Cannot is 0 - must is 1 - all others are in between.

8. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Set y = 0 - and solve.
1 is a divisor (or factor) of every integer.
Then the product xy is a constant.
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.

9. What does it mean if y is inversely proportional to x?
At least one of the factors is 0.
(Circumference/diameter) of a circle - or approximately 3.14.
Then the product xy is a constant.
360

10. In a circle of radius r - what is the formula for the circumference?
Shifted down 2 units.
Arc = (x/360)(2pr) where x is the central angle.
C = p2r
A = 2(lw + lh + hw)

11. What is a multiple of an integer?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
(n - 2)(180)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.

12. What is the formula for the area of a parallelogram?
0 is the only number that is neither positive nor negative.
A = bh
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = 2(lw + lh + hw)

13. 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.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number b: b = -b if and only if b = 0.
A fraction whose denominator is 100 i.e. 17% = 17/100

14. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted right 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
D = 2r

15. What is an exponent?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
In the expression x^b - x is the base and b is the exponent.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

16. Properties of zero 5
Set y = 0 - and solve.
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.
For any number b: b = -b if and only if b = 0.

17. Law of exponents 1
A = 2(lw + lh + hw)
B^m*b^n = b^m+n
Set x = 0 - and solve.
360

18. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
(x + y)(x - y) = x^2 - y^2
The product of their slopes is -1 (negative reciprocal).
Write the percent as a decimal - and multiply.

19. What are the median and the mode of a set of data?
Write the percent as a decimal - and multiply.
Shifted down 2 units.
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.

20. What do we mean by the slope of the line?
Set y = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 180.

21. Law of exponents 3
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(b^m)^n = b^mn
A = s^2 or A =d^2/2 where d is the diagonal
In the expression x^b - x is the base and b is the exponent.

22. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
(x + y)(x - y) = x^2 - y^2
Write the percent as a decimal - and multiply.
The ratio of corresponding sides of similar triangles.
Shifted down 2 units.

23. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
V = lwh
For any right triangle - a^2 + b^2 = c^2.
D = 2r

24. Properties of zero 2
0 is a multiple of every 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.
At least one of the factors is 0.
If a is negative and b is positive - then a < 0 < b.

25. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = s^2 or A =d^2/2 where d is the diagonal

26. How do you calculate a weighted average?
The set of all ordered pairs (x -y) such that y = f(x).
A = pr^2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Write the percent over 100 and reduce.

27. What are the sum - difference - products - and quotient of two numbers?
360
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Cannot is 0 - must is 1 - all others are in between.
A = [(s^2*v3)/4]

28. Important binomial 3
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.
Shifted left 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Then the product xy is a constant.

29. What is the square root of a number?
1 is the smallest positive odd integer.
Their sum is 180.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
0 is a multiple of every integer.

30. Properties of zero 4
Their sum is 180.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number b: b = -b if and only if b = 0.

31. What are the quotient and the remainder?
The set of all ordered pairs (x -y) such that y = f(x).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

32. In a circle of radius r - what is the formula for the diameter?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
D = 2r
Set y = 0 - and solve.
0 is a multiple of every integer.

33. Law of exponents 2
B^m/b^n = b^m-n
(x + y)(x - y) = x^2 - 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.

34. What is the sum of the measures of the n angles of a polygon with n sides?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
A = (1/2)bh.
A = lw
(n - 2)(180)

35. What is the relationship between a radius of a circle and a line that is tangent to the circle?
360
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.

36. What is a negative exponent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
The ratio of corresponding sides of similar triangles.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any number n: x^-n means 1/x^n.

37. 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.
1 is the smallest positive odd integer.
Their sum is 90.
Corresponding sides of similar triangles are in proportion.

38. What is the formula for the area of a rectangle?
Shifted up 2 units.
A = [(s^2*v3)/4]
V = l^3
A = lw

39. For what values of a function is the function undefined?
(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.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

40. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
360
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

41. What is the formula for the volume of a cylinder?
For any number n: x^-n means 1/x^n.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any integer n: 1^n = 1.
V = pr^2h

42. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = lwh
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Set y = 0 - and solve.

43. 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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.
Shifted down 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]

44. What is the probability of an event that cannot occur? That must occur?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.
A = (1/2)bh.
Cannot is 0 - must is 1 - all others are in between.
M = (y2 - y1)/(x2 - x1)

45. In a circle of radius r - what is the formula for the area?
A = pr^2
B^m/b^n = b^m-n
A^m/b^m = (a/b)^m
(n - 2)(180)

46. What is a proportion?
No matter how many angles there are - the sum around the point is 360.
A = (1/2)bh.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the product xy is a constant.

47. Properties of one 2
0 is the only number that is neither positive nor negative.
For any right triangle - a^2 + b^2 = c^2.
(Circumference/diameter) of a circle - or approximately 3.14.
For any integer n: 1^n = 1.

48. What is a fractional exponent?
(Circumference/diameter) of a circle - or approximately 3.14.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
All positive and negative whole numbers - and zero.
Write the percent over 100 and reduce.

49. What is an even and an odd number?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
The set of all ordered pairs (x -y) such that y = f(x).
Even numbers are divisible by 2 and odd numbers are not.
Write the percent as a decimal - and multiply.

50. How do you convert a percent to a fraction or a decimal?
180. If two or more angles form a straight angle - their sum is 180.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Write the percent over 100 and reduce.

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