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GRE Math: Facts

Subjects : gre, math

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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 do we mean by the slope of the line?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = pr^2
Cannot is 0 - must is 1 - all others are in between.
How steep the line is. Horizontal line = 0 - vertical has no slope.

2. What is the sum of the measures of the n angles of a polygon with n sides?
Then the product xy is a constant.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Their sum is 180°.
(n - 2)(180°)

3. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Write the percent over 100 and reduce.
Then the product xy is a constant.

4. What is a ratio?

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5. What is the formula for the volume of a rectangular solid?
V = lwh
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.
Shifted up 2 units.

6. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
All positive and negative whole numbers - and zero.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An angle formed by extending the side of the polygon.

7. How do you calculate a weighted average?
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.
The two pairs of opposite angles formed are equal to each other.
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.

8. What is true about the measures of the four angles formed by two intersecting lines?
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°.
The two pairs of opposite angles formed are equal to each other.
The ratio of corresponding sides of similar triangles.
Cannot is 0 - must is 1 - all others are in between.

9. What is true about the slopes of perpendicular lines?
For any number b: b = -b if and only if b = 0.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The product of their slopes is -1 (negative reciprocal).
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°.

10. What is the formula for the surface area of a cube?
A = 6(l^2)
A = 2(lw + lh + hw)
0 is the only number that is neither positive nor negative.
Corresponding sides of similar triangles are in proportion.

11. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Even numbers are divisible by 2 and odd numbers are not.
A = bh
No matter how many angles there are - the sum around the point is 360°.
Shifted down 2 units.

12. What are the quotient and the remainder?

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13. What is a Venn diagram?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An integer greater than one that is not prime.
V = pr^2h

14. How you convert a fraction or a decimal to a percent?
0 is the only number that is neither positive nor negative.
Area = (x°/360)(pr^2) where x is the central angle.
Divide - then multiply by 100.
Corresponding sides of similar triangles are in proportion.

15. What is the formula for the area of a rectangle?
Set y = 0 - and solve.
A = lw
Arc = (x°/360)(2pr) where x is the central angle.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

16. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
A^m/b^m = (a/b)^m
All positive and negative whole numbers - and zero.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

17. Important binomial 1
Even numbers are divisible by 2 and odd numbers are not.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The two pairs of opposite angles formed are equal to each other.
(x + y)(x - y) = x^2 - y^2

18. What is the sum of the measures of the four angles in a quadrilateral?
360°
A = 6(l^2)
An equation that states that two ratios are equivalent. 4/6 = 10/15
In the expression x^b - x is the base and b is the exponent.

19. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A^m*b^m = (ab)^m
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°.
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.

20. Properties of square roots
A^m*b^m = (ab)^m
[(x1 + x2)/2] -[(y1 + y2)/2]
For any integer n: 1^n = 1.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

21. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Shifted down 2 units.
Write the percent as a decimal - and multiply.
(b^m)^n = b^mn

22. In a circle of radius r - what is the formula for the area?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A^m*b^m = (ab)^m
A = pr^2
An angle formed by extending the side of the polygon.

23. What are the sum - difference - products - and quotient of two numbers?
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.
A = s^2 or A =d^2/2 where d is the diagonal
V = lwh
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

24. What are the properties of a parallelogram?
D = 2r
The ratio of corresponding sides of similar triangles.
A = bh
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

25. Law of exponents 3
They are both the same. A divisor or factor of an integer leaves no remainder.
(b^m)^n = b^mn
The ratio of corresponding sides of similar triangles.
Write the percent as a decimal - and multiply.

26. What is a percent?
How steep the line is. Horizontal line = 0 - vertical has no slope.
(n - 2)(180°)
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A fraction whose denominator is 100 i.e. 17% = 17/100

27. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Avg = sum of n numbers/n
A = pr^2

28. What is a proportion?
The ratio of corresponding sides of similar triangles.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(n - 2)(180°)

29. What is true about the areas of similar triangles?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Set y = 0 - and solve.

30. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At least one of the factors is 0.
Even numbers are divisible by 2 and odd numbers are not.
Equal slopes.

31. How do you find the area of a sector of a circle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m/b^n = b^m-n
Area = (x°/360)(pr^2) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

32. What is a prime number?
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted left 2 units.
An integer greater than one that is not prime.
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.

33. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
Arc = (x°/360)(2pr) where x is the central angle.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

34. What is a multiple of an integer?
In the expression x^b - x is the base and b is the exponent.
Shifted right 2 units.
For any right triangle - a^2 + b^2 = c^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.

35. What is the formula for the volume of a cylinder?
V = pr^2h
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(n - 2)(180°)
Shifted right 2 units.

36. How do you find the x-intercept of a graph?
A^m/b^m = (a/b)^m
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Set y = 0 - and solve.

37. Properties of zero 1
V = l^3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
0 is the only number that is neither positive nor negative.

38. What is a negative exponent?
Then the quotient y/x is a constant.
For any number n: x^-n means 1/x^n.
V = lwh
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. What is a fractional exponent?
In the expression x^b - x is the base and b is the exponent.
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.
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.

40. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
For any right triangle - a^2 + b^2 = c^2.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
[(x1 + x2)/2] -[(y1 + y2)/2]

41. What is the formula for the area of a triangle?
Set y = 0 - and solve.
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)
A = (1/2)bh.

42. Important binomial 3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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 = bh
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

43. In a circle of radius r - what is the formula for the diameter?
D = 2r
Shifted right 2 units.
Corresponding sides of similar triangles are in proportion.
Then the quotient y/x is a constant.

44. What is the distributive law?
0 is a multiple of every integer.
They are both the same. A divisor or factor of an integer leaves no remainder.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Their sum is 180°.

45. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
At least one of the factors is 0.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Write the percent over 100 and reduce.

46. Properties of zero 3
0 is a multiple of every integer.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
180°. If two or more angles form a straight angle - their sum is 180°.
If a is negative and b is positive - then a < 0 < b.

47. What is the formula for the surface area of a rectangular solid?
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.
All positive and negative whole numbers - and zero.
Then the product xy is a constant.
A = 2(lw + lh + hw)

48. What is the ratio of similitude?
Corresponding sides of similar triangles are in proportion.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The ratio of corresponding sides of similar triangles.
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.

49. If you were given the graph of y = f(x) - what does f(a) represent?
Arc = (x°/360)(2pr) where x is the central angle.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Avg = sum of n numbers/n
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

50. Properties of zero 2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
0 is a multiple of every integer.
If a is negative and b is positive - then a < 0 < b.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

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