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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 is the volume of a cube?
A = 2(lw + lh + hw)
V = l^3
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

2. If you were given the graph of y = f(x) - what does f(a) represent?
B^m*b^n = b^m+n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
No matter how many angles there are - the sum around the point is 360°.
M = (y2 - y1)/(x2 - x1)

3. Properties of zero 3
0 is a multiple of every integer.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Divide - then multiply by 100.
Set x = 0 - and solve.

4. How do you convert a percent to a fraction or a decimal?
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is a multiple of every integer.
Write the percent over 100 and reduce.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

5. Law of exponents 5
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A^m/b^m = (a/b)^m
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = l^3

6. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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 = pr^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)

7. What is true about the measures of the two acute angles in a right triangle?
Write the percent as a decimal - and multiply.
Their sum is 90°.
Shifted up 2 units.
For any integer n: 1^n = 1.

8. What is a multiple of an integer?
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

9. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 180°.
(b^m)^n = b^mn

10. What is a Venn diagram?
How steep the line is. Horizontal line = 0 - vertical has no slope.
If a is negative and b is positive - then a < 0 < b.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

11. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A = pr^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted left 2 units.
For any number a: a * 1 = a and a / 1 = a.

12. How do you find the y-intercept of a graph?
Shifted down 2 units.
Set x = 0 - and solve.
(n - 2)(180°)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

13. What is a percent?
Shifted down 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100
No matter how many angles there are - the sum around the point is 360°.
Corresponding sides of similar triangles are in proportion.

14. 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.
A = pr^2
V = l^3
Is a right triangle with a ratio of sides x:xv3:2x.

15. Important binomial 3
A fraction whose denominator is 100 i.e. 17% = 17/100
(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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

16. What is a ratio?

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17. Properties of zero 4
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = 2(lw + lh + hw)

18. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any right triangle - a^2 + b^2 = c^2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
B^m/b^n = b^m-n

19. What is the ratio of similitude?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
The two pairs of opposite angles formed are equal to each other.
1 is the smallest positive odd integer.
The ratio of corresponding sides of similar triangles.

20. What is the measure of a straight angle?
Cannot is 0 - must is 1 - all others are in between.
360°
180°. If two or more angles form a straight angle - their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]

21. What does it mean if y is directly proportional to x?
360°
Then the quotient y/x is a constant.
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 = [(s^2*v3)/4]

22. What is the formula for the surface area of a rectangular solid?
Arc = (x°/360)(2pr) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.
A = 2(lw + lh + hw)
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

23. How do you find a percent of a number?
Arc = (x°/360)(2pr) where x is the central angle.
The product of their slopes is -1 (negative reciprocal).
Write the percent as a decimal - and multiply.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

24. What is true about the slopes of perpendicular lines?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
V = l^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.
The product of their slopes is -1 (negative reciprocal).

25. What is true about the slopes of parallel lines?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted up 2 units.
A = 6(l^2)
Equal slopes.

26. What is the formula for the volume of a cylinder?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
V = pr^2h
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.

27. What is an integer?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
An integer greater than one that is not prime.
All positive and negative whole numbers - and zero.
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.

28. What is true about the measures of the three angles in a 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.
0 is a multiple of every integer.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 180°.

29. What is a composite number?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The product of their slopes is -1 (negative reciprocal).
An integer greater than one that is not prime.

30. What does it mean if y is inversely proportional to x?
Even numbers are divisible by 2 and odd numbers are not.
Then the product xy is a constant.
A = bh
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

31. Properties of square roots
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
V = l^3
Shifted right 2 units.

32. Important binomial 1
C = p2r
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°.
(x + y)(x - y) = x^2 - y^2
At least one of the factors is 0.

33. What is the distance formula?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Is a right triangle with a ratio of sides x:xv3:2x.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

34. What is the midpoint formula?
How steep the line is. Horizontal line = 0 - vertical has no slope.
[(x1 + x2)/2] -[(y1 + y2)/2]
An integer greater than one that is not prime.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

35. What are the properties of a rectangle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = bh
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

36. Properties of zero 2
At least one of the factors is 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
If a is negative and b is positive - then a < 0 < b.
For any number b: b = -b if and only if b = 0.

37. What are the properties of a square?
Is a right triangle with a ratio of sides x:xv3:2x.
C = p2r
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
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.

38. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = [(s^2*v3)/4]
V = l^3

39. What is the distributive law?
For any integer n: 1^n = 1.
At least one of the factors is 0.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

40. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
How steep the line is. Horizontal line = 0 - vertical has no slope.
V = l^3
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.

41. What are the important properties of a 45-45 - 90 triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
The product of their slopes is -1 (negative reciprocal).
For any integer n: 1^n = 1.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

42. How do you find the x-intercept of a graph?
No matter how many angles there are - the sum around the point is 360°.
Set y = 0 - and solve.
A = 2(lw + lh + hw)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

43. How do you find the length of an arc of a circle?
A = 2(lw + lh + hw)
Arc = (x°/360)(2pr) where x is the central angle.
B^m/b^n = b^m-n
Write the percent over 100 and reduce.

44. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted up 2 units.
[(x1 + x2)/2] -[(y1 + y2)/2]
An integer greater than one that is not prime.

45. Law of exponents 4
Arc = (x°/360)(2pr) where x is the central angle.
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.
For any number b: b = -b if and only if b = 0.

46. 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.
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.
The ratio of corresponding sides of similar triangles.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

47. What is an even and an odd number?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = 6(l^2)
(n - 2)(180°)
Even numbers are divisible by 2 and odd numbers are not.

48. What is the formula for the area of a rectangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Then the quotient y/x is a constant.
Write the percent as a decimal - and multiply.
A = lw

49. What is the Pythagorean theorem?
V = l^3
1 is the smallest positive odd integer.
The product of their slopes is -1 (negative reciprocal).
For any right triangle - a^2 + b^2 = c^2.

50. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
An angle formed by extending the side of the polygon.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

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