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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. How do you find the length of an arc of a circle?
180. If two or more angles form a straight angle - their sum is 180.
1 is a divisor (or factor) of every integer.
Their sum is 90.
Arc = (x/360)(2pr) where x is the central angle.

2. Important binomial 1
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n
(x + y)(x - y) = x^2 - y^2

3. What is the formula for the volume of a cylinder?
(n - 2)(180)
V = pr^2h
B^m/b^n = b^m-n
Their sum is 90.

4. What formula is used for an average?
A = bh
Avg = sum of n numbers/n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

5. What is the area of a square?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = s^2 or A =d^2/2 where d is the diagonal
V = pr^2h
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.

6. What is special formula for the area of an equilateral triangle?
A = s^2 or A =d^2/2 where d is the diagonal
A = [(s^2*v3)/4]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An equation that states that two ratios are equivalent. 4/6 = 10/15

7. What is true about the slopes of parallel lines?
Equal slopes.
360
(x + y)(x - y) = x^2 - y^2
A^m/b^m = (a/b)^m

8. What are the sum - difference - products - and quotient of two numbers?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m/b^m = (a/b)^m
(x + y)(x - y) = x^2 - y^2

9. What is the ratio of similitude?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted down 2 units.
B^m*b^n = b^m+n
The ratio of corresponding sides of similar triangles.

10. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
The set of all ordered pairs (x -y) such that y = f(x).
Shifted down 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
1 is the smallest positive odd integer.

11. 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.
Cannot is 0 - must is 1 - all others are in between.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number b: b = -b if and only if b = 0.

12. What is the sum of the measures of all angles around a point?
No matter how many angles there are - the sum around the point is 360.
Even numbers are divisible by 2 and odd numbers are not.
1 is the smallest positive odd integer.
A = 2(lw + lh + hw)

13. What is the graph of a function?
360
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The set of all ordered pairs (x -y) such that y = f(x).

14. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
D = 2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

15. What is the distributive law?
A = s^2 or A =d^2/2 where d is the diagonal
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A^m/b^m = (a/b)^m
Equal slopes.

16. What is the sum of the measures of the n angles of a polygon with n sides?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(n - 2)(180)
At least one of the factors is 0.

17. 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.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
A = 6(l^2)
(Circumference/diameter) of a circle - or approximately 3.14.

18. What is a negative exponent?
A = lw
For any number n: x^-n means 1/x^n.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any right triangle - a^2 + b^2 = c^2.

19. What is the measure of a straight angle?
A^m*b^m = (ab)^m
A = [(s^2*v3)/4]
180. If two or more angles form a straight angle - their sum is 180.
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.

20. What is p?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = 2(lw + lh + hw)
(Circumference/diameter) of a circle - or approximately 3.14.

21. Important binomial 2
V = l^3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(n - 2)(180)
A = pr^2

22. Properties of one 3
For any integer n: 1^n = 1.
1 is a divisor (or factor) of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
No matter how many angles there are - the sum around the point is 360.

23. What is the triangle inequality?
[(x1 + x2)/2] -[(y1 + y2)/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.
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.

24. What is a function?
A^m/b^m = (a/b)^m
(n - 2)(180)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
They are both the same. A divisor or factor of an integer leaves no remainder.

25. How do you find the probability that an event will occur?
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

26. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(n - 2)(180)

27. Law of exponents 4
Write the percent over 100 and reduce.
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 = lw
A^m*b^m = (ab)^m

28. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
They are both the same. A divisor or factor of an integer leaves no remainder.
360
An angle formed by extending the side of the polygon.
Shifted right 2 units.

29. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A = [(s^2*v3)/4]
360
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Their sum is 180.

30. What is an exterior angle of a triangle?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any right triangle - a^2 + b^2 = c^2.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

31. What is a composite number?
The ratio of corresponding sides of similar triangles.
An integer greater than one that is not prime.
An angle formed by extending the side of the polygon.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

32. What are the quotient and the remainder?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Arc = (x/360)(2pr) where x is the central angle.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m/b^n = b^m-n

33. Properties of zero 1
A = 6(l^2)
B^m*b^n = b^m+n
Corresponding sides of similar triangles are in proportion.
0 is the only number that is neither positive nor negative.

34. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
360

35. How do you convert a percent to a fraction or a decimal?
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.
180. If two or more angles form a straight angle - their sum is 180.
B^m*b^n = b^m+n
Write the percent over 100 and reduce.

36. What is a percent?
V = pr^2h
Write the percent over 100 and reduce.
A fraction whose denominator is 100 i.e. 17% = 17/100
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

37. What is an even and an odd number?
Set x = 0 - and solve.
A = bh
The ratio of corresponding sides of similar triangles.
Even numbers are divisible by 2 and odd numbers are not.

38. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
An angle formed by extending the side of the polygon.
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.
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.

39. Properties of one 4
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = pr^2
Avg = sum of n numbers/n
1 is the smallest positive odd integer.

40. What are the median and the mode of a set of data?
For any right triangle - a^2 + b^2 = c^2.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

41. What are the properties of a parallelogram?
360
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
V = pr^2h

42. In a circle of radius r - what is the formula for the area?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = pr^2

43. What is the formula for the surface area of a cube?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = 2(lw + lh + hw)
Divide - then multiply by 100.
A = 6(l^2)

44. What is true about the slopes of perpendicular lines?
A = pr^2
The product of their slopes is -1 (negative reciprocal).
0 is a multiple of every integer.
0 is the only number that is neither positive nor negative.

45. If the product of two or more numbers is 0 - what do you know about the numbers?
For any integer n: 1^n = 1.
The two pairs of opposite angles formed are equal to each other.
At least one of the factors is 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

46. For what values of a function is the function undefined?
0 is the only number that is neither positive nor negative.
The ratio of corresponding sides of similar triangles.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

47. Properties of one 2
Their sum is 90.
For any integer n: 1^n = 1.
All positive and negative whole numbers - and zero.
A = lw

48. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Set x = 0 - and solve.

49. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Equal slopes.
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.

50. How you convert a fraction or a decimal to a percent?
V = lwh
A = (1/2)bh.
Write the percent as a decimal - and multiply.
Divide - then multiply by 100.

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