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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 surface area of a rectangular solid?
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 set of all ordered pairs (x -y) such that y = f(x).
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 = 2(lw + lh + hw)

2. Important binomial 1
A = (1/2)bh.
A = pr^2
(x + y)(x - y) = x^2 - y^2
For any number b: b = -b if and only if b = 0.

3. How do you find the y-intercept of a graph?
360°
A = 6(l^2)
Set x = 0 - and solve.
Avg = sum of n numbers/n

4. What are the quotient and the remainder?

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5. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Write the percent over 100 and reduce.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

6. How do you find the slope of a line?
V = lwh
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
M = (y2 - y1)/(x2 - x1)
Shifted right 2 units.

7. What are the properties of a parallelogram?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For any number b: b = -b if and only if b = 0.

8. What is a divisor and a factor of an integer?
Their sum is 90°.
A = lw
They are both the same. A divisor or factor of an integer leaves no remainder.
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.

9. What is a composite number?
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.
Area = (x°/360)(pr^2) where x is the central angle.
An integer greater than one that is not prime.
No matter how many angles there are - the sum around the point is 360°.

10. What is the square root of a number?
360°
(n - 2)(180°)
(x + y)(x - y) = x^2 - y^2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

11. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted down 2 units.
(b^m)^n = b^mn
Avg = sum of n numbers/n

12. Properties of zero 1
A = bh
0 is the only number that is neither positive nor negative.
The ratio of corresponding sides of similar triangles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

13. In a circle of radius r - what is the formula for the circumference?
(n - 2)(180°)
No matter how many angles there are - the sum around the point is 360°.
C = p2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

14. What are the properties of a square?
The product of their slopes is -1 (negative reciprocal).
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
360°

15. How do you find the length of an arc of a circle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any integer n: 1^n = 1.
Arc = (x°/360)(2pr) where x is the central angle.
(x + y)(x - y) = x^2 - y^2

16. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Then the product xy is a constant.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Equal slopes.
360°

17. What is the volume of a cube?
A = 6(l^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°.
V = l^3
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

18. What are the important properties of a 45-45 - 90 triangle?
At least one of the factors is 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted left 2 units.
Corresponding sides of similar triangles are in proportion.

19. Properties of one 3
1 is a divisor (or factor) of every integer.
All positive and negative whole numbers - and zero.
Avg = sum of n numbers/n
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

20. What is the graph of a function?
1 is a divisor (or factor) of every integer.
The set of all ordered pairs (x -y) such that y = f(x).
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set y = 0 - and solve.

21. 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.
Cannot is 0 - must is 1 - all others are in between.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
B^m*b^n = b^m+n

22. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted down 2 units.

23. Properties of zero 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°.
A = [(s^2*v3)/4]
For any number b: b = -b if and only if b = 0.
B^m*b^n = b^m+n

24. What is an exponent?
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.
In the expression x^b - x is the base and b is the exponent.
Then the product xy is a constant.
No matter how many angles there are - the sum around the point is 360°.

25. What is a function?
Arc = (x°/360)(2pr) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(b^m)^n = b^mn

26. What is the formula for the volume of a rectangular solid?
Arc = (x°/360)(2pr) where x is the central angle.
360°
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 = lwh

27. What are the important properties of 30-60-90 triangle?
All positive and negative whole numbers - and zero.
Write the percent over 100 and reduce.
Arc = (x°/360)(2pr) where x is the central angle.
Is a right triangle with a ratio of sides x:xv3:2x.

28. Properties of one 1
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number a: a * 1 = a and a / 1 = a.
(Circumference/diameter) of a circle - or approximately 3.14.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

29. How do you find the probability that an event will occur?
A = pr^2
Set y = 0 - and solve.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

30. Properties of zero 3
All positive and negative whole numbers - and zero.
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.
(Circumference/diameter) of a circle - or approximately 3.14.
0 is a multiple of every integer.

31. What are the sum - difference - products - and quotient of two numbers?
Their sum is 90°.
A^m*b^m = (ab)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

32. Properties of zero 2
Set y = 0 - and solve.
If a is negative and b is positive - then a < 0 < b.
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 quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

33. 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.
A fraction whose denominator is 100 i.e. 17% = 17/100
A = bh
A^m/b^m = (a/b)^m

34. For what values of a function is the function undefined?
V = l^3
For any number a: a * 1 = a and a / 1 = a.
A^m/b^m = (a/b)^m
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

35. What is the formula for the volume of a cylinder?
0 is the only number that is neither positive nor negative.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
V = pr^2h

36. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Corresponding sides of similar triangles are in proportion.
Then the quotient y/x is a constant.
Even numbers are divisible by 2 and odd numbers are not.
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.

37. How do you convert a percent to a fraction or a decimal?
Cannot is 0 - must is 1 - all others are in between.
Write the percent over 100 and reduce.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
360°

38. What is the ratio of similitude?
V = lwh
The ratio of corresponding sides of similar triangles.
A = 2(lw + lh + hw)
Their sum is 180°.

39. What is true about the slopes of parallel lines?
D = 2r
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Corresponding sides of similar triangles are in proportion.
Equal slopes.

40. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Corresponding sides of similar triangles are in proportion.
Shifted left 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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 is the distributive law?
A = 6(l^2)
Write the percent over 100 and reduce.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
They are both the same. A divisor or factor of an integer leaves no remainder.

42. How do you find the x-intercept of a graph?
(n - 2)(180°)
Write the percent over 100 and reduce.
Set y = 0 - and solve.
M = (y2 - y1)/(x2 - x1)

43. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Shifted up 2 units.
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°.
If a is negative and b is positive - then a < 0 < b.

44. 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 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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Equal slopes.

45. What is true about the measures of the two acute angles in a right triangle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any right triangle - a^2 + b^2 = c^2.
Their sum is 90°.
Then the quotient y/x is a constant.

46. Law of exponents 4
P(e) = (# of favorable outcomes)/(# of possible outcomes)
They are both the same. A divisor or factor of an integer leaves no remainder.
Set y = 0 - and solve.
A^m*b^m = (ab)^m

47. Important binomial 3
An angle formed by extending the side of the polygon.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

48. What is the formula for the surface area of a cube?
A^m*b^m = (ab)^m
The two pairs of opposite angles formed are equal to each other.
Cannot is 0 - must is 1 - all others are in between.
A = 6(l^2)

49. What is a fractional exponent?
M = (y2 - y1)/(x2 - x1)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = 6(l^2)
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

50. How do you find a percent of a number?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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.
Write the percent as a decimal - and multiply.