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GRE Math: Common Errors

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 ratio of the sides of a 30-60-90 triangle?
The curve opens downward and the vertex is the maximum point on the graph.
90 degrees
8
1:sqrt3:2

2. What is an arc of a circle?
The longest arc between points A and B on a circle'S diameter.
An arc is a portion of a circumference of a circle.
55%
10! / 3!(10-3)! = 120

3. Simplify the expression [(b^2 - c^2) / (b - c)]
(a - b)^2
... the square of the ratios of the corresponding sides.
(base*height) / 2
(b + c)

4. a^0 =
(a - b)^2
1
1.7
A central angle is an angle formed by 2 radii.

5. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
I
Two angles whose sum is 180.
2.592 kg
2(pi)r^2 + 2(pi)rh

6. What is the name of set with a number of elements which cannot be counted?
I
Members or elements
1/2 times 7/3
An infinite set.

7. How to determine percent decrease?
71 - 73 - 79
37.5%
(amount of decrease/original price) x 100%
72

8. Find the surface area of a cylinder with radius 3 and height 12.
90pi
2^9 / 2 = 256
2(pi)r^2 + 2(pi)rh
4725

9. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
(amount of increase/original price) x 100%
13
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

10. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
7 / 1000
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
x(x - y + 1)

11. What are 'Supplementary angles?'
180
Two angles whose sum is 180.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

12. Formula to calculate arc length?
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
180
Arc length = (n/360) x pi(2r) where n is the number of degrees.
8

13. Formula of rectangle where l increases by 20% and w decreases by 20%
x= (1.2)(.8)lw
83.333%
The set of input values for a function.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

14. What is an isoceles triangle?
9 : 25
Two equal sides and two equal angles.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
28. n = 8 - k = 2. n! / k!(n-k)!

15. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
(a + b)^2
37.5%
I
1

16. What is the area of a regular hexagon with side 6?
71 - 73 - 79
The steeper the slope.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
72

17. When does a function automatically have a restricted domain (2)?
...multiply by 100.
N! / (k!)(n-k)!
52
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

18. What is the absolute value function?
G(x) = {x}
Undefined - because we can'T divide by 0.
The set of output values for a function.
2

19. a^2 - 2ab + b^2
3/2 - 5/3
180
62.5%
(a - b)^2

20. The objects in a set are called two names:
The shortest arc between points A and B on a circle'S diameter.
Members or elements
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Ax^2 + bx + c where a -b and c are constants and a /=0

21. What is the 'Solution' for a system of linear equations?
(a + b)^2
37.5%
The point of intersection of the systems.
N! / (k!)(n-k)!

22. (a^-1)/a^5
The sum of its digits is divisible by 3.
1/a^6
3
Relationship cannot be determined (what if x is negative?)

23. How to determine percent increase?
C = 2(pi)r
(amount of increase/original price) x 100%
III
x^(6-3) = x^3

24. Whats the difference between factors and multiples?
1
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
(b + c)
Factors are few - multiples are many.

25. A number is divisible by 4 is...
1:sqrt3:2
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Its last two digits are divisible by 4.
16.6666%

26. What are the members or elements of a set?
x= (1.2)(.8)lw
62.5%
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The objects within a set.

27. 40 < all primes<50
12.5%
41 - 43 - 47
2
Yes - like radicals can be added/subtracted.

28. Evaluate 4/11 + 11/12
The empty set - denoted by a circle with a diagonal through it.
1:sqrt3:2
1 & 37/132
Angle/360 x (pi)r^2

29. What are complementary angles?
Two angles whose sum is 90.
2sqrt6
(amount of decrease/original price) x 100%
71 - 73 - 79

30. What is the slope of a vertical line?

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31. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
G(x) = {x}
1 & 37/132
The steeper the slope.

32. Simplify 9^(1/2) X 4^3 X 2^(-6)?
The set of input values for a function.
3
Triangles with same measure and same side lengths.
(a - b)^2

33. What is the set of elements which can be found in either A or B?
The union of A and B.
$3 -500 in the 9% and $2 -500 in the 7%.
Relationship cannot be determined (what if x is negative?)
4096

34. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
83.333%
2.4. We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6
2.592 kg
(b + c)

35. What is the 'Range' of a series of numbers?
2^9 / 2 = 256
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The greatest value minus the smallest.
An arc is a portion of a circumference of a circle.

36. What is the intersection of A and B?
The set of elements found in both A and B.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
True
Infinite.

37. 1/2 divided by 3/7 is the same as
1/2 times 7/3
288 (8 9 4)
$11 -448
37.5%

38. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
Angle/360 x (pi)r^2
An expression with just one term (-6x - 2a^2)
A = pi(r^2)

39. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1
1/2 times 7/3
(p + q)/5
The empty set - denoted by a circle with a diagonal through it.

40. Define an 'expression'.
An algebraic expression is a combination of one of more terms. Terms in an expression are separated by either addition or subtraction signs. (3xy - 4ab - -5cd - x^2 + x - 1)
Yes - like radicals can be added/subtracted.
Angle/360 x 2(pi)r
Undefined - because we can'T divide by 0.

41. 20<all primes<30
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
IV
N! / (k!)(n-k)!
23 - 29

42. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
1
(a - b)(a + b)
An isosceles right triangle.
4:5

43. Volume for a cylinder?
23 - 29
Area of the base X height = (pi)hr^2
4725
12sqrt2

44. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
(amount of decrease/original price) x 100%
N! / (n-k)!
The set of elements found in both A and B.
62.5%

45. Formula for the area of a circle?
13pi / 2
The set of input values for a function.
Its divisible by 2 and by 3.
A = pi(r^2)

46. Formula to find a circle'S circumference from its diameter?
C = (pi)d
Members or elements
180
10! / (10-3)! = 720

47. 7/8 in percent?
87.5%
(a + b)^2
The empty set - denoted by a circle with a diagonal through it.
Its negative reciprocal. (-b/a)

48. What is the 'union' of A and B?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
48
Its last two digits are divisible by 4.
The set of elements which can be found in either A or B.

49. Factor a^2 + 2ab + b^2
Sector area = (n/360) X (pi)r^2
52
(a + b)^2
Relationship cannot be determined (what if x is negative?)

50. Can the output value of a function have more than one input value?
1.0843 X 10^11
Yes. [i.e. f(x) = x^2 - 1
4096
2.592 kg

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GRE Math: Common Errors

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