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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 a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
20.5
(a - b)(a + b)
The set of output values for a function.

2. Solve the quadratic equation ax^2 + bx + c= 0
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
0

3. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
F(x) - c
53 - 59
The curve opens downward and the vertex is the maximum point on the graph.

4. What is the percent formula?
A reflection about the axis.
$3 -500 in the 9% and $2 -500 in the 7%.
Part = Percent X Whole
1/2 times 7/3

5. Which quandrant is the lower right hand?
4725
IV
6 : 1 : 2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

6. What is an isoceles triangle?
Two equal sides and two equal angles.
A= I (1 + (r/c))^tC - where I is the investment - C is the number of times compounded annually - and t is the number of years.
A = I (1 + rt)
G(x) = {x}

7. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
F(x) + c
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
3
4.25 - 6 - 22

8. What is the slope of a vertical line?

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9. When the 'a' in the parabola is negative...
3 - -3
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
F(x) - c
The curve opens downward and the vertex is the maximum point on the graph.

10. What is the area of a regular hexagon with side 6?
II
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
180 degrees
No - only like radicals can be added.

11. Simplify the expression (p^2 - q^2)/ -5(q - p)
Cd
x^(2(4)) =x^8 = (x^4)^2
(p + q)/5
(n-2) x 180

12. Evaluate 4/11 + 11/12
1 & 37/132
1:sqrt3:2
72
The curve opens upward and the vertex is the minimal point on the graph.

13. (6sqrt3) x (2sqrt5) =
(a + b)^2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
441000 = 1 10 10 10 21 * 21
500

14. Define a 'monomial'
4:5
Angle/360 x 2(pi)r
An expression with just one term (-6x - 2a^2)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

15. Factor a^2 + 2ab + b^2
90
(a + b)^2
All numbers multiples of 1.
3

16. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
No - only like radicals can be added.
70
62.5%
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)

17. Formula to find a circle'S circumference from its diameter?
3
An arc is a portion of a circumference of a circle.
1
C = (pi)d

18. 5/8 in percent?
Part = Percent X Whole
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
62.5%
Pi is the ratio of a circle'S circumference to its diameter.

19. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
62.5%
4725
A set with no members - denoted by a circle with a diagonal through it.

20. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
$3 -500 in the 9% and $2 -500 in the 7%.
1
Sector area = (n/360) X (pi)r^2
413.03 / 10^4 (move the decimal point 4 places to the left)

21. What does scientific notation mean?
A 30-60-90 triangle.
87.5%
All numbers multiples of 1.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

22. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
A central angle is an angle formed by 2 radii.
1
Yes. [i.e. f(x) = x^2 - 1
4096

23. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
From northeast - counterclockwise. I - II - III - IV
Lies opposite the greater angle

24. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
10
A central angle is an angle formed by 2 radii.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

25. What are complementary angles?
No - only like radicals can be added.
5 OR -5
(amount of increase/original price) x 100%
Two angles whose sum is 90.

26. The ratio of the areas of two similar polygons is ...
N! / (k!)(n-k)!
27^(-4)
... the square of the ratios of the corresponding sides.
12sqrt2

27. 60 < all primes <70
53 - 59
61 - 67
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
2 & 3/7

28. a^2 - b^2
(a - b)(a + b)
A = I (1 + rt)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
0

29. What is the set of elements which can be found in either A or B?
The union of A and B.
(amount of increase/original price) x 100%
10! / 3!(10-3)! = 120
Yes. [i.e. f(x) = x^2 - 1

30. What are the real numbers?
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)
90
The set of elements found in both A and B.
Area of the base X height = (pi)hr^2

31. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
The two xes after factoring.
7 / 1000
(a + b)^2

32. What is the surface area of a cylinder with radius 5 and height 8?
1/a^6
An isosceles right triangle.
130pi
13pi / 2

33. 25^(1/2) or sqrt. 25 =
5 OR -5
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
90 degrees
$3 -500 in the 9% and $2 -500 in the 7%.

34. Can the output value of a function have more than one input value?
Yes. [i.e. f(x) = x^2 - 1
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
0
The set of output values for a function.

35. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
10! / (10-3)! = 720
3
Angle/360 x 2(pi)r
(a + b)^2

36. What is a subset?
The sum of digits is divisible by 9.
The curve opens upward and the vertex is the minimal point on the graph.
A grouping of the members within a set based on a shared characteristic.
N! / (k!)(n-k)!

37. 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?
180 degrees
When the function is not defined for all real numbers -; only a subset of the real numbers.
3
N! / (n-k)!

38. (-1)^3 =
No - the input value has exactly one output.
55%
All numbers multiples of 1.
1

39. Which quadrant is the lower left hand?
III
1 & 37/132
41 - 43 - 47
10

40. a^2 - b^2 =
... the square of the ratios of the corresponding sides.
3 - -3
.0004809 X 10^11
(a - b)(a + b)

41. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
11 - 13 - 17 - 19
1
y = (x + 5)/2
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)

42. Describe the relationship between the graphs of x^2 and (1/2)x^2
Relationship cannot be determined (what if x is negative?)
The second graph is less steep.
Move the decimal point to the right x places
(a - b)(a + b)

43. What is the sum of the angles of a triangle?
No - the input value has exactly one output.
4.25 - 6 - 22
180 degrees
Infinite.

44. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
10! / (10-3)! = 720
72
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
The greatest value minus the smallest.

45. Evaluate (4^3)^2
2(pi)r^2 + 2(pi)rh
x^(6-3) = x^3
$11 -448
4096

46. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
4096
1.7
The objects within a set.
75:11

47. a^0 =
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
1
23 - 29
2.592 kg

48. Which is greater? 200x^295 or 10x^294?
The curve opens upward and the vertex is the minimal point on the graph.
III
12sqrt2
Relationship cannot be determined (what if x is negative?)

49. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
0
Its negative reciprocal. (-b/a)
Sector area = (n/360) X (pi)r^2
N! / (k!)(n-k)!

50. What are the irrational numbers?

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GRE Math: Common Errors

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