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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. 7/8 in percent?
87.5%
The union of A and B.
23 - 29
Undefined

2. Area of a triangle?
13pi / 2
(base*height) / 2
Infinite.
y = 2x^2 - 3

3. What is the order of operations?
The set of input values for a function.
4sqrt3. The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...
Move the decimal point to the right x places
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

4. 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.
...multiply by 100.
Angle/360 x 2(pi)r
(n-2) x 180

5. Which quadrant is the upper right hand?
The set of elements which can be found in either A or B.
I
Divide by 100.
... the square of the ratios of the corresponding sides.

6. What is the 'Solution' for a system of linear equations?
F(x + c)
An expression with just one term (-6x - 2a^2)
Yes. [i.e. f(x) = x^2 - 1
The point of intersection of the systems.

7. How many sides does a hexagon have?
G(x) = {x}
6
The shortest arc between points A and B on a circle'S diameter.
Undefined

8. How many 3-digit positive integers are even and do not contain the digit 4?
The two xes after factoring.
288 (8 9 4)
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
F(x + c)

9. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
18
48
500
F(x) - c

10. A number is divisible by 9 if...
4a^2(b)
The sum of digits is divisible by 9.
Cd
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

11. If a=-1 and b=3 - what is the value of (4(a^3)(b^2) - 12(a^2)(b^5)) / (16(a^3)(b^2))?
Cd
The set of elements which can be found in either A or B.
20.5
31 - 37

12. 1/2 divided by 3/7 is the same as
1/2 times 7/3
Divide by 100.
A tangent is a line that only touches one point on the circumference of a circle.
16.6666%

13. P and r are factors of 100. What is greater - pr or 100?
Indeterminable.
The sum of its digits is divisible by 3.
Undefined - because we can'T divide by 0.
The union of A and B.

14. What is a major arc?

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15. Simplify the expression (p^2 - q^2)/ -5(q - p)
72
23 - 29
(p + q)/5
N! / (k!)(n-k)!

16. When the 'a' in the parabola is negative...
3/2 - 5/3
288 (8 9 4)
x(x - y + 1)
The curve opens downward and the vertex is the maximum point on the graph.

17. The objects in a set are called two names:
G(x) = {x}
27^(-4)
Two equal sides and two equal angles.
Members or elements

18. The perimeter of a square is 48 inches. The length of its diagonal is:
28. n = 8 - k = 2. n! / k!(n-k)!
37.5%
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)
12sqrt2

19. A number is divisible by 3 if ...
6
9 & 6/7
83.333%
The sum of its digits is divisible by 3.

20. 5/6 in percent?
The longest arc between points A and B on a circle'S diameter.
10! / (10-3)! = 720
1:sqrt3:2
83.333%

21. What is the 'union' of A and B?
The direction of the inequality is reversed.
The set of elements which can be found in either A or B.
F(x-c)
Ax^2 + bx + c where a -b and c are constants and a /=0

22. 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)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The steeper the slope.
x^(4+7) = x^11

23. What is the graph of f(x) shifted left c units or spaces?
A set with no members - denoted by a circle with a diagonal through it.
90 degrees
F(x + c)
The empty set - denoted by a circle with a diagonal through it.

24. What is the graph of f(x) shifted downward c units or spaces?
6
75:11
F(x) - c
288 (8 9 4)

25. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
11 - 13 - 17 - 19
7 / 1000
The third side is greater than the difference and less than the sum.

26. Which is greater? 64^5 or 16^8
90 degrees
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
5 OR -5
Angle/360 x 2(pi)r

27. If the two sides of a triangle are unequal then the longer side...
87.5%
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Triangles with same measure and same side lengths.
Lies opposite the greater angle

28. 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?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
F(x + c)
N! / (k!)(n-k)!
A subset.

29. 413.03 x 10^(-4) =
When the function is not defined for all real numbers -; only a subset of the real numbers.
Part = Percent X Whole
An infinite set.
413.03 / 10^4 (move the decimal point 4 places to the left)

30. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A chord is a line segment joining two points on a circle.
y = (x + 5)/2
The union of A and B.

31. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
The curve opens downward and the vertex is the maximum point on the graph.
13
4096
8

32. (-1)^2 =
1
0
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
(n-2) x 180

33. How to find the diagonal of a rectangular solid?
28. n = 8 - k = 2. n! / k!(n-k)!
1
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
(base*height) / 2

34. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A circle centered at -2 - -2 with radius 3.
... the square of the ratios of the corresponding sides.
The overlapping sections.

35. 50 < all primes< 60
53 - 59
Angle/360 x (pi)r^2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
G(x) = {x}

36. What is the ratio of the sides of a 30-60-90 triangle?
3
I
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
1:sqrt3:2

37. (a^-1)/a^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)
1/a^6
The second graph is less steep.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

38. Formula to calculate arc length?
An isosceles right triangle.
1.0843 X 10^11
The curve opens downward and the vertex is the maximum point on the graph.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

39. Find the surface area of a cylinder with radius 3 and height 12.
2 & 3/7
90 degrees
90pi
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

40. What are the rational numbers?
500
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
130pi
Factors are few - multiples are many.

41. What is the surface area of a cylinder with radius 5 and height 8?
1
130pi
Two angles whose sum is 90.
True

42. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Relationship cannot be determined (what if x is negative?)
(a - b)^2
28. n = 8 - k = 2. n! / k!(n-k)!
The longest arc between points A and B on a circle'S diameter.

43. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
72
Ax^2 + bx + c where a -b and c are constants and a /=0
8

44. What is the ratio of the sides of an isosceles right triangle?
130pi
0
2
1:1:sqrt2

45. What is the set of elements found in both A and B?
Part = Percent X Whole
(a - b)(a + b)
The set of elements found in both A and B.
The interesection of A and B.

46. How many multiples does a given number have?
3 - -3
4:5
12sqrt2
Infinite.

47. Which quandrant is the lower right hand?
A 30-60-90 triangle.
All numbers multiples of 1.
20.5
IV

48. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
70
87.5%
10! / 3!(10-3)! = 120
2

49. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Its negative reciprocal. (-b/a)
2^9 / 2 = 256
Cd
...multiply by 100.

50. What is the 'Restricted domain of a function'?
20.5
Undefined - because we can'T divide by 0.
II
When the function is not defined for all real numbers -; only a subset of the real numbers.

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GRE Math: Common Errors

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