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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 'domain' of a function?
The set of input values for a function.
3/2 - 5/3
(a + b)^2
The set of output values for a function.

2. (6sqrt3) x (2sqrt5) =
1/2 times 7/3
Ax^2 + bx + c where a -b and c are constants and a /=0
C = (pi)d
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

3. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
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.
Two angles whose sum is 180.
13pi / 2

4. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
The sum of its digits is divisible by 3.
Relationship cannot be determined (what if x is negative?)
The third side is greater than the difference and less than the sum.

5. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
23 - 29
The curve opens upward and the vertex is the minimal point on the graph.
1

6. What is an arc of a circle?
(amount of decrease/original price) x 100%
The sum of digits is divisible by 9.
An arc is a portion of a circumference of a circle.
Even

7. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
1
180 degrees

8. 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?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Sqrt 12
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
N! / (n-k)!

9. What are the roots of the quadrinomial x^2 + 2x + 1?
1.0843 X 10^11
The two xes after factoring.
3
4.25 - 6 - 22

10. What is the graph of f(x) shifted upward c units or spaces?
Its divisible by 2 and by 3.
F(x) + c
12sqrt2
1/a^6

11. What is the name of set with a number of elements which cannot be counted?
From northeast - counterclockwise. I - II - III - IV
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
An infinite set.
Two angles whose sum is 90.

12. 5x^2 - 35x -55 = 0
G(x) = {x}
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(n-2) x 180
The sum of its digits is divisible by 3.

13. A number is divisible by 6 if...
True
6 : 1 : 2
Its divisible by 2 and by 3.
Two angles whose sum is 180.

14. Reduce: 4.8 : 0.8 : 1.6
1
27^(-4)
6 : 1 : 2
From northeast - counterclockwise. I - II - III - IV

15. 5/6 in percent?
All numbers multiples of 1.
C = 2(pi)r
No - the input value has exactly one output.
83.333%

16. x^4 + x^7 =
x^(4+7) = x^11
When the function is not defined for all real numbers -; only a subset of the real numbers.
A = pi(r^2)
An angle which is supplementary to an interior angle.

17. 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?
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
.0004809 X 10^11
Angle/360 x (pi)r^2
83.333%

18. What is the order of operations?
3 - -3
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.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

19. Which quadrant is the lower left hand?
III
Cd
Area of the base X height = (pi)hr^2
Divide by 100.

20. Which quandrant is the lower right hand?
9 : 25
IV
180
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

21. Which is greater? 200x^295 or 10x^294?
413.03 / 10^4 (move the decimal point 4 places to the left)
Relationship cannot be determined (what if x is negative?)
6
(a - b)(a + b)

22. a^0 =
The objects within a set.
A reflection about the origin.
Sector area = (n/360) X (pi)r^2
1

23. What is the slope of a horizontal line?
37.5%
(a - b)(a + b)
0
1:sqrt3:2

24. To convert a percent to a fraction....
The point of intersection of the systems.
The interesection of A and B.
Divide by 100.
288 (8 9 4)

25. Simplify the expression (p^2 - q^2)/ -5(q - p)
(base*height) / 2
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
(p + q)/5
The direction of the inequality is reversed.

26. Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
180 degrees
4096
4a^2(b)

27. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
13
3/2 - 5/3
x= (1.2)(.8)lw
Cd

28. a^2 + 2ab + b^2
2 & 3/7
(a + b)^2
Even
130pi

29. 6w^2 - w - 15 = 0
A circle centered at -2 - -2 with radius 3.
3/2 - 5/3
72
(a + b)^2

30. 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)?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The set of input values for a function.
y = (x + 5)/2
0

31. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
F(x + c)
3
13pi / 2
Pi is the ratio of a circle'S circumference to its diameter.

32. What is the graph of f(x) shifted left c units or spaces?
The set of input values for a function.
1 & 37/132
F(x + c)
1

33. What is a central angle?
Even
A central angle is an angle formed by 2 radii.
F(x-c)
(a - b)^2

34. 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)
71 - 73 - 79
0
4.25 - 6 - 22
3/2 - 5/3

35. 3/8 in percent?
37.5%
A circle centered at -2 - -2 with radius 3.
20.5
Part = Percent X Whole

36. 10<all primes<20
The set of input values for a function.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
11 - 13 - 17 - 19
Sqrt 12

37. When does a function automatically have a restricted domain (2)?
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...
90pi
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

38. Evaluate 3& 2/7 / 1/3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
12sqrt2
$11 -448
9 & 6/7

39. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
12.5%
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
71 - 73 - 79

40. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
4.25 - 6 - 22
Triangles with same measure and same side lengths.
18
6

41. x^6 / x^3
A circle centered on the origin with radius 8.
3
x^(6-3) = x^3
Arc length = (n/360) x pi(2r) where n is the number of degrees.

42. What is the name for a grouping of the members within a set based on a shared characteristic?
True
A reflection about the axis.
55%
A subset.

43. What does the graph x^2 + y^2 = 64 look like?
52
A circle centered on the origin with radius 8.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
x^(4+7) = x^11

44. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
An infinite set.
Factors are few - multiples are many.
62.5%

45. Length of an arc of a circle?
Angle/360 x 2(pi)r
Angle/360 x (pi)r^2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
75:11

46. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
True
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
No - only like radicals can be added.

47. 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))?
A central angle is an angle formed by 2 radii.
12! / 5!7! = 792
An isosceles right triangle.
20.5

48. How to find the area of a sector?
413.03 / 10^4 (move the decimal point 4 places to the left)
12sqrt2
72
Angle/360 x (pi)r^2

49. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
4a^2(b)
2 & 3/7
The interesection of A and B.
Move the decimal point to the right x places

50. Define a 'Term' -
A tangent is a line that only touches one point on the circumference of a circle.
20.5
A term is a numerical constant or the product (or quotient) of a numerical constant and one or more variables. (3x - 4x^2 and 2a/c)
C = 2(pi)r

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