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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. To convert a percent to a fraction....
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)
(a + b)^2
A chord is a line segment joining two points on a circle.
Divide by 100.

2. The objects in a set are called two names:
An infinite set.
90pi
Members or elements
The union of A and B.

3. What is the measure of an exterior angle of a regular pentagon?
7 / 1000
27^(-4)
Yes. [i.e. f(x) = x^2 - 1
72

4. Max and Min lengths for a side of a triangle?
1/2 times 7/3
The third side is greater than the difference and less than the sum.
.0004809 X 10^11
12.5%

5. Can you add sqrt 3 and sqrt 5?
1
No - only like radicals can be added.
Lies opposite the greater angle
F(x) + c

6. a^2 - b^2
4a^2(b)
2sqrt6
(a - b)(a + b)
The set of output values for a function.

7. Describe the relationship between 3x^2 and 3(x - 1)^2
(n-2) x 180
The union of A and B.
Infinite.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

8. P and r are factors of 100. What is greater - pr or 100?
83.333%
Indeterminable.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

9. 1/6 in percent?
16.6666%
1/(x^y)
Its divisible by 2 and by 3.
2

10. What is the 'union' of A and B?
10
The set of elements which can be found in either A or B.
Yes - like radicals can be added/subtracted.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

11. What is the 'Range' of a series of numbers?
IV
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
III
The greatest value minus the smallest.

12. What is the set of elements which can be found in either A or B?
.0004809 X 10^11
Its negative reciprocal. (-b/a)
11 - 13 - 17 - 19
The union of A and B.

13. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
All numbers multiples of 1.
A = pi(r^2)
IV
52

14. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
N! / (n-k)!
9 : 25
12! / 5!7! = 792
The set of input values for a function.

15. Formula for the area of a circle?
A = pi(r^2)
7 / 1000
6
The steeper the slope.

16. What is an exterior angle?
An angle which is supplementary to an interior angle.
The set of output values for a function.
The set of input values for a function.
3

17. What is the formula for compounded interest?
... the square of the ratios of the corresponding sides.
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.
The overlapping sections.
A set with no members - denoted by a circle with a diagonal through it.

18. x^(-y)=
5 OR -5
F(x-c)
1/(x^y)
Part = Percent X Whole

19. What is a piecewise equation?
4:5
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
3
27^(-4)

20. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
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)
Its divisible by 2 and by 3.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

21. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Sqrt 12
A circle centered at -2 - -2 with radius 3.
8

22. What is the surface area of a cylinder with radius 5 and height 8?
67 - 71 - 73
130pi
(p + q)/5
1

23. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
55%
3 - -3
(a + b)^2

24. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Undefined
(a + b)^2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

25. Write 10 -843 X 10^7 in scientific notation
1
Yes - like radicals can be added/subtracted.
48
1.0843 X 10^11

26. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
441000 = 1 10 10 10 21 * 21
0
413.03 / 10^4 (move the decimal point 4 places to the left)
62.5%

27. Factor x^2 - xy + x.
x(x - y + 1)
G(x) = {x}
4.25 - 6 - 22
C = 2(pi)r

28. 0^0
Undefined
An expression with just one term (-6x - 2a^2)
75:11
The curve opens downward and the vertex is the maximum point on the graph.

29. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Triangles with same measure and same side lengths.
28. n = 8 - k = 2. n! / k!(n-k)!
G(x) = {x}
1/(x^y)

30. What is the intersection of A and B?
Sqrt 12
The set of elements found in both A and B.
4725
An isosceles right triangle.

31. Circumference of a circle?
The two xes after factoring.
Diameter(Pi)
12! / 5!7! = 792
Triangles with same measure and same side lengths.

32. Simplify (a^2 + b)^2 - (a^2 - b)^2
413.03 / 10^4 (move the decimal point 4 places to the left)
1
4a^2(b)
90 degrees

33. 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?
The curve opens downward and the vertex is the maximum point on the graph.
$3 -500 in the 9% and $2 -500 in the 7%.
Infinite.
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)

34. How to determine percent increase?
2(pi)r^2 + 2(pi)rh
The point of intersection of the systems.
$3 -500 in the 9% and $2 -500 in the 7%.
(amount of increase/original price) x 100%

35. 60 < all primes <70
Lies opposite the greater angle
61 - 67
18
16.6666%

36. To multiply a number by 10^x
Move the decimal point to the right x places
An arc is a portion of a circumference of a circle.
x^(2(4)) =x^8 = (x^4)^2
2sqrt6

37. Factor a^2 + 2ab + b^2
12.5%
All numbers multiples of 1.
(a + b)^2
1/2 times 7/3

38. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
1 & 37/132
2 & 3/7
4725
1

39. When does a function automatically have a restricted domain (2)?
Triangles with same measure and same side lengths.
180 degrees
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The greatest value minus the smallest.

40. What is the name of set with a number of elements which cannot be counted?
Two equal sides and two equal angles.
72
II
An infinite set.

41. 50 < all primes< 60
53 - 59
7 / 1000
A circle centered at -2 - -2 with radius 3.
x^(2(4)) =x^8 = (x^4)^2

42. Define a 'monomial'
The second graph is less steep.
41 - 43 - 47
An expression with just one term (-6x - 2a^2)
2 & 3/7

43. Pi is a ratio of what to what?

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44. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Diameter(Pi)
IV
A grouping of the members within a set based on a shared characteristic.

45. What is the area of a regular hexagon with side 6?
Ax^2 + bx + c where a -b and c are constants and a /=0
Undefined
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
2^9 / 2 = 256

46. Which quadrant is the lower left hand?
(base*height) / 2
C = (pi)d
III
75:11

47. 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?
All numbers multiples of 1.
0
10! / 3!(10-3)! = 120
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

48. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
37.5%
Indeterminable.
An arc is a portion of a circumference of a circle.
8

49. What is the maximum value for the function g(x) = (-2x^2) -1?
A central angle is an angle formed by 2 radii.
48
1
The set of input values for a function.

50. 413.03 x 10^(-4) =
1
87.5%
x(x - y + 1)
413.03 / 10^4 (move the decimal point 4 places to the left)