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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. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
(p + q)/5
20.5
Indeterminable.
8

2. What are the real numbers?
The overlapping sections.
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)
N! / (k!)(n-k)!
90 degrees

3. A number is divisible by 4 is...
Its last two digits are divisible by 4.
The direction of the inequality is reversed.
2
0

4. (-1)^2 =
1
A subset.
A grouping of the members within a set based on a shared characteristic.
Its negative reciprocal. (-b/a)

5. What is an exterior angle?
Factors are few - multiples are many.
An angle which is supplementary to an interior angle.
Diameter(Pi)
x^(4+7) = x^11

6. What are the rational numbers?
Part = Percent X Whole
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
III
8

7. What is the order of operations?
4.25 - 6 - 22
1
x^(4+7) = x^11
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

8. 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)
1/(x^y)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

9. sqrt 2(sqrt 6)=
Sqrt 12
An angle which is supplementary to an interior angle.
Two equal sides and two equal angles.
y = 2x^2 - 3

10. The objects in a set are called two names:
Members or elements
1
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
III

11. 30< all primes<40
Undefined
31 - 37
N! / (k!)(n-k)!
1

12. If an inequality is multiplied or divided by a negative number....
Its negative reciprocal. (-b/a)
The direction of the inequality is reversed.
75:11
3

13. What is a parabola?
Members or elements
The objects within a set.
Ax^2 + bx + c where a -b and c are constants and a /=0
90pi

14. 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/(x^y)
3
Its negative reciprocal. (-b/a)

15. x^6 / x^3
x^(6-3) = x^3
16.6666%
1.0843 X 10^11
3sqrt4

16. (12sqrt15) / (2sqrt5) =
1.0843 X 10^11
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
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...
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

17. Legs 6 - 8. Hypotenuse?
1
10
Its negative reciprocal. (-b/a)
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

18. 50 < all primes< 60
1/(x^y)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
12sqrt2
53 - 59

19. Evaluate 4/11 + 11/12
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Indeterminable.
1/a^6
1 & 37/132

20. What are the irrational numbers?

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21. x^2 = 9. What is the value of x?
20.5
67 - 71 - 73
1.7
3 - -3

22. When the 'a' in the parabola is negative...
The curve opens downward and the vertex is the maximum point on the graph.
2sqrt6
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)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

23. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
IV
72
2sqrt6
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

24. Find the surface area of a cylinder with radius 3 and height 12.
83.333%
The set of elements found in both A and B.
90pi
10! / (10-3)! = 720

25. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
Angle/360 x (pi)r^2
Two angles whose sum is 180.
90
Relationship cannot be determined (what if x is negative?)

26. What does the graph x^2 + y^2 = 64 look like?
.0004809 X 10^11
A circle centered on the origin with radius 8.
The curve opens upward and the vertex is the minimal point on the graph.
No - only like radicals can be added.

27. 10<all primes<20
11 - 13 - 17 - 19
3sqrt4
C = (pi)d
23 - 29

28. Pi is a ratio of what to what?

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29. How to determine percent decrease?
10! / (10-3)! = 720
37.5%
Yes. [i.e. f(x) = x^2 - 1
(amount of decrease/original price) x 100%

30. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
The greatest value minus the smallest.
Part = Percent X Whole
An infinite set.

31. What is the sum of the angles of a triangle?
A subset.
3sqrt4
180 degrees
90

32. In a regular polygon with n sides - the formula for the sum of interior angles
An angle which is supplementary to an interior angle.
(n-2) x 180
G(x) = {x}
6 : 1 : 2

33. How many 3-digit positive integers are even and do not contain the digit 4?
Area of the base X height = (pi)hr^2
Yes - like radicals can be added/subtracted.
288 (8 9 4)
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.

34. What is the maximum value for the function g(x) = (-2x^2) -1?
1
A grouping of the members within a set based on a shared characteristic.
4096
Sector area = (n/360) X (pi)r^2

35. How to determine percent increase?
A = pi(r^2)
3
Cd
(amount of increase/original price) x 100%

36. 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)
Sqrt 12
Indeterminable.
10! / (10-3)! = 720
4.25 - 6 - 22

37. 5/8 in percent?
The curve opens downward and the vertex is the maximum point on the graph.
62.5%
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x^(2(4)) =x^8 = (x^4)^2

38. Can the input value of a function have more than one output value (i.e. x: y - y1)?
$11 -448
11 - 13 - 17 - 19
1:sqrt3:2
No - the input value has exactly one output.

39. 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?
67 - 71 - 73
4725
70
9 : 25

40. Which quadrant is the upper right hand?
41 - 43 - 47
I
An expression with just one term (-6x - 2a^2)
(amount of increase/original price) x 100%

41. To convert a decimal to a percent...
$11 -448
x^(6-3) = x^3
...multiply by 100.
When the function is not defined for all real numbers -; only a subset of the real numbers.

42. Area of a triangle?
The sum of its digits is divisible by 3.
70
(base*height) / 2
The set of input values for a function.

43. 5x^2 - 35x -55 = 0
[(7+ sqrt93) /2] - [(7 - sqrt93) / 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)
71 - 73 - 79
(a - b)(a + b)

44. Surface area for a cylinder?
31 - 37
4725
2(pi)r^2 + 2(pi)rh
1.0843 X 10^11

45. x^4 + x^7 =
90pi
x^(4+7) = x^11
62.5%
A 30-60-90 triangle.

46. (-1)^3 =
G(x) = {x}
x= (1.2)(.8)lw
1
Move the decimal point to the right x places

47. What is the 'domain' of a function?
(a - b)(a + b)
27^(-4)
180
The set of input values for a function.

48. a^2 - b^2 =
A grouping of the members within a set based on a shared characteristic.
12! / 5!7! = 792
(a - b)(a + b)
IV

49. What percent of 40 is 22?
Part = Percent X Whole
(b + c)
90pi
55%

50. a^2 - 2ab + b^2
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(a - b)^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)
Arc length = (n/360) x pi(2r) where n is the number of degrees.