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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. What is the name for a grouping of the members within a set based on a shared characteristic?
I
Its negative reciprocal. (-b/a)
The longest arc between points A and B on a circle'S diameter.
A subset.

2. What is a minor arc?

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3. What is the empty set?
A = I (1 + rt)
Relationship cannot be determined (what if x is negative?)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A set with no members - denoted by a circle with a diagonal through it.

4. Can you add sqrt 3 and sqrt 5?
.0004809 X 10^11
Yes. [i.e. f(x) = x^2 - 1
70
No - only like radicals can be added.

5. What is the 'domain' of a function?
The set of input values for a function.
No - only like radicals can be added.
IV
31 - 37

6. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
(b + c)
.0004809 X 10^11
18
1

7. 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?
N! / (k!)(n-k)!
9 : 25
2 & 3/7
The set of elements which can be found in either A or B.

8. The perimeter of a square is 48 inches. The length of its diagonal is:
Move the decimal point to the right x places
x= (1.2)(.8)lw
12sqrt2
Arc length = (n/360) x pi(2r) where n is the number of degrees.

9. 25^(1/2) or sqrt. 25 =
The sum of digits is divisible by 9.
48
5 OR -5
Undefined

10. 8.84 / 5.2
A circle centered at -2 - -2 with radius 3.
x= (1.2)(.8)lw
71 - 73 - 79
1.7

11. Solve the quadratic equation ax^2 + bx + c= 0
10! / 3!(10-3)! = 120
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
A set with a number of elements which can be counted.
The curve opens downward and the vertex is the maximum point on the graph.

12. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
x^(6-3) = x^3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
x= (1.2)(.8)lw
III

13. Simplify 9^(1/2) X 4^3 X 2^(-6)?
The interesection of A and B.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
3
13pi / 2

14. What is a set with no members called?
The curve opens upward and the vertex is the minimal point on the graph.
The empty set - denoted by a circle with a diagonal through it.
A set with no members - denoted by a circle with a diagonal through it.
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)

15. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
x^(2(4)) =x^8 = (x^4)^2
41 - 43 - 47
1/(x^y)

16. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
(a - b)(a + b)
Yes. [i.e. f(x) = x^2 - 1
Two angles whose sum is 90.

17. Volume for a cylinder?
52
Area of the base X height = (pi)hr^2
4096
F(x-c)

18. What is the graph of f(x) shifted upward c units or spaces?
.0004809 X 10^11
A reflection about the axis.
F(x) + c
62.5%

19. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
12.5%
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(amount of increase/original price) x 100%

20. Reduce: 4.8 : 0.8 : 1.6
F(x-c)
The set of elements which can be found in either A or B.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
6 : 1 : 2

21. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
1:1:sqrt2
C = (pi)d
Two equal sides and two equal angles.

22. Can you simplify sqrt72?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
13
1/2 times 7/3

23. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
1
1
Cd
A reflection about the axis.

24. 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)
70
The objects within a set.
F(x-c)

25. What is the ratio of the sides of a 30-60-90 triangle?
37.5%
$11 -448
Two angles whose sum is 90.
1:sqrt3:2

26. (6sqrt3) x (2sqrt5) =
Cd
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

27. 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?
10! / 3!(10-3)! = 120
A central angle is an angle formed by 2 radii.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Its last two digits are divisible by 4.

28. To convert a percent to a fraction....
The curve opens downward and the vertex is the maximum point on the graph.
x^(6-3) = x^3
Divide by 100.
5 OR -5

29. What does scientific notation mean?
A circle centered at -2 - -2 with radius 3.
Sqrt 12
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
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

30. 60 < all primes <70
II
The second graph is less steep.
The union of A and B.
61 - 67

31. What is a central angle?
A central angle is an angle formed by 2 radii.
Sqrt 12
1
Sector area = (n/360) X (pi)r^2

32. Max and Min lengths for a side of a triangle?
The third side is greater than the difference and less than the sum.
An isosceles right triangle.
The set of elements which can be found in either A or B.
Sector area = (n/360) X (pi)r^2

33. 7/8 in percent?
2 & 3/7
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
87.5%
Members or elements

34. In a regular polygon with n sides - the formula for the sum of interior angles
4a^2(b)
Angle/360 x 2(pi)r
(n-2) x 180
1/(x^y)

35. How to determine percent increase?
10! / 3!(10-3)! = 120
$11 -448
(amount of increase/original price) x 100%
75:11

36. What is the 'union' of A and B?
52
The set of elements which can be found in either A or B.
4096
1

37. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^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.
4.25 - 6 - 22
(a + b)^2

38. What are the smallest three prime numbers greater than 65?
9 & 6/7
(a + b)^2
Pi is the ratio of a circle'S circumference to its diameter.
67 - 71 - 73

39. x^6 / x^3
Ax^2 + bx + c where a -b and c are constants and a /=0
4096
x^(6-3) = x^3
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

40. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
No - only like radicals can be added.
A circle centered at -2 - -2 with radius 3.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

41. Formula to find a circle'S circumference from its radius?
6
C = 2(pi)r
83.333%
Divide by 100.

42. What is the maximum value for the function g(x) = (-2x^2) -1?
x(x - y + 1)
True
(a + b)^2
1

43. What is the graph of f(x) shifted left c units or spaces?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Ax^2 + bx + c where a -b and c are constants and a /=0
F(x + c)
True

44. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
20.5
53 - 59
1
2sqrt6

45. To convert a decimal to a percent...
...multiply by 100.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
$3 -500 in the 9% and $2 -500 in the 7%.
Even

46. Simplify the expression (p^2 - q^2)/ -5(q - p)
23 - 29
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(p + q)/5
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

47. Is 0 even or odd?
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)
Even
3
Factors are few - multiples are many.

48. 6w^2 - w - 15 = 0
41 - 43 - 47
3/2 - 5/3
1
Relationship cannot be determined (what if x is negative?)

49. 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))?
20.5
y = 2x^2 - 3
The longest arc between points A and B on a circle'S diameter.
A set with a number of elements which can be counted.

50. Evaluate 3& 2/7 / 1/3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
10! / (10-3)! = 720
9 & 6/7