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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. Solve the quadratic equation ax^2 + bx + c= 0
12sqrt2
28. n = 8 - k = 2. n! / k!(n-k)!
(a + b)^2
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

2. 3/8 in percent?
(amount of increase/original price) x 100%
72
37.5%
20.5

3. What is the graph of f(x) shifted downward c units or spaces?
The direction of the inequality is reversed.
3
From northeast - counterclockwise. I - II - III - IV
F(x) - c

4. What is the ratio of the sides of a 30-60-90 triangle?
(n-2) x 180
1:sqrt3:2
180
IV

5. What is a subset?
61 - 67
12sqrt2
x^(2(4)) =x^8 = (x^4)^2
A grouping of the members within a set based on a shared characteristic.

6. What is a set with no members called?
Angle/360 x 2(pi)r
70
The empty set - denoted by a circle with a diagonal through it.
A = I (1 + rt)

7. Evaluate (4^3)^2
From northeast - counterclockwise. I - II - III - IV
N! / (n-k)!
III
4096

8. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
12! / 5!7! = 792
II
4.25 - 6 - 22

9. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
Members or elements
90 degrees
Area of the base X height = (pi)hr^2
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

10. (a^-1)/a^5
1/a^6
90pi
F(x-c)
The direction of the inequality is reversed.

11. Evaluate 4/11 + 11/12
A reflection about the origin.
1 & 37/132
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Part = Percent X Whole

12. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
7 / 1000
Undefined - because we can'T divide by 0.
An isosceles right triangle.
Diameter(Pi)

13. sqrt 2(sqrt 6)=
Sqrt 12
4725
90 degrees
The greatest value minus the smallest.

14. 25^(1/2) or sqrt. 25 =
Undefined
III
5 OR -5
6

15. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
12sqrt2
28. n = 8 - k = 2. n! / k!(n-k)!
13pi / 2

16. 6w^2 - w - 15 = 0
G(x) = {x}
3/2 - 5/3
71 - 73 - 79
The two xes after factoring.

17. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
Sqrt 12
71 - 73 - 79
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)

18. The objects in a set are called two names:
An arc is a portion of a circumference of a circle.
A circle centered at -2 - -2 with radius 3.
Its negative reciprocal. (-b/a)
Members or elements

19. Formula to find a circle'S circumference from its diameter?
1
C = (pi)d
... the square of the ratios of the corresponding sides.
3

20. What is the surface area of a cylinder with radius 5 and height 8?
(a + b)^2
Yes - like radicals can be added/subtracted.
130pi
Two equal sides and two equal angles.

21. How to find the diagonal of a rectangular solid?
x= (1.2)(.8)lw
An expression with just one term (-6x - 2a^2)
90
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

22. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
16.6666%
3/2 - 5/3
A circle centered on the origin with radius 8.
10! / (10-3)! = 720

23. What is the slope of a vertical line?

24. When the 'a' in the parabola is negative...
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
180
The curve opens downward and the vertex is the maximum point on the graph.
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...

25. a^2 - b^2
(a - b)(a + b)
1 & 37/132
N! / (n-k)!
The second graph is less steep.

26. Whats the difference between factors and multiples?
5
9 : 25
Factors are few - multiples are many.
288 (8 9 4)

27. What are congruent triangles?
The longest arc between points A and B on a circle'S diameter.
Triangles with same measure and same side lengths.
Yes - like radicals can be added/subtracted.
The union of A and B.

28. a^2 - 2ab + b^2
The second graph is less steep.
Angle/360 x (pi)r^2
(a - b)^2
23 - 29

29. What are the smallest three prime numbers greater than 65?
3 - -3
67 - 71 - 73
(p + q)/5
A reflection about the axis.

30. Circumference of a circle?
Diameter(Pi)
A circle centered at -2 - -2 with radius 3.
An expression with just one term (-6x - 2a^2)
70

31. What is the empty set?
A set with no members - denoted by a circle with a diagonal through it.
3
61 - 67
8

32. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
180
1/(x^y)
Diameter(Pi)
2

33. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
500
2 & 3/7
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

34. 5/6 in percent?
A tangent is a line that only touches one point on the circumference of a circle.
83.333%
F(x + c)
The greatest value minus the smallest.

35. Which quadrant is the upper right hand?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(base*height) / 2
I

36. x^4 + x^7 =
9 & 6/7
x^(4+7) = x^11
G(x) = {x}
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

37. 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)?
1
Its last two digits are divisible by 4.
y = (x + 5)/2
12! / 5!7! = 792

38. What are the irrational numbers?

39. (x^2)^4
x^(4+7) = x^11
6
x^(2(4)) =x^8 = (x^4)^2
1

40. Factor a^2 + 2ab + b^2
(a + b)^2
Two angles whose sum is 90.
5 OR -5
2 & 3/7

41. What are the real numbers?
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)
Sqrt 12
.0004809 X 10^11
(b + c)

42. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
4725
The sum of digits is divisible by 9.

43. Formula for the area of a sector of a circle?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Even
Sector area = (n/360) X (pi)r^2
(p + q)/5

44. Legs: 3 - 4. Hypotenuse?
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.
5
...multiply by 100.

45. What is the formula for computing simple interest?
A = I (1 + rt)
70
The greatest value minus the smallest.
10! / (10-3)! = 720

46. (6sqrt3) x (2sqrt5) =
F(x-c)
When the function is not defined for all real numbers -; only a subset of the real numbers.
1.0843 X 10^11
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

47. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
5
37.5%
62.5%

48. What is the name for a grouping of the members within a set based on a shared characteristic?
Two angles whose sum is 180.
N! / (n-k)!
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A subset.

49. What is an arc of a circle?
x^(2(4)) =x^8 = (x^4)^2
An arc is a portion of a circumference of a circle.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
6 : 1 : 2

50. Define an 'expression'.
4096
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)
Pi is the ratio of a circle'S circumference to its diameter.
Sector area = (n/360) X (pi)r^2