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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 does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A reflection about the origin.
N! / (n-k)!
Move the decimal point to the right x places
A circle centered at -2 - -2 with radius 3.

2. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
75:11
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

3. x^6 / x^3
IV
Diameter(Pi)
x^(6-3) = x^3
72

4. P and r are factors of 100. What is greater - pr or 100?
A grouping of the members within a set based on a shared characteristic.
Indeterminable.
F(x + c)
0

5. To convert a percent to a fraction....
9 : 25
Divide by 100.
Two angles whose sum is 180.
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...

6. To multiply a number by 10^x
90
Two angles whose sum is 90.
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)
Move the decimal point to the right x places

7. Formula to calculate arc length?
From northeast - counterclockwise. I - II - III - IV
Arc length = (n/360) x pi(2r) where n is the number of degrees.
C = 2(pi)r
F(x) + c

8. What are the smallest three prime numbers greater than 65?
A circle centered at -2 - -2 with radius 3.
67 - 71 - 73
A reflection about the axis.
Ax^2 + bx + c where a -b and c are constants and a /=0

9. What is the graph of f(x) shifted left c units or spaces?
III
The second graph is less steep.
F(x + c)
5

10. Define a 'Term' -
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)(a + b)
0
23 - 29

11. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
500
2sqrt6
4:5
4a^2(b)

12. Evaluate 4/11 + 11/12
1 & 37/132
The curve opens downward and the vertex is the maximum point on the graph.
Two equal sides and two equal angles.
A 30-60-90 triangle.

13. How to find the area of a sector?
1.7
N! / (n-k)!
All numbers multiples of 1.
Angle/360 x (pi)r^2

14. a^2 - b^2
True
(a - b)(a + b)
A grouping of the members within a set based on a shared characteristic.
Yes. [i.e. f(x) = x^2 - 1

15. What is the 'Range' of a function?
4a^2(b)
Sqrt 12
The set of output values for a function.
...multiply by 100.

16. Is 0 even or odd?
90
5 OR -5
True
Even

17. How to determine percent increase?
3
(amount of increase/original price) x 100%
IV
3 - -3

18. What is the set of elements which can be found in either A or B?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Undefined - because we can'T divide by 0.
7 / 1000
The union of A and B.

19. What are the irrational numbers?

20. What is the formula for compounded interest?
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.
9 & 6/7
28. n = 8 - k = 2. n! / k!(n-k)!
(amount of increase/original price) x 100%

21. Pi is a ratio of what to what?

22. What is the side length of an equilateral triangle with altitude 6?
Yes - like radicals can be added/subtracted.
3
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
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...

23. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(n-2) x 180
The curve opens downward and the vertex is the maximum point on the graph.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

24. 5/6 in percent?
83.333%
The set of output values for a function.
4725
13

25. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
(b + c)
6
$3 -500 in the 9% and $2 -500 in the 7%.
70

26. If the two sides of a triangle are unequal then the longer side...
Lies opposite the greater angle
180
y = 2x^2 - 3
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

27. Number of degrees in a triangle
A 30-60-90 triangle.
10! / 3!(10-3)! = 120
180
The point of intersection of the systems.

28. 413.03 x 10^(-4) =
A circle centered on the origin with radius 8.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
413.03 / 10^4 (move the decimal point 4 places to the left)
A circle centered at -2 - -2 with radius 3.

29. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
6 : 1 : 2
Yes - like radicals can be added/subtracted.

30. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
An infinite set.
2^9 / 2 = 256
N! / (n-k)!

31. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
441000 = 1 10 10 10 21 * 21
Cd
The overlapping sections.
87.5%

32. What is a finite set?
52
83.333%
The longest arc between points A and B on a circle'S diameter.
A set with a number of elements which can be counted.

33. 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
2 & 3/7
18
No - only like radicals can be added.
The point of intersection of the systems.

34. What are 'Supplementary angles?'
III
A reflection about the origin.
A circle centered at -2 - -2 with radius 3.
Two angles whose sum is 180.

35. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
No - the input value has exactly one output.
Part = Percent X Whole
2 & 3/7

36. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
The point of intersection of the systems.
4:5
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
.0004809 X 10^11

37. How many multiples does a given number have?
The sum of digits is divisible by 9.
N! / (k!)(n-k)!
1
Infinite.

38. How to determine percent decrease?
(amount of decrease/original price) x 100%
41 - 43 - 47
An expression with just one term (-6x - 2a^2)
Triangles with same measure and same side lengths.

39. Define an 'expression'.
Sector area = (n/360) X (pi)r^2
31 - 37
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
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)

40. 1/8 in percent?
12.5%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Move the decimal point to the right x places
1 & 37/132

41. What is the set of elements found in both A and B?
1
70
The interesection of A and B.
A chord is a line segment joining two points on a circle.

42. Which quadrant is the upper left hand?
2^9 / 2 = 256
A 30-60-90 triangle.
II
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

43. 0^0
Indeterminable.
Undefined
2
An isosceles right triangle.

44. x^2 = 9. What is the value of x?
x^(6-3) = x^3
Sqrt 12
C = 2(pi)r
3 - -3

45. Write 10 -843 X 10^7 in scientific notation
A tangent is a line that only touches one point on the circumference of a circle.
1.0843 X 10^11
20.5
13

46. Simplify the expression (p^2 - q^2)/ -5(q - p)
G(x) = {x}
C = 2(pi)r
3/2 - 5/3
(p + q)/5

47. a^2 - b^2 =
12! / 5!7! = 792
(a - b)(a + b)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
A grouping of the members within a set based on a shared characteristic.

48. When does a function automatically have a restricted domain (2)?
The point of intersection of the systems.
16.6666%
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

49. Can you simplify sqrt72?
4a^2(b)
0
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

50. Reduce: 4.8 : 0.8 : 1.6
III
10! / (10-3)! = 720
C = (pi)d
6 : 1 : 2