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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. Which is greater? 200x^295 or 10x^294?
10! / 3!(10-3)! = 120
Relationship cannot be determined (what if x is negative?)
When the function is not defined for all real numbers -; only a subset of the real numbers.
A circle centered at -2 - -2 with radius 3.

2. What is the slope of a horizontal line?
I
F(x) + c
No - only like radicals can be added.
0

3. 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%.
The third side is greater than the difference and less than the sum.
A grouping of the members within a set based on a shared characteristic.
Its negative reciprocal. (-b/a)

4. Which quadrant is the upper right hand?
The interesection of A and B.
72
A subset.
I

5. What does the graph x^2 + y^2 = 64 look like?
x^(2(4)) =x^8 = (x^4)^2
3/2 - 5/3
N! / (k!)(n-k)!
A circle centered on the origin with radius 8.

6. (12sqrt15) / (2sqrt5) =
71 - 73 - 79
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
413.03 / 10^4 (move the decimal point 4 places to the left)
6

7. What is the empty set?
10! / 3!(10-3)! = 120
441000 = 1 10 10 10 21 * 21
2 & 3/7
A set with no members - denoted by a circle with a diagonal through it.

8. 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?
Cd
83.333%
10! / (10-3)! = 720
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)

9. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
(n-2) x 180
Divide by 100.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

10. Can you simplify sqrt72?
... the square of the ratios of the corresponding sides.
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...
7 / 1000
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

11. 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?
From northeast - counterclockwise. I - II - III - IV
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)
1/(x^y)
9 : 25

12. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
130pi
1/(x^y)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

13. Formula of rectangle where l increases by 20% and w decreases by 20%
71 - 73 - 79
x= (1.2)(.8)lw
C = 2(pi)r
Its negative reciprocal. (-b/a)

14. Max and Min lengths for a side of a triangle?
A grouping of the members within a set based on a shared characteristic.
The third side is greater than the difference and less than the sum.
$3 -500 in the 9% and $2 -500 in the 7%.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

15. Whats the difference between factors and multiples?
x^(6-3) = x^3
Factors are few - multiples are many.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
67 - 71 - 73

16. Legs: 3 - 4. Hypotenuse?
5
x= (1.2)(.8)lw
...multiply by 100.
The interesection of A and B.

17. What is the graph of f(x) shifted left c units or spaces?
13
1
Members or elements
F(x + c)

18. A number is divisible by 9 if...
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...
The sum of digits is divisible by 9.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

19. Area of a triangle?
.0004809 X 10^11
(base*height) / 2
18
F(x + c)

20. Define an 'expression'.
The direction of the inequality is reversed.
9 & 6/7
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)

21. What is the set of elements found in both A and B?
The interesection of A and B.
The two xes after factoring.
Cd
I

22. What is a set with no members called?
(a - b)^2
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)
The empty set - denoted by a circle with a diagonal through it.
288 (8 9 4)

23. How many 3-digit positive integers are even and do not contain the digit 4?
70
The steeper the slope.
288 (8 9 4)
9 & 6/7

24. What is the name of set with a number of elements which cannot be counted?
An infinite set.
(a - b)(a + b)
A = I (1 + rt)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

25. The slope of a line perpendicular to (a/b)?
Its negative reciprocal. (-b/a)
Angle/360 x 2(pi)r
Lies opposite the greater angle
1

26. Pi is a ratio of what to what?

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27. 10^6 has how many zeroes?
(a - b)(a + b)
The empty set - denoted by a circle with a diagonal through it.
6
52

28. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
1
12sqrt2
(b + c)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

29. What are the members or elements of a set?
2 & 3/7
Two equal sides and two equal angles.
The objects within a set.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

30. 5x^2 - 35x -55 = 0
F(x-c)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
48
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

31. Formula for the area of a circle?
Relationship cannot be determined (what if x is negative?)
A = pi(r^2)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
II

32. Can you add sqrt 3 and sqrt 5?
Two angles whose sum is 90.
No - only like radicals can be added.
1
x(x - y + 1)

33. Which is greater? 27^(-4) or 9^(-8)
18
27^(-4)
90 degrees
10! / (10-3)! = 720

34. When the 'a' in a parabola is positive....
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
10! / (10-3)! = 720
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The curve opens upward and the vertex is the minimal point on the graph.

35. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
Infinite.
12! / 5!7! = 792
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
90

36. What is a minor arc?

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37. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
Area of the base X height = (pi)hr^2
Infinite.
2
(b + c)

38. a^2 + 2ab + b^2
1
(a + b)^2
An expression with just one term (-6x - 2a^2)
4:5

39. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
No - the input value has exactly one output.
An expression with just one term (-6x - 2a^2)
2^9 / 2 = 256
13

40. x^4 + x^7 =
x^(4+7) = x^11
F(x) - c
28. n = 8 - k = 2. n! / k!(n-k)!
Indeterminable.

41. Can the input value of a function have more than one output value (i.e. x: y - y1)?
The set of output values for a function.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
No - the input value has exactly one output.
180 degrees

42. (-1)^2 =
Factors are few - multiples are many.
1
N! / (k!)(n-k)!
IV

43. 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?
(b + c)
10! / (10-3)! = 720
52
7 / 1000

44. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
4:5
Pi is the ratio of a circle'S circumference to its diameter.
Diameter(Pi)

45. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
20.5
180
Undefined - because we can'T divide by 0.
48

46. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
130pi
An angle which is supplementary to an interior angle.
0
... the square of the ratios of the corresponding sides.

47. 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?
10! / (10-3)! = 720
3
y = 2x^2 - 3
(amount of decrease/original price) x 100%

48. (-1)^3 =
x(x - y + 1)
3sqrt4
IV
1

49. What is an exterior angle?
(n-2) x 180
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
An angle which is supplementary to an interior angle.
12.5%

50. 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)
75:11
An infinite set.
13pi / 2