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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. (-1)^2 =
Divide by 100.
13
1
The greatest value minus the smallest.

2. x^6 / x^3
x^(6-3) = x^3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
53 - 59
The steeper the slope.

3. 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?
180 degrees
3/2 - 5/3
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
N! / (k!)(n-k)!

4. 60 < all primes <70
Cd
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
1/2 times 7/3
61 - 67

5. Evaluate (4^3)^2
4096
The objects within a set.
F(x) + c
10! / (10-3)! = 720

6. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
1:sqrt3:2
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
70
F(x + c)

7. 1/6 in percent?
16.6666%
A grouping of the members within a set based on a shared characteristic.
Members or elements
1:sqrt3:2

8. a^2 - b^2 =
5 OR -5
3 - -3
(a - b)(a + b)
... the square of the ratios of the corresponding sides.

9. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
23 - 29
The longest arc between points A and B on a circle'S diameter.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

10. What is the side length of an equilateral triangle with altitude 6?
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 set of elements which can be found in either A or B.
(a - b)^2
61 - 67

11. Evaluate 3& 2/7 / 1/3
The curve opens upward and the vertex is the minimal point on the graph.
9 & 6/7
72
(amount of increase/original price) x 100%

12. What is the set of elements found in both A and B?
288 (8 9 4)
1:sqrt3:2
The interesection of A and B.
12sqrt2

13. What is the 'Restricted domain of a function'?
(a + b)^2
37.5%
When the function is not defined for all real numbers -; only a subset of the real numbers.
500

14. 50 < all primes< 60
53 - 59
(p + q)/5
The interesection of A and B.
(a - b)(a + b)

15. a^2 - b^2
Angle/360 x (pi)r^2
(a - b)(a + b)
1
23 - 29

16. 1/8 in percent?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
12.5%
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
(a + b)^2

17. x^(-y)=
Move the decimal point to the right x places
1/(x^y)
52
The two xes after factoring.

18. Max and Min lengths for a side of a triangle?
1:1:sqrt2
The third side is greater than the difference and less than the sum.
Triangles with same measure and same side lengths.
90pi

19. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
No - the input value has exactly one output.
11 - 13 - 17 - 19
1
The set of output values for a function.

20. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
No - only like radicals can be added.
G(x) = {x}
87.5%

21. Factor x^2 - xy + x.
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)
x(x - y + 1)
x^(4+7) = x^11
1.0843 X 10^11

22. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
4:5
13pi / 2
y = 2x^2 - 3

23. How to find the circumference of a circle which circumscribes a square?
6
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Cd
87.5%

24. 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?
9 : 25
1
F(x + c)
2(pi)r^2 + 2(pi)rh

25. Define a 'Term' -
A grouping of the members within a set based on a shared characteristic.
83.333%
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)
53 - 59

26. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
4725
28. n = 8 - k = 2. n! / k!(n-k)!
27^(-4)
A circle centered on the origin with radius 8.

27. 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?
II
10! / (10-3)! = 720
F(x) + c
x^(2(4)) =x^8 = (x^4)^2

28. Legs: 3 - 4. Hypotenuse?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
4.25 - 6 - 22
5
The interesection of A and B.

29. 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%.
(a + b)^2
Sqrt 12
The sum of digits is divisible by 9.

30. (-1)^3 =
Members or elements
(amount of increase/original price) x 100%
1
Area of the base X height = (pi)hr^2

31. 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?
The sum of digits is divisible by 9.
1
75:11
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

32. What is the 'domain' of a function?
Lies opposite the greater angle
6
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The set of input values for a function.

33. x^4 + x^7 =
13pi / 2
x^(4+7) = x^11
12.5%
Two angles whose sum is 180.

34. What are the real numbers?
10! / 3!(10-3)! = 120
1:1:sqrt2
The curve opens upward and the vertex is the minimal point on the graph.
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)

35. Whats the difference between factors and multiples?
No - only like radicals can be added.
A = pi(r^2)
The objects within a set.
Factors are few - multiples are many.

36. What are the members or elements of a set?
When the function is not defined for all real numbers -; only a subset of the real numbers.
The objects within a set.
(n-2) x 180
1.7

37. Area of a triangle?
(base*height) / 2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The set of elements which can be found in either A or B.
Area of the base X height = (pi)hr^2

38. Volume for a cylinder?
8
When the function is not defined for all real numbers -; only a subset of the real numbers.
Area of the base X height = (pi)hr^2
(base*height) / 2

39. 20<all primes<30
23 - 29
Ax^2 + bx + c where a -b and c are constants and a /=0
0
6

40. What is the formula for compounded interest?
3
(b + c)
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.
The shortest arc between points A and B on a circle'S diameter.

41. What is an exterior angle?
An angle which is supplementary to an interior angle.
4725
2(pi)r^2 + 2(pi)rh
x= (1.2)(.8)lw

42. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
1
0
13
Yes. [i.e. f(x) = x^2 - 1

43. What is a tangent?
C = (pi)d
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
180 degrees
A tangent is a line that only touches one point on the circumference of a circle.

44. How to find the area of a sector?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
55%
Its last two digits are divisible by 4.
Angle/360 x (pi)r^2

45. Legs 6 - 8. Hypotenuse?
Diameter(Pi)
The third side is greater than the difference and less than the sum.
10
Angle/360 x (pi)r^2

46. Formula for the area of a sector of a circle?
2 & 3/7
True
Sector area = (n/360) X (pi)r^2
$11 -448

47. 10<all primes<20
288 (8 9 4)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
1/(x^y)
11 - 13 - 17 - 19

48. 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.
(amount of decrease/original price) x 100%
Infinite.
.0004809 X 10^11
90 degrees

49. When the 'a' in a parabola is positive....
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
3/2 - 5/3
The curve opens upward and the vertex is the minimal point on the graph.

50. Reduce: 4.8 : 0.8 : 1.6
2^9 / 2 = 256
6 : 1 : 2
10
The union of A and B.

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GRE Math: Common Errors

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