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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. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
20.5
A circle centered at -2 - -2 with radius 3.
5
2^9 / 2 = 256

2. What are the members or elements of a set?
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
I
The objects within a set.
18

3. To convert a decimal to a percent...
Undefined - because we can'T divide by 0.
...multiply by 100.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
20.5

4. How many multiples does a given number have?
90
Infinite.
Its last two digits are divisible by 4.
61 - 67

5. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
9 & 6/7
When the function is not defined for all real numbers -; only a subset of the real numbers.
2sqrt6

6. What is the ratio of the sides of a 30-60-90 triangle?
Pi is the ratio of a circle'S circumference to its diameter.
III
2
1:sqrt3:2

7. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(a - b)(a + b)
(p + q)/5
0

8. What is the 'Restricted domain of a function'?
Angle/360 x (pi)r^2
When the function is not defined for all real numbers -; only a subset of the real numbers.
41 - 43 - 47
A chord is a line segment joining two points on a circle.

9. 413.03 x 10^(-4) =
Undefined - because we can'T divide by 0.
3/2 - 5/3
413.03 / 10^4 (move the decimal point 4 places to the left)
7 / 1000

10. a^2 + 2ab + b^2
No - the input value has exactly one output.
16.6666%
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

11. What are the rational numbers?
I
90pi
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
413.03 / 10^4 (move the decimal point 4 places to the left)

12. The ratio of the areas of two similar polygons is ...
Move the decimal point to the right x places
Ax^2 + bx + c where a -b and c are constants and a /=0
4725
... the square of the ratios of the corresponding sides.

13. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
70
An isosceles right triangle.
12.5%
41 - 43 - 47

14. The objects in a set are called two names:
An expression with just one term (-6x - 2a^2)
0
Members or elements
x(x - y + 1)

15. Formula for the area of a circle?
Ax^2 + bx + c where a -b and c are constants and a /=0
An expression with just one term (-6x - 2a^2)
A = pi(r^2)
72

16. 30< all primes<40
1
31 - 37
72
500

17. Whats the difference between factors and multiples?
Cd
The empty set - denoted by a circle with a diagonal through it.
Factors are few - multiples are many.
The greatest value minus the smallest.

18. Define a 'monomial'
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
An expression with just one term (-6x - 2a^2)
6 : 1 : 2
A circle centered at -2 - -2 with radius 3.

19. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
y = (x + 5)/2
6
All numbers multiples of 1.

20. 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
F(x + c)
1:1:sqrt2
An arc is a portion of a circumference of a circle.

21. 0^0
Undefined
An angle which is supplementary to an interior angle.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A circle centered on the origin with radius 8.

22. What is the formula for compounded interest?
10
A circle centered on the origin with radius 8.
(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.

23. Which is greater? 64^5 or 16^8
No - the input value has exactly one output.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
62.5%
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

24. When does a function automatically have a restricted domain (2)?
Indeterminable.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Angle/360 x 2(pi)r
1

25. 1/6 in percent?
1
16.6666%
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)
7 / 1000

26. Describe the relationship between the graphs of x^2 and (1/2)x^2
(a - b)^2
The second graph is less steep.
Indeterminable.
2 & 3/7

27. Find the surface area of a cylinder with radius 3 and height 12.
90pi
C = (pi)d
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
10

28. What is the absolute value function?
8
2(pi)r^2 + 2(pi)rh
The overlapping sections.
G(x) = {x}

29. 6w^2 - w - 15 = 0
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...
A chord is a line segment joining two points on a circle.
3/2 - 5/3
The set of elements which can be found in either A or B.

30. 40 < all primes<50
6
Two equal sides and two equal angles.
41 - 43 - 47
2sqrt6

31. What is the intersection of A and B?
The set of elements found in both A and B.
1.0843 X 10^11
When the function is not defined for all real numbers -; only a subset of the real numbers.
87.5%

32. What are the real numbers?
1
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)
70
The second graph is less steep.

33. 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?
The curve opens downward and the vertex is the maximum point on the graph.
6 : 1 : 2
N! / (k!)(n-k)!
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

34. 5x^2 - 35x -55 = 0
Lies opposite the greater angle
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
90
413.03 / 10^4 (move the decimal point 4 places to the left)

35. 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)
4a^2(b)
2sqrt6
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

36. 5/8 in percent?
F(x + c)
The curve opens downward and the vertex is the maximum point on the graph.
75:11
62.5%

37. Legs 5 - 12. Hypotenuse?
x^(2(4)) =x^8 = (x^4)^2
37.5%
13
11 - 13 - 17 - 19

38. Can you subtract 3sqrt4 from sqrt4?
90pi
II
F(x) - c
Yes - like radicals can be added/subtracted.

39. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
70
90pi
83.333%

40. What is an exterior angle?
1:sqrt3:2
An angle which is supplementary to an interior angle.
9 & 6/7
41 - 43 - 47

41. What is the graph of f(x) shifted upward c units or spaces?
A central angle is an angle formed by 2 radii.
52
F(x) + c
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)

42. (x^2)^4
The sum of its digits is divisible by 3.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The interesection of A and B.
x^(2(4)) =x^8 = (x^4)^2

43. 4.809 X 10^7 =
6
The curve opens downward and the vertex is the maximum point on the graph.
A set with no members - denoted by a circle with a diagonal through it.
.0004809 X 10^11

44. What is the name of set with a number of elements which cannot be counted?
An infinite set.
180 degrees
23 - 29
A chord is a line segment joining two points on a circle.

45. 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
A chord is a line segment joining two points on a circle.
67 - 71 - 73
The overlapping sections.

46. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
No - only like radicals can be added.
The set of elements found in both A and B.

47. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
3/2 - 5/3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Factors are few - multiples are many.

48. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
13pi / 2
27^(-4)
(amount of decrease/original price) x 100%

49. Which quadrant is the upper right hand?
Even
F(x-c)
I
N! / (n-k)!

50. x^6 / x^3
x^(6-3) = x^3
31 - 37
C = 2(pi)r
(a - b)^2