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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.
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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. 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))?
x(x - y + 1)
9 & 6/7
20.5
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

2. Max and Min lengths for a side of a triangle?
The third side is greater than the difference and less than the sum.
180
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
13

3. x^4 + x^7 =
No - only like radicals can be added.
x^(4+7) = x^11
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 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)

4. x^6 / x^3
2sqrt6
The shortest arc between points A and B on a circle'S diameter.
x^(6-3) = x^3
C = (pi)d

5. Can you subtract 3sqrt4 from sqrt4?
Even
The sum of digits is divisible by 9.
N! / (k!)(n-k)!
Yes - like radicals can be added/subtracted.

6. Can you add sqrt 3 and sqrt 5?
6
No - only like radicals can be added.
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.
When the function is not defined for all real numbers -; only a subset of the real numbers.

7. 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?
10! / (10-3)! = 720
52
180 degrees
The direction of the inequality is reversed.

8. What is the 'Range' of a function?
The sum of its digits is divisible by 3.
20.5
The set of output values for a function.
5 OR -5

9. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
0
A 30-60-90 triangle.
8
72

10. Is 0 even or odd?
Move the decimal point to the right x places
Even
Diameter(Pi)
F(x-c)

11. What is the 'domain' of a function?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
90 degrees
The set of input values for a function.
The second graph is less steep.

12. What is the 'Restricted domain of a function'?
90 degrees
When the function is not defined for all real numbers -; only a subset of the real numbers.
11 - 13 - 17 - 19
Members or elements

13. (x^2)^4
Part = Percent X Whole
Move the decimal point to the right x places
x^(2(4)) =x^8 = (x^4)^2
12sqrt2

14. A number is divisible by 4 is...
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)
From northeast - counterclockwise. I - II - III - IV
Its last two digits are divisible by 4.
Move the decimal point to the right x places

15. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
A tangent is a line that only touches one point on the circumference of a circle.
37.5%
11 - 13 - 17 - 19

16. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
4.25 - 6 - 22
2 & 3/7
A chord is a line segment joining two points on a circle.
90 degrees

17. What is the set of elements found in both A and B?
Its negative reciprocal. (-b/a)
The interesection of A and B.
83.333%
3/2 - 5/3

18. What is the order of operations?
(a - b)(a + b)
C = (pi)d
441000 = 1 10 10 10 21 * 21
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

19. Order of quadrants:
Its last two digits are divisible by 4.
From northeast - counterclockwise. I - II - III - IV
(a - b)(a + b)
Indeterminable.

20. Number of degrees in a triangle
Relationship cannot be determined (what if x is negative?)
180
A = I (1 + rt)
(a + b)^2

21. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
The objects within a set.
67 - 71 - 73
Ax^2 + bx + c where a -b and c are constants and a /=0

22. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
Cd
3
10! / 3!(10-3)! = 120
The curve opens upward and the vertex is the minimal point on the graph.

23. 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?
(a - b)^2
52
62.5%
3/2 - 5/3

24. What is the area of a regular hexagon with side 6?
The sum of its digits is divisible by 3.
From northeast - counterclockwise. I - II - III - IV
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
72

25. Evaluate 3& 2/7 / 1/3
0
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
9 & 6/7
55%

26. What is the absolute value function?
72
G(x) = {x}
1
2.592 kg

27. What is the 'union' of A and B?
The shortest arc between points A and B on a circle'S diameter.
The set of elements which can be found in either A or B.
The union of A and B.
The empty set - denoted by a circle with a diagonal through it.

28. The larger the absolute value of the slope...
The steeper the slope.
The shortest arc between points A and B on a circle'S diameter.
IV
Two angles whose sum is 90.

29. To convert a decimal to a percent...
A = pi(r^2)
6
The set of output values for a function.
...multiply by 100.

30. What is the ratio of the sides of an isosceles right triangle?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
1/2 times 7/3
1:1:sqrt2
3 - -3

31. How many 3-digit positive integers are even and do not contain the digit 4?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
288 (8 9 4)
4725
A reflection about the origin.

32. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
67 - 71 - 73
180
1/(x^y)

33. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
Diameter(Pi)
Factors are few - multiples are many.
4:5
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

34. (-1)^3 =
1
2
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

35. 70 < all primes< 80
The set of input values for a function.
23 - 29
Cd
71 - 73 - 79

36. What is the graph of f(x) shifted right c units or spaces?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
F(x-c)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1

37. What are the real numbers?
72
90pi
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)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

38. Which quadrant is the upper left hand?
II
0
90 degrees
An expression with just one term (-6x - 2a^2)

39. To convert a percent to a fraction....
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)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Divide by 100.
A set with no members - denoted by a circle with a diagonal through it.

40. a^0 =
(amount of decrease/original price) x 100%
3
1
Its divisible by 2 and by 3.

41. How to determine percent decrease?
Sqrt 12
(amount of decrease/original price) x 100%
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)
Its divisible by 2 and by 3.

42. What is the empty set?
The set of output values for a function.
A set with no members - denoted by a circle with a diagonal through it.
1
2^9 / 2 = 256

43. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
2.592 kg
1
An isosceles right triangle.
An arc is a portion of a circumference of a circle.

44. What are complementary angles?
41 - 43 - 47
Two angles whose sum is 90.
90pi
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

45. Write 10 -843 X 10^7 in scientific notation
130pi
(a - b)(a + b)
27^(-4)
1.0843 X 10^11

46. Whats the difference between factors and multiples?
Factors are few - multiples are many.
70
5 OR -5
F(x-c)

47. How many sides does a hexagon have?
6
The second graph is less steep.
83.333%
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)

48. What is a piecewise equation?
20.5
37.5%
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
12! / 5!7! = 792

49. What is the graph of f(x) shifted left c units or spaces?
No - the input value has exactly one output.
F(x + c)
10! / 3!(10-3)! = 120
Two equal sides and two equal angles.

50. (12sqrt15) / (2sqrt5) =
16.6666%
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
1

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GRE Math: Common Errors

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