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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 are the real numbers?
37.5%
The set of elements found in both A and B.
Factors are few - multiples are many.
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)

2. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
An isosceles right triangle.
.0004809 X 10^11
288 (8 9 4)

3. What does scientific notation mean?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
I
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
y = 2x^2 - 3

4. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
10
53 - 59
An infinite set.

5. 5/8 in percent?
62.5%
II
A reflection about the axis.
2sqrt6

6. Formula to calculate arc length?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
When the function is not defined for all real numbers -; only a subset of the real numbers.
Sector area = (n/360) X (pi)r^2
Arc length = (n/360) x pi(2r) where n is the number of degrees.

7. x^4 + x^7 =
413.03 / 10^4 (move the decimal point 4 places to the left)
2^9 / 2 = 256
Yes. [i.e. f(x) = x^2 - 1
x^(4+7) = x^11

8. Write 10 -843 X 10^7 in scientific notation
A reflection about the axis.
1.0843 X 10^11
A reflection about the origin.
$11 -448

9. a^0 =
x^(6-3) = x^3
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
70
1

10. What is the 'Range' of a function?
2 & 3/7
An isosceles right triangle.
The set of output values for a function.
Members or elements

11. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
441000 = 1 10 10 10 21 * 21
2sqrt6
16.6666%
True

12. What are the irrational numbers?

13. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
The steeper the slope.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
G(x) = {x}

14. What is the name for a grouping of the members within a set based on a shared characteristic?
3
x^(4+7) = x^11
A subset.
1 & 37/132

15. What is the surface area of a cylinder with radius 5 and height 8?
130pi
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Angle/360 x (pi)r^2
An expression with just one term (-6x - 2a^2)

16. What is the measure of an exterior angle of a regular pentagon?
The union of A and B.
A reflection about the origin.
Ax^2 + bx + c where a -b and c are constants and a /=0
72

17. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
N! / (n-k)!
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

18. What are the smallest three prime numbers greater than 65?
1
67 - 71 - 73
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 graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

19. Legs 6 - 8. Hypotenuse?
Move the decimal point to the right x places
10
An arc is a portion of a circumference of a circle.
11 - 13 - 17 - 19

20. 60 < all primes <70
No - the input value has exactly one output.
61 - 67
Two angles whose sum is 90.
1.7

21. What is the graph of f(x) shifted left c units or spaces?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
20.5
F(x + c)
x= (1.2)(.8)lw

22. A number is divisible by 3 if ...
52
A central angle is an angle formed by 2 radii.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The sum of its digits is divisible by 3.

23. What is a piecewise equation?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Part = Percent X Whole
4.25 - 6 - 22
Divide by 100.

24. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
A = pi(r^2)
6
Two equal sides and two equal angles.
500

25. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
IV
1
12! / 5!7! = 792
52

26. When does a function automatically have a restricted domain (2)?
61 - 67
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
(a - b)(a + b)
6 : 1 : 2

27. 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?
A circle centered on the origin with radius 8.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
10! / 3!(10-3)! = 120
x^(2(4)) =x^8 = (x^4)^2

28. Which quadrant is the upper left hand?
The set of output values for a function.
II
The greatest value minus the smallest.
Yes. [i.e. f(x) = x^2 - 1

29. What is a finite set?
I
6 : 1 : 2
A set with a number of elements which can be counted.
The set of elements which can be found in either A or B.

30. Area of a triangle?
A chord is a line segment joining two points on a circle.
3sqrt4
Angle/360 x 2(pi)r
(base*height) / 2

31. What is an arc of a circle?
70
IV
10
An arc is a portion of a circumference of a circle.

32. (-1)^3 =
x^(4+7) = x^11
1
3/2 - 5/3
Members or elements

33. (x^2)^4
Cd
x^(2(4)) =x^8 = (x^4)^2
(amount of increase/original price) x 100%
13

34. 1/8 in percent?
A subset.
Its negative reciprocal. (-b/a)
2sqrt6
12.5%

35. 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.
The curve opens upward and the vertex is the minimal point on the graph.
(a - b)^2
5
90 degrees

36. 413.03 x 10^(-4) =
G(x) = {x}
413.03 / 10^4 (move the decimal point 4 places to the left)
Its last two digits are divisible by 4.
A circle centered on the origin with radius 8.

37. What is the empty set?
Triangles with same measure and same side lengths.
A reflection about the axis.
A set with no members - denoted by a circle with a diagonal through it.
The longest arc between points A and B on a circle'S diameter.

38. 10^6 has how many zeroes?
1
6
A reflection about the origin.
F(x + c)

39. 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?
A set with no members - denoted by a circle with a diagonal through it.
48
No - the input value has exactly one output.
Part = Percent X Whole

40. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
13pi / 2
Angle/360 x (pi)r^2
Ax^2 + bx + c where a -b and c are constants and a /=0

41. What are congruent triangles?
(p + q)/5
Triangles with same measure and same side lengths.
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 curve opens downward and the vertex is the maximum point on the graph.

42. 2sqrt4 + sqrt4 =
1.0843 X 10^11
The curve opens downward and the vertex is the maximum point on the graph.
3sqrt4
Its negative reciprocal. (-b/a)

43. Can you subtract 3sqrt4 from sqrt4?
6
Its divisible by 2 and by 3.
Yes - like radicals can be added/subtracted.
Yes. [i.e. f(x) = x^2 - 1

44. What are 'Supplementary angles?'
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
130pi
An expression with just one term (-6x - 2a^2)
Two angles whose sum is 180.

45. How many 3-digit positive integers are even and do not contain the digit 4?
83.333%
288 (8 9 4)
F(x) - c
441000 = 1 10 10 10 21 * 21

46. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
41 - 43 - 47
True
x= (1.2)(.8)lw
(amount of decrease/original price) x 100%

47. How to determine percent increase?
A circle centered on the origin with radius 8.
90
Two angles whose sum is 180.
(amount of increase/original price) x 100%

48. What is the maximum value for the function g(x) = (-2x^2) -1?
Part = Percent X Whole
F(x + c)
1
A = I (1 + rt)

49. What is the 'Restricted domain of a function'?
When the function is not defined for all real numbers -; only a subset of the real numbers.
(amount of decrease/original price) x 100%
The second graph is less steep.
$11 -448

50. How many multiples does a given number have?
Infinite.
500
18
10! / 3!(10-3)! = 120