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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. The ratio of the areas of two similar polygons is ...
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A circle centered on the origin with radius 8.
... the square of the ratios of the corresponding sides.

2. What is a minor arc?

3. 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...
71 - 73 - 79
6
An infinite set.

4. Simplify the expression [(b^2 - c^2) / (b - c)]
41 - 43 - 47
Diameter(Pi)
71 - 73 - 79
(b + c)

5. 1/8 in percent?
...multiply by 100.
Yes - like radicals can be added/subtracted.
12.5%
The objects within a set.

6. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
An infinite set.
y = (x + 5)/2
Its last two digits are divisible by 4.
3

7. Circumference of a circle?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Diameter(Pi)
3
The set of elements which can be found in either A or B.

8. Describe the relationship between the graphs of x^2 and (1/2)x^2
Divide by 100.
The second graph is less steep.
28. n = 8 - k = 2. n! / k!(n-k)!
3sqrt4

9. 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?
A reflection about the axis.
Its negative reciprocal. (-b/a)
A circle centered at -2 - -2 with radius 3.
y = 2x^2 - 3

10. Whats the difference between factors and multiples?
4096
A = pi(r^2)
Factors are few - multiples are many.
52

11. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
(b + c)
2^9 / 2 = 256
Diameter(Pi)
67 - 71 - 73

12. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
Part = Percent X Whole
The direction of the inequality is reversed.
Undefined - because we can'T divide by 0.

13. What is the 'domain' of a function?
90 degrees
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The set of input values for a function.
3/2 - 5/3

14. What does scientific notation mean?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
441000 = 1 10 10 10 21 * 21
A 30-60-90 triangle.
12! / 5!7! = 792

15. What is an arc of a circle?
83.333%
An arc is a portion of a circumference of a circle.
Even
1.0843 X 10^11

16. How to find the diagonal of a rectangular solid?
13pi / 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...
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

17. What is the 'Range' of a series of numbers?
7 / 1000
The greatest value minus the smallest.
The curve opens upward and the vertex is the minimal point on the graph.
Angle/360 x 2(pi)r

18. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
C = (pi)d
(b + c)
Ax^2 + bx + c where a -b and c are constants and a /=0

19. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
8
1
27^(-4)
Area of the base X height = (pi)hr^2

20. What is the 'union' of A and B?
5 OR -5
The set of elements which can be found in either A or B.
27^(-4)
y = 2x^2 - 3

21. What is the area of a regular hexagon with side 6?
8
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Yes. [i.e. f(x) = x^2 - 1
(a - b)(a + b)

22. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Cd
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A = I (1 + rt)
An infinite set.

23. What are the members or elements of a set?
The objects within a set.
A subset.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
y = 2x^2 - 3

24. Find the surface area of a cylinder with radius 3 and height 12.
37.5%
1
The sum of its digits is divisible by 3.
90pi

25. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
Lies opposite the greater angle
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
87.5%
70

26. 10^6 has how many zeroes?
6
A chord is a line segment joining two points on a circle.
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...
27^(-4)

27. 0^0
Its last two digits are divisible by 4.
130pi
10
Undefined

28. The perimeter of a square is 48 inches. The length of its diagonal is:
1.0843 X 10^11
(a - b)(a + b)
12sqrt2
8

29. Formula for the area of a circle?
A = pi(r^2)
2(pi)r^2 + 2(pi)rh
Undefined - because we can'T divide by 0.
7 / 1000

30. What are the rational numbers?
2 & 3/7
72
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
8

31. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
(n-2) x 180
2(pi)r^2 + 2(pi)rh
Lies opposite the greater angle
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

32. What are the roots of the quadrinomial x^2 + 2x + 1?
C = (pi)d
x^(4+7) = x^11
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 two xes after factoring.

33. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
2 & 3/7
500
13

34. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
4a^2(b)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
I

35. How many sides does a hexagon have?
C = 2(pi)r
6
Yes - like radicals can be added/subtracted.
3/2 - 5/3

36. Formula to find a circle'S circumference from its radius?
1/a^6
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
C = 2(pi)r
1

37. 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?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Even
500
Members or elements

38. Which is greater? 64^5 or 16^8
1
1:1:sqrt2
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
5 OR -5

39. Which is greater? 200x^295 or 10x^294?
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)
IV
Relationship cannot be determined (what if x is negative?)
413.03 / 10^4 (move the decimal point 4 places to the left)

40. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
$11 -448
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
4:5

41. What is the maximum value for the function g(x) = (-2x^2) -1?
III
18
1
An arc is a portion of a circumference of a circle.

42. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
37.5%
(b + c)
The two xes after factoring.
3

43. 4.809 X 10^7 =
.0004809 X 10^11
F(x-c)
N! / (n-k)!
True

44. 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?
(b + c)
(a - b)(a + b)
37.5%
10! / 3!(10-3)! = 120

45. What does the graph x^2 + y^2 = 64 look like?
2^9 / 2 = 256
A circle centered on the origin with radius 8.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
A grouping of the members within a set based on a shared characteristic.

46. Number of degrees in a triangle
Members or elements
180
55%
The set of elements found in both A and B.

47. Max and Min lengths for a side of a triangle?
The direction of the inequality is reversed.
3/2 - 5/3
12! / 5!7! = 792
The third side is greater than the difference and less than the sum.

48. Pi is a ratio of what to what?

49. a^2 + 2ab + b^2
Two angles whose sum is 90.
1
(a + b)^2
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

50. The slope of a line perpendicular to (a/b)?
Its negative reciprocal. (-b/a)
Cd
0
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.