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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. 25^(1/2) or sqrt. 25 =
5 OR -5
A tangent is a line that only touches one point on the circumference of a circle.
(amount of decrease/original price) x 100%
55%

2. Max and Min lengths for a side of a triangle?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
Angle/360 x (pi)r^2
The third side is greater than the difference and less than the sum.
The greatest value minus the smallest.

3. 4.809 X 10^7 =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
C = (pi)d
.0004809 X 10^11
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

4. What are the rational numbers?
Two angles whose sum is 90.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
$3 -500 in the 9% and $2 -500 in the 7%.
The steeper the slope.

5. To multiply a number by 10^x
Move the decimal point to the right x places
The two xes after factoring.
From northeast - counterclockwise. I - II - III - IV
288 (8 9 4)

6. Formula of rectangle where l increases by 20% and w decreases by 20%
...multiply by 100.
x= (1.2)(.8)lw
13pi / 2
Move the decimal point to the right x places

7. Pi is a ratio of what to what?

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8. How to find the area of a sector?
2
Angle/360 x (pi)r^2
1 & 37/132
72

9. The ratio of the areas of two similar polygons is ...
The direction of the inequality is reversed.
x^(4+7) = x^11
... the square of the ratios of the corresponding sides.
(amount of decrease/original price) x 100%

10. How to find the diagonal of a rectangular solid?
(a + b)^2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
(n-2) x 180

11. When the 'a' in a parabola is positive....
III
The curve opens upward and the vertex is the minimal point on the graph.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Two equal sides and two equal angles.

12. Formula for the area of a sector of a circle?
A = I (1 + rt)
Area of the base X height = (pi)hr^2
4725
Sector area = (n/360) X (pi)r^2

13. What is a major arc?

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14. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
75:11
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.
Cd
4:5

15. 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?
I
The union of A and B.
$3 -500 in the 9% and $2 -500 in the 7%.
Yes. [i.e. f(x) = x^2 - 1

16. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
Indeterminable.
1
All numbers multiples of 1.
A tangent is a line that only touches one point on the circumference of a circle.

17. 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?
A central angle is an angle formed by 2 radii.
72
N! / (k!)(n-k)!
From northeast - counterclockwise. I - II - III - IV

18. 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
A circle centered on the origin with radius 8.
The objects within a set.
1

19. Factor x^2 - xy + x.
The curve opens upward and the vertex is the minimal point on the graph.
x(x - y + 1)
1 & 37/132
Factors are few - multiples are many.

20. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
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
90
Undefined - because we can'T divide by 0.
An isosceles right triangle.

21. What is the formula for compounded interest?
(b + c)
(a + b)^2
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.
4725

22. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
48
13pi / 2
1

23. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
All numbers multiples of 1.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
True

24. The slope of a line perpendicular to (a/b)?
6 : 1 : 2
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
1
Its negative reciprocal. (-b/a)

25. a^2 + 2ab + b^2
4725
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(a + b)^2
The objects within a set.

26. The perimeter of a square is 48 inches. The length of its diagonal is:
Indeterminable.
67 - 71 - 73
(amount of increase/original price) x 100%
12sqrt2

27. Is 0 even or odd?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
1.0843 X 10^11
Even
2sqrt6

28. The objects in a set are called two names:
1 & 37/132
No - the input value has exactly one output.
G(x) = {x}
Members or elements

29. 5/8 in percent?
Even
1/a^6
The third side is greater than the difference and less than the sum.
62.5%

30. What is the intersection of A and B?
Lies opposite the greater angle
The second graph is less steep.
The set of elements found in both A and B.
Sector area = (n/360) X (pi)r^2

31. Define a 'monomial'
288 (8 9 4)
Its divisible by 2 and by 3.
(p + q)/5
An expression with just one term (-6x - 2a^2)

32. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Infinite.
0
2
The point of intersection of the systems.

33. (x^2)^4
Yes - like radicals can be added/subtracted.
x^(2(4)) =x^8 = (x^4)^2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

34. Which is greater? 200x^295 or 10x^294?
y = (x + 5)/2
The second graph is less steep.
An infinite set.
Relationship cannot be determined (what if x is negative?)

35. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
$11 -448
Divide by 100.
An infinite set.

36. What is the graph of f(x) shifted left c units or spaces?
F(x + c)
The sum of digits is divisible by 9.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
When the function is not defined for all real numbers -; only a subset of the real numbers.

37. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
No - the input value has exactly one output.
Cd
1.0843 X 10^11

38. How many sides does a hexagon have?
6
3
1 & 37/132
1/a^6

39. What are the smallest three prime numbers greater than 65?
Divide by 100.
130pi
67 - 71 - 73
Part = Percent X Whole

40. 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)?
The set of output values for a function.
13
y = (x + 5)/2
The set of input values for a function.

41. Convert 0.7% to a fraction.
1:sqrt3:2
12! / 5!7! = 792
(a - b)(a + b)
7 / 1000

42. What is a chord of a circle?
A set with no members - denoted by a circle with a diagonal through it.
(b + c)
A chord is a line segment joining two points on a circle.
6

43. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
The greatest value minus the smallest.
Area of the base X height = (pi)hr^2
A 30-60-90 triangle.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

44. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
All numbers multiples of 1.
3 - -3
7 / 1000

45. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
75:11
3sqrt4
70
From northeast - counterclockwise. I - II - III - IV

46. What is the 'Restricted domain of a function'?
2 & 3/7
When the function is not defined for all real numbers -; only a subset of the real numbers.
N! / (k!)(n-k)!
(amount of increase/original price) x 100%

47. (6sqrt3) x (2sqrt5) =
6
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
3
23 - 29

48. Describe the relationship between 3x^2 and 3(x - 1)^2
3/2 - 5/3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
The third side is greater than the difference and less than the sum.
1

49. Legs 5 - 12. Hypotenuse?
90 degrees
53 - 59
413.03 / 10^4 (move the decimal point 4 places to the left)
13

50. Find the surface area of a cylinder with radius 3 and height 12.
28. n = 8 - k = 2. n! / k!(n-k)!
180 degrees
13pi / 2
90pi