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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. Simplify the expression (p^2 - q^2)/ -5(q - p)
10! / (10-3)! = 720
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)
(p + q)/5
Angle/360 x (pi)r^2

2. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
Pi is the ratio of a circle'S circumference to its diameter.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
0
10! / 3!(10-3)! = 120

3. 10^6 has how many zeroes?
13
A reflection about the origin.
Its last two digits are divisible by 4.
6

4. What is the formula for compounded interest?
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.
23 - 29
72

5. a^2 - b^2 =
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
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(a - b)(a + b)

6. What is the maximum value for the function g(x) = (-2x^2) -1?
28. n = 8 - k = 2. n! / k!(n-k)!
1
1/2 times 7/3
441000 = 1 10 10 10 21 * 21

7. Can you add sqrt 3 and sqrt 5?
A = pi(r^2)
No - only like radicals can be added.
N! / (k!)(n-k)!
x^(4+7) = x^11

8. 10<all primes<20
11 - 13 - 17 - 19
The shortest arc between points A and B on a circle'S diameter.
No - only like radicals can be added.
Pi is the ratio of a circle'S circumference to its diameter.

9. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
The set of input values for a function.
72
A reflection about the origin.
3

10. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
4096
A tangent is a line that only touches one point on the circumference of a circle.
4725

11. The slope of a line perpendicular to (a/b)?
Its negative reciprocal. (-b/a)
Sector area = (n/360) X (pi)r^2
2.592 kg
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

12. 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?
1 & 37/132
True
$3 -500 in the 9% and $2 -500 in the 7%.
The curve opens upward and the vertex is the minimal point on the graph.

13. What is the slope of a horizontal line?
1
0
23 - 29
An isosceles right triangle.

14. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The longest arc between points A and B on a circle'S diameter.
6
The point of intersection of the systems.

15. What is the name of set with a number of elements which cannot be counted?
52
2 & 3/7
An infinite set.
The second graph is less steep.

16. 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?
3/2 - 5/3
500
y = 2x^2 - 3
A set with no members - denoted by a circle with a diagonal through it.

17. 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?
The longest arc between points A and B on a circle'S diameter.
7 / 1000
500
G(x) = {x}

18. How many sides does a hexagon have?
6
2^9 / 2 = 256
Indeterminable.
An angle which is supplementary to an interior angle.

19. What is the order of operations?
y = 2x^2 - 3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(a - b)^2
Angle/360 x (pi)r^2

20. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
1
8
.0004809 X 10^11
1.0843 X 10^11

21. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
9 & 6/7
4:5
31 - 37
72

22. What is the set of elements which can be found in either A or B?
(amount of decrease/original price) x 100%
The point of intersection of the systems.
The union of A and B.
IV

23. 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 second graph is less steep.
90 degrees
y = (x + 5)/2
0

24. What are the smallest three prime numbers greater than 65?
All numbers multiples of 1.
67 - 71 - 73
I
An infinite set.

25. To multiply a number by 10^x
1
Move the decimal point to the right x places
16.6666%
III

26. (-1)^2 =
1
6
...multiply by 100.
1:sqrt3:2

27. x^4 + x^7 =
1
x^(4+7) = x^11
y = 2x^2 - 3
The overlapping sections.

28. Find the surface area of a cylinder with radius 3 and height 12.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
90pi
41 - 43 - 47
The union of A and B.

29. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
2(pi)r^2 + 2(pi)rh
12! / 5!7! = 792
83.333%
An angle which is supplementary to an interior angle.

30. What is the 'Range' of a series of numbers?
20.5
The greatest value minus the smallest.
9 : 25
A = pi(r^2)

31. 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= 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.
F(x + c)
75:11
N! / (k!)(n-k)!

32. If an inequality is multiplied or divided by a negative number....
1
130pi
The direction of the inequality is reversed.
The curve opens upward and the vertex is the minimal point on the graph.

33. The ratio of the areas of two similar polygons is ...
... the square of the ratios of the corresponding sides.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
A grouping of the members within a set based on a shared characteristic.
0

34. What percent of 40 is 22?
Undefined - because we can'T divide by 0.
No - the input value has exactly one output.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
55%

35. What is the ratio of the sides of a 30-60-90 triangle?
11 - 13 - 17 - 19
12! / 5!7! = 792
1.0843 X 10^11
1:sqrt3:2

36. What is an exterior angle?
3/2 - 5/3
4:5
An angle which is supplementary to an interior angle.
4725

37. Define a 'monomial'
27^(-4)
The union of A and B.
A tangent is a line that only touches one point on the circumference of a circle.
An expression with just one term (-6x - 2a^2)

38. Simplify the expression [(b^2 - c^2) / (b - c)]
A circle centered at -2 - -2 with radius 3.
The sum of its digits is divisible by 3.
(b + c)
1/a^6

39. a^2 - 2ab + b^2
16.6666%
41 - 43 - 47
(a - b)^2
1

40. 40 < all primes<50
.0004809 X 10^11
41 - 43 - 47
500
3sqrt4

41. What is the 'Restricted domain of a function'?
12.5%
From northeast - counterclockwise. I - II - III - IV
When the function is not defined for all real numbers -; only a subset of the real numbers.
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)

42. (-1)^3 =
37.5%
3/2 - 5/3
55%
1

43. What is the empty set?
55%
When the function is not defined for all real numbers -; only a subset of the real numbers.
III
A set with no members - denoted by a circle with a diagonal through it.

44. What are the members or elements of a set?
The objects within a set.
31 - 37
4725
The shortest arc between points A and B on a circle'S diameter.

45. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2sqrt6
The set of output values for a function.
I

46. 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?
3
48
y = (x + 5)/2
1

47. 30< all primes<40
The overlapping sections.
True
31 - 37
A chord is a line segment joining two points on a circle.

48. When the 'a' in the parabola is negative...
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 curve opens downward and the vertex is the maximum point on the graph.
Move the decimal point to the right x places
True

49. Legs 5 - 12. Hypotenuse?
C = 2(pi)r
13
The objects within a set.
I

50. What are congruent triangles?
A circle centered at -2 - -2 with radius 3.
The point of intersection of the systems.
Triangles with same measure and same side lengths.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.