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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. Length of an arc of a circle?
A grouping of the members within a set based on a shared characteristic.
y = 2x^2 - 3
Angle/360 x 2(pi)r
Its negative reciprocal. (-b/a)

2. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
A subset.
(a - b)(a + b)
N! / (k!)(n-k)!
75:11

3. 50 < all primes< 60
(base*height) / 2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
12! / 5!7! = 792
53 - 59

4. What is the empty set?
$3 -500 in the 9% and $2 -500 in the 7%.
A set with no members - denoted by a circle with a diagonal through it.
4725
13

5. In a regular polygon with n sides - the formula for the sum of interior angles
70
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(n-2) x 180
x^(4+7) = x^11

6. 413.03 x 10^(-4) =
1:sqrt3:2
413.03 / 10^4 (move the decimal point 4 places to the left)
.0004809 X 10^11
(amount of increase/original price) x 100%

7. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
12! / 5!7! = 792
Two angles whose sum is 90.

8. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
Cd
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
II

9. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
2 & 3/7
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
$11 -448

10. What is the sum of the angles of a triangle?
180 degrees
The longest arc between points A and B on a circle'S diameter.
Undefined
28. n = 8 - k = 2. n! / k!(n-k)!

11. What are the rational numbers?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
3
$11 -448

12. Pi is a ratio of what to what?

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13. What is the slope of a horizontal line?
A = pi(r^2)
0
F(x + c)
The curve opens upward and the vertex is the minimal point on the graph.

14. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
A reflection about the axis.
4:5
20.5

15. a^2 + 2ab + b^2
9 : 25
(a + b)^2
6 : 1 : 2
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

16. What is the graph of f(x) shifted left c units or spaces?
6
413.03 / 10^4 (move the decimal point 4 places to the left)
F(x + c)
9 & 6/7

17. Area of a triangle?
2(pi)r^2 + 2(pi)rh
(base*height) / 2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
When the function is not defined for all real numbers -; only a subset of the real numbers.

18. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
When the function is not defined for all real numbers -; only a subset of the real numbers.
90 degrees
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
3

19. To convert a percent to a fraction....
(a - b)^2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
1.7
Divide by 100.

20. 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)]?
90 degrees
Even
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)
True

21. 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?
y = 2x^2 - 3
12! / 5!7! = 792
F(x-c)
G(x) = {x}

22. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
62.5%
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Its last two digits are divisible by 4.

23. Formula for the area of a circle?
Infinite.
18
441000 = 1 10 10 10 21 * 21
A = pi(r^2)

24. Which quadrant is the upper left hand?
Two angles whose sum is 90.
An infinite set.
II
Pi is the ratio of a circle'S circumference to its diameter.

25. How to find the diagonal of a rectangular solid?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A reflection about the axis.
(a + b)^2
Sqrt 12

26. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
41 - 43 - 47
The third side is greater than the difference and less than the sum.
0
The set of elements found in both A and B.

27. 7/8 in percent?
A set with no members - denoted by a circle with a diagonal through it.
87.5%
90 degrees
The union of A and B.

28. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Factors are few - multiples are many.
28. n = 8 - k = 2. n! / k!(n-k)!
III
52

29. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
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 + b)^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A reflection about the origin.

30. Reduce: 4.8 : 0.8 : 1.6
441000 = 1 10 10 10 21 * 21
3/2 - 5/3
A = I (1 + rt)
6 : 1 : 2

31. What are the roots of the quadrinomial x^2 + 2x + 1?
x(x - y + 1)
4725
y = (x + 5)/2
The two xes after factoring.

32. What is the name of set with a number of elements which cannot be counted?
An infinite set.
8
Sqrt 12
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

33. 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?
1
10! / 3!(10-3)! = 120
Its last two digits are divisible by 4.
48

34. How to determine percent decrease?
C = 2(pi)r
A set with no members - denoted by a circle with a diagonal through it.
(amount of decrease/original price) x 100%
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

35. 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?
1
G(x) = {x}
500
87.5%

36. To multiply a number by 10^x
8
1/2 times 7/3
Yes - like radicals can be added/subtracted.
Move the decimal point to the right x places

37. What is a major arc?

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38. 2sqrt4 + sqrt4 =
... the square of the ratios of the corresponding sides.
3sqrt4
1:sqrt3:2
C = 2(pi)r

39. 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.
3
IV
The empty set - denoted by a circle with a diagonal through it.

40. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
An infinite set.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(b + c)

41. Solve the quadratic equation ax^2 + bx + c= 0
(amount of increase/original price) x 100%
A 30-60-90 triangle.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
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...

42. Which quandrant is the lower right hand?
70
IV
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
Undefined

43. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
2.592 kg
413.03 / 10^4 (move the decimal point 4 places to the left)
7 / 1000

44. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Yes. [i.e. f(x) = x^2 - 1
(a + b)^2
A 30-60-90 triangle.

45. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
3
I
A set with a number of elements which can be counted.

46. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
The empty set - denoted by a circle with a diagonal through it.
3
N! / (n-k)!
An isosceles right triangle.

47. 8.84 / 5.2
A tangent is a line that only touches one point on the circumference of a circle.
10! / (10-3)! = 720
1.7
Relationship cannot be determined (what if x is negative?)

48. What is the set of elements found in both A and B?
(a - b)(a + b)
IV
The empty set - denoted by a circle with a diagonal through it.
The interesection of A and B.

49. Number of degrees in a triangle
The set of output values for a function.
An angle which is supplementary to an interior angle.
180
Sqrt 12

50. What is the 'Solution' for a system of linear equations?
The point of intersection of the systems.
Two angles whose sum is 90.
(n-2) x 180
Arc length = (n/360) x pi(2r) where n is the number of degrees.