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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 is the 'union' of A and B?
The set of elements which can be found in either A or B.
23 - 29
... the square of the ratios of the corresponding sides.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

2. Evaluate 4/11 + 11/12
Members or elements
1 & 37/132
1.0843 X 10^11
An expression with just one term (-6x - 2a^2)

3. What is the surface area of a cylinder with radius 5 and height 8?
12.5%
True
A = I (1 + rt)
130pi

4. 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?
2(pi)r^2 + 2(pi)rh
N! / (n-k)!
(a + b)^2
2^9 / 2 = 256

5. What are congruent triangles?
The direction of the inequality is reversed.
Triangles with same measure and same side lengths.
y = 2x^2 - 3
F(x) + c

6. Max and Min lengths for a side of a triangle?
Factors are few - multiples are many.
The third side is greater than the difference and less than the sum.
1
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

7. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
Triangles with same measure and same side lengths.
6 : 1 : 2
13pi / 2
The set of input values for a function.

8. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
Divide by 100.
7 / 1000
37.5%

9. Area of a triangle?
x^(2(4)) =x^8 = (x^4)^2
(base*height) / 2
The set of elements which can be found in either A or B.
500

10. Describe the relationship between 3x^2 and 3(x - 1)^2
(a + b)^2
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)
10! / 3!(10-3)! = 120

11. Describe the relationship between the graphs of x^2 and (1/2)x^2
53 - 59
The steeper the slope.
The second graph is less steep.
A 30-60-90 triangle.

12. 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?
Ax^2 + bx + c where a -b and c are constants and a /=0
75:11
0
F(x) - c

13. What is a piecewise equation?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
A central angle is an angle formed by 2 radii.
The set of input values for a function.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

14. How to determine percent decrease?
No - only like radicals can be added.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
(amount of decrease/original price) x 100%
G(x) = {x}

15. How many sides does a hexagon have?
6
A chord is a line segment joining two points on a circle.
Ax^2 + bx + c where a -b and c are constants and a /=0
The greatest value minus the smallest.

16. Volume for a cylinder?
No - the input value has exactly one output.
A circle centered on the origin with radius 8.
Area of the base X height = (pi)hr^2
2sqrt6

17. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
IV
Relationship cannot be determined (what if x is negative?)
2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

18. What is a major arc?

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19. 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)?
5 OR -5
10! / 3!(10-3)! = 120
Even
y = (x + 5)/2

20. 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?
$3 -500 in the 9% and $2 -500 in the 7%.
Relationship cannot be determined (what if x is negative?)
An angle which is supplementary to an interior angle.
The interesection of A and B.

21. Simplify 9^(1/2) X 4^3 X 2^(-6)?
II
48
3
90

22. 1/8 in percent?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1.0843 X 10^11
12.5%
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)

23. A number is divisible by 9 if...
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The sum of digits is divisible by 9.
62.5%
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

24. Evaluate 3& 2/7 / 1/3
1
An infinite set.
9 & 6/7
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

25. When does a function automatically have a restricted domain (2)?
288 (8 9 4)
(amount of increase/original price) x 100%
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
.0004809 X 10^11

26. Circumference of a circle?
C = (pi)d
Diameter(Pi)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
28. n = 8 - k = 2. n! / k!(n-k)!

27. Which quadrant is the lower left hand?
The two xes after factoring.
III
(amount of decrease/original price) x 100%
The shortest arc between points A and B on a circle'S diameter.

28. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
90
N! / (n-k)!
87.5%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

29. 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))?
The third side is greater than the difference and less than the sum.
20.5
3
y = 2x^2 - 3

30. What is the empty set?
(amount of increase/original price) x 100%
Yes. [i.e. f(x) = x^2 - 1
A set with no members - denoted by a circle with a diagonal through it.
The union of A and B.

31. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
13
A = pi(r^2)
4.25 - 6 - 22
The union of A and B.

32. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
72
A circle centered at -2 - -2 with radius 3.
3/2 - 5/3
Undefined

33. What is a tangent?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A tangent is a line that only touches one point on the circumference of a circle.
61 - 67
1.0843 X 10^11

34. How to find the circumference of a circle which circumscribes a square?
The sum of digits is divisible by 9.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
A reflection about the axis.
3 - -3

35. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A set with a number of elements which can be counted.
(a - b)(a + b)
1.0843 X 10^11

36. Factor x^2 - xy + x.
62.5%
The point of intersection of the systems.
x(x - y + 1)
53 - 59

37. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(a - b)(a + b)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
18
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

38. What is the name of set with a number of elements which cannot be counted?
An infinite set.
The set of elements found in both A and B.
10
(b + c)

39. What is the graph of f(x) shifted downward c units or spaces?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
F(x) - c
0
(a - b)^2

40. What is the set of elements which can be found in either A or B?
Area of the base X height = (pi)hr^2
The sum of its digits is divisible by 3.
2
The union of A and B.

41. 7/8 in percent?
87.5%
x(x - y + 1)
A chord is a line segment joining two points on a circle.
0

42. Formula of rectangle where l increases by 20% and w decreases by 20%
1:sqrt3:2
x(x - y + 1)
x= (1.2)(.8)lw
The curve opens upward and the vertex is the minimal point on the graph.

43. What is a minor arc?

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44. 40 < all primes<50
41 - 43 - 47
The empty set - denoted by a circle with a diagonal through it.
13pi / 2
The curve opens upward and the vertex is the minimal point on the graph.

45. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
3sqrt4
The shortest arc between points A and B on a circle'S diameter.
Cd
87.5%

46. Whats the difference between factors and multiples?
x(x - y + 1)
90pi
Angle/360 x (pi)r^2
Factors are few - multiples are many.

47. Find the surface area of a cylinder with radius 3 and height 12.
18
48
90pi
A = I (1 + rt)

48. Formula to find a circle'S circumference from its radius?
90 degrees
C = 2(pi)r
2.592 kg
The direction of the inequality is reversed.

49. To convert a decimal to a percent...
Even
Its last two digits are divisible by 4.
...multiply by 100.
55%

50. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
x= (1.2)(.8)lw
90
Pi is the ratio of a circle'S circumference to its diameter.