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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. x^(-y)=
Area of the base X height = (pi)hr^2
1/(x^y)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
All numbers multiples of 1.

2. 1/2 divided by 3/7 is the same as
II
Pi is the ratio of a circle'S circumference to its diameter.
75:11
1/2 times 7/3

3. (-1)^3 =
$3 -500 in the 9% and $2 -500 in the 7%.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
1

4. 1/8 in percent?
70
A chord is a line segment joining two points on a circle.
12.5%
4:5

5. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
The sum of its digits is divisible by 3.
2 & 3/7
A set with a number of elements which can be counted.
441000 = 1 10 10 10 21 * 21

6. Formula for the area of a sector of a circle?
No - only like radicals can be added.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Sector area = (n/360) X (pi)r^2

7. Simplify 9^(1/2) X 4^3 X 2^(-6)?
5 OR -5
3
$3 -500 in the 9% and $2 -500 in the 7%.
II

8. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
20.5
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Pi is the ratio of a circle'S circumference to its diameter.
8

9. What is a subset?
A grouping of the members within a set based on a shared characteristic.
Sector area = (n/360) X (pi)r^2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

10. 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?
(a - b)(a + b)
10! / 3!(10-3)! = 120
Factors are few - multiples are many.
II

11. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4096
An expression with just one term (-6x - 2a^2)
4725
x= (1.2)(.8)lw

12. What is a piecewise equation?
Diameter(Pi)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
2sqrt6
C = (pi)d

13. Whats the difference between factors and multiples?
Factors are few - multiples are many.
52
(a + b)^2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.

14. To convert a decimal to a percent...
9 : 25
N! / (n-k)!
...multiply by 100.
90

15. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
(base*height) / 2
71 - 73 - 79

16. 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))?
23 - 29
20.5
288 (8 9 4)
3/2 - 5/3

17. What is the percent formula?
(b + c)
28. n = 8 - k = 2. n! / k!(n-k)!
Part = Percent X Whole
All the numbers on the number line (negative - rational - irrational - decimal - integer). All the numbers on the GRE are real. (-2 - 1 - .25 - 1/2 - pi)

18. 40 < all primes<50
C = (pi)d
$3 -500 in the 9% and $2 -500 in the 7%.
41 - 43 - 47
The curve opens upward and the vertex is the minimal point on the graph.

19. What is the slope of a horizontal line?
0
A subset.
A chord is a line segment joining two points on a circle.
90pi

20. Legs: 3 - 4. Hypotenuse?
27^(-4)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Move the decimal point to the right x places
5

21. 1/6 in percent?
1/2 times 7/3
16.6666%
(amount of increase/original price) x 100%
5 OR -5

22. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
The third side is greater than the difference and less than the sum.
18
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.
13pi / 2

23. If the two sides of a triangle are unequal then the longer side...
500
1 & 37/132
Lies opposite the greater angle
An arc is a portion of a circumference of a circle.

24. If an inequality is multiplied or divided by a negative number....
y = 2x^2 - 3
The direction of the inequality is reversed.
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 & 37/132

25. Can the input value of a function have more than one output value (i.e. x: y - y1)?
Yes. [i.e. f(x) = x^2 - 1
87.5%
No - the input value has exactly one output.
41 - 43 - 47

26. Length of an arc of a circle?
Angle/360 x 2(pi)r
Yes. [i.e. f(x) = x^2 - 1
1 & 37/132
1.0843 X 10^11

27. 6w^2 - w - 15 = 0
F(x) + c
28. n = 8 - k = 2. n! / k!(n-k)!
37.5%
3/2 - 5/3

28. What is the empty set?
2.592 kg
Factors are few - multiples are many.
A set with no members - denoted by a circle with a diagonal through it.
Two equal sides and two equal angles.

29. When the 'a' in a parabola is positive....
Move the decimal point to the right x places
F(x) - c
4725
The curve opens upward and the vertex is the minimal point on the graph.

30. What is the 'union' of A and B?
Ax^2 + bx + c where a -b and c are constants and a /=0
5
The set of elements which can be found in either A or B.
Angle/360 x 2(pi)r

31. Can the output value of a function have more than one input value?
All numbers multiples of 1.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Triangles with same measure and same side lengths.
Yes. [i.e. f(x) = x^2 - 1

32. Can you simplify sqrt72?
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.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

33. 60 < all primes <70
A 30-60-90 triangle.
A circle centered at -2 - -2 with radius 3.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
61 - 67

34. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
9 : 25
An angle which is supplementary to an interior angle.
$11 -448
Members or elements

35. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
x= (1.2)(.8)lw
1
2
9 & 6/7

36. What are the roots of the quadrinomial x^2 + 2x + 1?
90pi
1.7
1
The two xes after factoring.

37. What is the slope of a vertical line?

38. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
The set of input values for a function.
90
1
180 degrees

39. What is a chord of a circle?
(p + q)/5
2^9 / 2 = 256
12! / 5!7! = 792
A chord is a line segment joining two points on a circle.

40. What is the ratio of the sides of a 30-60-90 triangle?
A central angle is an angle formed by 2 radii.
1:sqrt3:2
F(x-c)
Relationship cannot be determined (what if x is negative?)

41. What is a finite set?
4725
A set with a number of elements which can be counted.
Two angles whose sum is 180.
The set of elements found in both A and B.

42. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
62.5%
52
1
I

43. What is the graph of f(x) shifted left c units or spaces?
130pi
F(x + c)
Diameter(Pi)
67 - 71 - 73

44. 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?
8
500
A set with a number of elements which can be counted.
Its last two digits are divisible by 4.

45. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
12.5%
A tangent is a line that only touches one point on the circumference of a circle.
x^(4+7) = x^11
28. n = 8 - k = 2. n! / k!(n-k)!

46. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
(a - b)(a + b)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
90 degrees
1

47. To multiply a number by 10^x
Move the decimal point to the right x places
II
53 - 59
x= (1.2)(.8)lw

48. a^2 - b^2
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 - b)(a + b)
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...
2 & 3/7

49. Can you add sqrt 3 and sqrt 5?
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.
The curve opens downward and the vertex is the maximum point on the graph.
No - only like radicals can be added.
2^9 / 2 = 256

50. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
70
Pi is the ratio of a circle'S circumference to its diameter.
3/2 - 5/3