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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 are the roots of the quadrinomial x^2 + 2x + 1?
6
The two xes after factoring.
5 OR -5
12! / 5!7! = 792

2. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
4096
1
4a^2(b)
The point of intersection of the systems.

3. Simplify the expression (p^2 - q^2)/ -5(q - p)
Yes. [i.e. f(x) = x^2 - 1
10! / (10-3)! = 720
(p + q)/5
(base*height) / 2

4. What is a finite set?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
A set with a number of elements which can be counted.
Two angles whose sum is 90.
37.5%

5. Describe the relationship between 3x^2 and 3(x - 1)^2
4.25 - 6 - 22
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
13pi / 2
Area of the base X height = (pi)hr^2

6. What is the 'Solution' for a system of linear equations?
The curve opens upward and the vertex is the minimal point on the graph.
1
48
The point of intersection of the systems.

7. 6w^2 - w - 15 = 0
x(x - y + 1)
2sqrt6
Undefined
3/2 - 5/3

8. 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 reflection about the origin.
Two angles whose sum is 90.
y = 2x^2 - 3

9. 7/8 in percent?
4096
87.5%
12! / 5!7! = 792
True

10. Which quadrant is the lower left hand?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
9 : 25
A reflection about the origin.
III

11. Formula of rectangle where l increases by 20% and w decreases by 20%
A 30-60-90 triangle.
x= (1.2)(.8)lw
4725
20.5

12. Is 0 even or odd?
(a - b)(a + b)
Two angles whose sum is 180.
Even
$11 -448

13. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
(a - b)(a + b)
The set of input values for a function.
10! / (10-3)! = 720
A tangent is a line that only touches one point on the circumference of a circle.

14. Define an 'expression'.
The direction of the inequality is reversed.
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)
Sqrt 12
Factors are few - multiples are many.

15. 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?
C = (pi)d
10! / 3!(10-3)! = 120
When the function is not defined for all real numbers -; only a subset of the real numbers.
The curve opens upward and the vertex is the minimal point on the graph.

16. Number of degrees in a triangle
True
A = I (1 + rt)
2(pi)r^2 + 2(pi)rh
180

17. 70 < all primes< 80
71 - 73 - 79
48
53 - 59
1/2 times 7/3

18. To convert a percent to a fraction....
52
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...
90
Divide by 100.

19. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The two xes after factoring.
1.7
An infinite set.

20. What is the empty set?
18
A set with no members - denoted by a circle with a diagonal through it.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The union of A and B.

21. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
10
18
12.5%
12! / 5!7! = 792

22. What number between 70 & 75 - inclusive - has the greatest number of factors?
(n-2) x 180
No - only like radicals can be added.
72
83.333%

23. What is a piecewise equation?
The two xes after factoring.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

24. 30< all primes<40
Its last two digits are divisible by 4.
Part = Percent X Whole
31 - 37
48

25. 10^6 has how many zeroes?
A central angle is an angle formed by 2 radii.
A reflection about the axis.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
6

26. How many 3-digit positive integers are even and do not contain the digit 4?
Even
Diameter(Pi)
288 (8 9 4)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

27. 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?
3 - -3
441000 = 1 10 10 10 21 * 21
31 - 37
Members or elements

28. How many sides does a hexagon have?
4.25 - 6 - 22
The point of intersection of the systems.
An angle which is supplementary to an interior angle.
6

29. Legs 6 - 8. Hypotenuse?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
...multiply by 100.
10
2(pi)r^2 + 2(pi)rh

30. Which is greater? 27^(-4) or 9^(-8)
1 & 37/132
1
The steeper the slope.
27^(-4)

31. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
x^(6-3) = x^3
(n-2) x 180
31 - 37

32. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
70
The point of intersection of the systems.
28. n = 8 - k = 2. n! / k!(n-k)!
II

33. a^2 - 2ab + b^2
37.5%
(a - b)^2
A chord is a line segment joining two points on a circle.
Yes. [i.e. f(x) = x^2 - 1

34. a^0 =
1
67 - 71 - 73
6
41 - 43 - 47

35. What are congruent triangles?
Triangles with same measure and same side lengths.
6
(a + b)^2
16.6666%

36. Which quandrant is the lower right hand?
3/2 - 5/3
4096
IV
1 & 37/132

37. What is the formula for compounded interest?
Angle/360 x (pi)r^2
A reflection about the axis.
The steeper the slope.
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.

38. 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?
130pi
The third side is greater than the difference and less than the sum.
$3 -500 in the 9% and $2 -500 in the 7%.
N! / (k!)(n-k)!

39. 3/8 in percent?
The curve opens upward and the vertex is the minimal point on the graph.
37.5%
1 & 37/132
Yes. [i.e. f(x) = x^2 - 1

40. What is the graph of f(x) shifted left c units or spaces?
3
F(x + c)
Infinite.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

41. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
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)
Arc length = (n/360) x pi(2r) where n is the number of degrees.

42. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
F(x) + c
A circle centered at -2 - -2 with radius 3.
12! / 5!7! = 792
5

43. Formula for the area of a sector of a circle?
When the function is not defined for all real numbers -; only a subset of the real numbers.
(amount of increase/original price) x 100%
Sector area = (n/360) X (pi)r^2
Divide by 100.

44. 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)?
A chord is a line segment joining two points on a circle.
Yes. [i.e. f(x) = x^2 - 1
Undefined - because we can'T divide by 0.
y = (x + 5)/2

45. What are the rational numbers?
N! / (k!)(n-k)!
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
7 / 1000
1

46. How many multiples does a given number have?
Infinite.
A set with a number of elements which can be counted.
Factors are few - multiples are many.
1.0843 X 10^11

47. 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?
Its divisible by 2 and by 3.
(amount of increase/original price) x 100%
48
90 degrees

48. Can the output value of a function have more than one input value?
(p + q)/5
3sqrt4
Area of the base X height = (pi)hr^2
Yes. [i.e. f(x) = x^2 - 1

49. 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?
N! / (n-k)!
8
0
75:11

50. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
F(x + c)
1/(x^y)
4096
8