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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 irrational numbers?

2. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
A tangent is a line that only touches one point on the circumference of a circle.
1
Lies opposite the greater angle
18

3. 70 < all primes< 80
71 - 73 - 79
$3 -500 in the 9% and $2 -500 in the 7%.
Diameter(Pi)
41 - 43 - 47

4. Pi is a ratio of what to what?

5. What are congruent triangles?
18
(b + c)
A set with no members - denoted by a circle with a diagonal through it.
Triangles with same measure and same side lengths.

6. When does a function automatically have a restricted domain (2)?
An isosceles right triangle.
Relationship cannot be determined (what if x is negative?)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Yes. [i.e. f(x) = x^2 - 1

7. What is the slope of a vertical line?

8. x^4 + x^7 =
3 - -3
1.0843 X 10^11
10! / 3!(10-3)! = 120
x^(4+7) = x^11

9. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
10! / 3!(10-3)! = 120
Infinite.
2

10. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The sum of digits is divisible by 9.
True

11. Describe the relationship between the graphs of x^2 and (1/2)x^2
10
75:11
The second graph is less steep.
(a - b)^2

12. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
The third side is greater than the difference and less than the sum.
2
Yes - like radicals can be added/subtracted.
1.0843 X 10^11

13. What is the maximum value for the function g(x) = (-2x^2) -1?
4a^2(b)
0
III
1

14. What is a central angle?
87.5%
A circle centered at -2 - -2 with radius 3.
A central angle is an angle formed by 2 radii.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

15. Can you add sqrt 3 and sqrt 5?
1 & 37/132
No - only like radicals can be added.
Diameter(Pi)
The direction of the inequality is reversed.

16. Find the surface area of a cylinder with radius 3 and height 12.
413.03 / 10^4 (move the decimal point 4 places to the left)
500
An expression with just one term (-6x - 2a^2)
90pi

17. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
3 - -3
(amount of decrease/original price) x 100%
8
1/a^6

18. Formula to find a circle'S circumference from its diameter?
16.6666%
Angle/360 x (pi)r^2
441000 = 1 10 10 10 21 * 21
C = (pi)d

19. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3
IV
The steeper the slope.

20. 1/2 divided by 3/7 is the same as
Two angles whose sum is 180.
18
1/2 times 7/3
The greatest value minus the smallest.

21. To convert a percent to a fraction....
Divide by 100.
90
The sum of digits is divisible by 9.
1/(x^y)

22. What number between 70 & 75 - inclusive - has the greatest number of factors?
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
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
72

23. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
x^(6-3) = x^3
87.5%
(a + b)^2
18

24. 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?
An angle which is supplementary to an interior angle.
3
Sector area = (n/360) X (pi)r^2
10! / (10-3)! = 720

25. Is 0 even or odd?
A central angle is an angle formed by 2 radii.
2sqrt6
Even
6

26. 1/6 in percent?
A subset.
16.6666%
180 degrees
y = 2x^2 - 3

27. Describe the relationship between 3x^2 and 3(x - 1)^2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The point of intersection of the systems.
1
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

28. What are the rational numbers?
87.5%
Yes. [i.e. f(x) = x^2 - 1
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

29. What are the roots of the quadrinomial x^2 + 2x + 1?
A set with a number of elements which can be counted.
1
3
The two xes after factoring.

30. Simplify the expression (p^2 - q^2)/ -5(q - p)
Undefined
6 : 1 : 2
An infinite set.
(p + q)/5

31. Evaluate 3& 2/7 / 1/3
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
9 & 6/7
Factors are few - multiples are many.
N! / (n-k)!

32. Factor x^2 - xy + x.
C = 2(pi)r
I
A central angle is an angle formed by 2 radii.
x(x - y + 1)

33. A number is divisible by 4 is...
Angle/360 x 2(pi)r
The set of elements found in both A and B.
Its last two digits are divisible by 4.
A reflection about the origin.

34. What is the slope of a horizontal line?
9 & 6/7
x^(4+7) = x^11
Sqrt 12
0

35. Formula for the area of a sector of a circle?
...multiply by 100.
Sector area = (n/360) X (pi)r^2
90
x^(4+7) = x^11

36. What is a set with no members called?
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)
The empty set - denoted by a circle with a diagonal through it.
Factors are few - multiples are many.
The shortest arc between points A and B on a circle'S diameter.

37. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
The sum of digits is divisible by 9.
The steeper the slope.
III
A reflection about the origin.

38. sqrt 2(sqrt 6)=
(a - b)(a + b)
x= (1.2)(.8)lw
Sqrt 12
12! / 5!7! = 792

39. (6sqrt3) x (2sqrt5) =
N! / (k!)(n-k)!
The empty set - denoted by a circle with a diagonal through it.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Diameter(Pi)

40. Surface area for a cylinder?
5 OR -5
x^(6-3) = x^3
2(pi)r^2 + 2(pi)rh
12.5%

41. 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
Divide by 100.
The sum of its digits is divisible by 3.
From northeast - counterclockwise. I - II - III - IV

42. What are the members or elements of a set?
The objects within a set.
Angle/360 x (pi)r^2
.0004809 X 10^11
90 degrees

43. What are the real numbers?
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)
When the function is not defined for all real numbers -; only a subset of the real numbers.
Sqrt 12
75:11

44. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
2.592 kg
III
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(b + c)

45. To multiply a number by 10^x
x^(4+7) = x^11
Yes. [i.e. f(x) = x^2 - 1
Move the decimal point to the right x places
27^(-4)

46. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
A subset.
$11 -448
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
3

47. 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?
Move the decimal point to the right x places
The interesection of A and B.
20.5
441000 = 1 10 10 10 21 * 21

48. What is the graph of f(x) shifted right c units or spaces?
Cd
F(x-c)
(n-2) x 180
12.5%

49. To convert a decimal to a percent...
16.6666%
...multiply by 100.
3/2 - 5/3
90 degrees

50. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
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
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
62.5%