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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. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
Relationship cannot be determined (what if x is negative?)
4725
...multiply by 100.

2. What are the integers?
Two angles whose sum is 180.
Angle/360 x (pi)r^2
All numbers multiples of 1.
Undefined

3. What is the side length of an equilateral triangle with altitude 6?
(amount of increase/original price) x 100%
F(x + c)
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...
The sum of its digits is divisible by 3.

4. What is the ratio of the sides of a 30-60-90 triangle?
Its negative reciprocal. (-b/a)
1:sqrt3:2
Infinite.
... the square of the ratios of the corresponding sides.

5. 5/8 in percent?
C = 2(pi)r
62.5%
The interesection of A and B.
0

6. What is an exterior angle?
(base*height) / 2
1
The steeper the slope.
An angle which is supplementary to an interior angle.

7. a^2 - b^2 =
18
(a - b)(a + b)
Its divisible by 2 and by 3.
180 degrees

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))?
Lies opposite the greater angle
(base*height) / 2
20.5
Triangles with same measure and same side lengths.

9. Describe the relationship between the graphs of x^2 and (1/2)x^2
6
Its negative reciprocal. (-b/a)
The second graph is less steep.
No - the input value has exactly one output.

10. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
500
F(x) - c
A set with a number of elements which can be counted.

11. a^2 + 2ab + b^2
130pi
C = (pi)d
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...
(a + b)^2

12. The perimeter of a square is 48 inches. The length of its diagonal is:
1/a^6
12sqrt2
Divide by 100.
Relationship cannot be determined (what if x is negative?)

13. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
F(x-c)
1.0843 X 10^11
2.592 kg
3

14. What are the members or elements of a set?
1
18
The objects within a set.
1/(x^y)

15. What is the 'domain' of a function?
37.5%
The set of input values for a function.
130pi
Move the decimal point to the right x places

16. Is 0 even or odd?
Even
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1.7
The steeper the slope.

17. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
The empty set - denoted by a circle with a diagonal through it.
An angle which is supplementary to an interior angle.
Two equal sides and two equal angles.

18. What is the graph of f(x) shifted downward c units or spaces?
When the function is not defined for all real numbers -; only a subset of the real numbers.
An expression with just one term (-6x - 2a^2)
F(x) - c
180 degrees

19. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
The shortest arc between points A and B on a circle'S diameter.
1 & 37/132
70
5

20. What is a subset?
1/(x^y)
8
F(x) + c
A grouping of the members within a set based on a shared characteristic.

21. (12sqrt15) / (2sqrt5) =
1
3/2 - 5/3
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Its negative reciprocal. (-b/a)

22. Evaluate 4/11 + 11/12
2 & 3/7
1 & 37/132
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)
41 - 43 - 47

23. Factor a^2 + 2ab + b^2
(n-2) x 180
(a + b)^2
6
12sqrt2

24. Length of an arc of a circle?
413.03 / 10^4 (move the decimal point 4 places to the left)
The sum of digits is divisible by 9.
Angle/360 x 2(pi)r
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)

25. When does a function automatically have a restricted domain (2)?
52
y = (x + 5)/2
4a^2(b)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

26. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
Two equal sides and two equal angles.
27^(-4)
90 degrees
18

27. 40 < all primes<50
441000 = 1 10 10 10 21 * 21
71 - 73 - 79
41 - 43 - 47
1.7

28. What percent of 40 is 22?
55%
Angle/360 x (pi)r^2
Divide by 100.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

29. Solve the quadratic equation ax^2 + bx + c= 0
The curve opens downward and the vertex is the maximum point on the graph.
F(x + c)
x^(4+7) = x^11
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

30. What is a tangent?
III
A tangent is a line that only touches one point on the circumference of a circle.
The interesection of A and B.
(a - b)(a + b)

31. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
An infinite set.
71 - 73 - 79
180 degrees

32. What are complementary angles?
The steeper the slope.
1
Two angles whose sum is 90.
6

33. Describe the relationship between 3x^2 and 3(x - 1)^2
Its divisible by 2 and by 3.
A set with a number of elements which can be counted.
6
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

34. What is a central angle?
x(x - y + 1)
A central angle is an angle formed by 2 radii.
y = 2x^2 - 3
N! / (k!)(n-k)!

35. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
N! / (k!)(n-k)!
18
F(x-c)

36. A number is divisible by 9 if...
180 degrees
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The sum of digits is divisible by 9.
The two xes after factoring.

37. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
61 - 67
An isosceles right triangle.
12.5%
2

38. Which is greater? 64^5 or 16^8
A circle centered on the origin with radius 8.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
90
3

39. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(b + c)
4725
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
1/2 times 7/3

40. Which quadrant is the upper left hand?
1
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
II
(b + c)

41. 1/2 divided by 3/7 is the same as
A circle centered on the origin with radius 8.
(amount of decrease/original price) x 100%
1/2 times 7/3
31 - 37

42. x^(-y)=
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.
1.0843 X 10^11
1/(x^y)
1

43. Formula to calculate arc length?
13pi / 2
A central angle is an angle formed by 2 radii.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The set of elements which can be found in either A or B.

44. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Move the decimal point to the right x places
Cd
Area of the base X height = (pi)hr^2
12.5%

45. 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?
(b + c)
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
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
N! / (n-k)!

46. Pi is a ratio of what to what?

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47. How many multiples does a given number have?
Undefined - because we can'T divide by 0.
11 - 13 - 17 - 19
Infinite.
62.5%

48. Convert 0.7% to a fraction.
An arc is a portion of a circumference of a circle.
2
7 / 1000
Its last two digits are divisible by 4.

49. 30< all primes<40
4a^2(b)
6
The overlapping sections.
31 - 37

50. What is a chord of a circle?
1.0843 X 10^11
A chord is a line segment joining two points on a circle.
The second graph is less steep.
Its negative reciprocal. (-b/a)