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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 'domain' of a function?
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.
31 - 37
12! / 5!7! = 792

2. Formula for the area of a circle?
The set of elements which can be found in either A or B.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
180 degrees
A = pi(r^2)

3. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Its last two digits are divisible by 4.
53 - 59
Area of the base X height = (pi)hr^2

4. Factor a^2 + 2ab + b^2
(a + b)^2
A set with a number of elements which can be counted.
4a^2(b)
288 (8 9 4)

5. Surface area for a cylinder?
(a + b)^2
13
2(pi)r^2 + 2(pi)rh
10! / 3!(10-3)! = 120

6. To convert a decimal to a percent...
37.5%
...multiply by 100.
The greatest value minus the smallest.
I

7. Which quadrant is the upper right hand?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The shortest arc between points A and B on a circle'S diameter.
Two angles whose sum is 180.
I

8. Evaluate 3& 2/7 / 1/3
9 & 6/7
Two equal sides and two equal angles.
1 & 37/132
3/2 - 5/3

9. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
The longest arc between points A and B on a circle'S diameter.
The direction of the inequality is reversed.
(a - b)(a + b)
8

10. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
6 : 1 : 2
52
No - the input value has exactly one output.
70

11. What is the 'Range' of a function?
Sector area = (n/360) X (pi)r^2
The set of output values for a function.
413.03 / 10^4 (move the decimal point 4 places to the left)
13

12. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
0
72

13. What is a chord of a circle?
A chord is a line segment joining two points on a circle.
3/2 - 5/3
A grouping of the members within a set based on a shared characteristic.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)

14. Describe the relationship between 3x^2 and 3(x - 1)^2
0
Angle/360 x (pi)r^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
12! / 5!7! = 792

15. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
The two xes after factoring.
71 - 73 - 79
2sqrt6
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

16. 1/6 in percent?
II
2.592 kg
16.6666%
1

17. What is the intersection of A and B?
83.333%
(a - b)(a + b)
A tangent is a line that only touches one point on the circumference of a circle.
The set of elements found in both A and B.

18. Describe the relationship between the graphs of x^2 and (1/2)x^2
500
The second graph is less steep.
All numbers multiples of 1.
1/(x^y)

19. What percent of 40 is 22?
A circle centered on the origin with radius 8.
55%
x^(2(4)) =x^8 = (x^4)^2
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)

20. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
A chord is a line segment joining two points on a circle.
2
3/2 - 5/3
Indeterminable.

21. 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.
(a - b)^2
28. n = 8 - k = 2. n! / k!(n-k)!
90 degrees
1/a^6

22. (a^-1)/a^5
27^(-4)
0
1/a^6
A 30-60-90 triangle.

23. What is a finite set?
x(x - y + 1)
Yes. [i.e. f(x) = x^2 - 1
A set with a number of elements which can be counted.
72

24. What is the slope of a vertical line?

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25. What does the graph x^2 + y^2 = 64 look like?
A circle centered on the origin with radius 8.
9 : 25
Members or elements
Pi is the ratio of a circle'S circumference to its diameter.

26. What is the absolute value function?
G(x) = {x}
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)
2^9 / 2 = 256
The direction of the inequality is reversed.

27. Max and Min lengths for a side of a triangle?
F(x) + c
The third side is greater than the difference and less than the sum.
1 & 37/132
3 - -3

28. Define an 'expression'.
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)
N! / (n-k)!
No - only like radicals can be added.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

29. Define a 'Term' -
The set of elements found in both A and B.
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)
62.5%
1

30. Formula to calculate arc length?
70
2
The union of A and B.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

31. 70 < all primes< 80
71 - 73 - 79
...multiply by 100.
The point of intersection of the systems.
N! / (n-k)!

32. 5x^2 - 35x -55 = 0
The set of input values for a function.
10! / (10-3)! = 720
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
441000 = 1 10 10 10 21 * 21

33. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
True
x= (1.2)(.8)lw
48

34. Factor x^2 - xy + x.
x(x - y + 1)
II
N! / (k!)(n-k)!
The greatest value minus the smallest.

35. What is an isoceles triangle?
Yes - like radicals can be added/subtracted.
53 - 59
A subset.
Two equal sides and two equal angles.

36. The ratio of the areas of two similar polygons is ...
75:11
... the square of the ratios of the corresponding sides.
90 degrees
1.0843 X 10^11

37. sqrt 2(sqrt 6)=
Sqrt 12
Two equal sides and two equal angles.
6 : 1 : 2
A reflection about the origin.

38. Reduce: 4.8 : 0.8 : 1.6
A = pi(r^2)
6 : 1 : 2
288 (8 9 4)
2.592 kg

39. What is the order of operations?
The greatest value minus the smallest.
23 - 29
27^(-4)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

40. Legs 6 - 8. Hypotenuse?
The set of elements which can be found in either A or B.
An arc is a portion of a circumference of a circle.
10
True

41. 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)?
130pi
y = (x + 5)/2
A tangent is a line that only touches one point on the circumference of a circle.
2(pi)r^2 + 2(pi)rh

42. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
12! / 5!7! = 792
87.5%
2sqrt6
x^(6-3) = x^3

43. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A reflection about the axis.
x^(4+7) = x^11
2.592 kg

44. 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?
(a - b)(a + b)
N! / (k!)(n-k)!
Pi is the ratio of a circle'S circumference to its diameter.
441000 = 1 10 10 10 21 * 21

45. What is a tangent?
Undefined
The shortest arc between points A and B on a circle'S diameter.
72
A tangent is a line that only touches one point on the circumference of a circle.

46. What is the name for a grouping of the members within a set based on a shared characteristic?
A subset.
x= (1.2)(.8)lw
6 : 1 : 2
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

47. What is the 'Solution' for a set of inequalities.
1:sqrt3:2
All numbers multiples of 1.
The overlapping sections.
130pi

48. x^2 = 9. What is the value of x?
3 - -3
72
(a + b)^2
F(x) + c

49. What is a subset?
The curve opens upward and the vertex is the minimal point on the graph.
(b + c)
A grouping of the members within a set based on a shared characteristic.
0

50. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
12! / 5!7! = 792
No - the input value has exactly one output.
6 : 1 : 2
y = 2x^2 - 3

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GRE Math: Common Errors

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