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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. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
5 OR -5
...multiply by 100.
13pi / 2
20.5

2. The larger the absolute value of the slope...
The steeper the slope.
10
Sector area = (n/360) X (pi)r^2
7 / 1000

3. How many 3-digit positive integers are even and do not contain the digit 4?
1/(x^y)
288 (8 9 4)
Yes. [i.e. f(x) = x^2 - 1
A chord is a line segment joining two points on a circle.

4. a^2 - 2ab + b^2
1:sqrt3:2
A 30-60-90 triangle.
(a - b)^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

5. What is a finite set?
4a^2(b)
9 : 25
A set with a number of elements which can be counted.
0

6. 1/6 in percent?
2 & 3/7
16.6666%
N! / (n-k)!
The union of A and B.

7. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
y = (x + 5)/2
11 - 13 - 17 - 19
8
(a - b)(a + b)

8. A number is divisible by 9 if...
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
IV
A chord is a line segment joining two points on a circle.
The sum of digits is divisible by 9.

9. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
13pi / 2
4:5
Its negative reciprocal. (-b/a)
The set of elements found in both A and B.

10. What is a tangent?
A tangent is a line that only touches one point on the circumference of a circle.
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.
Pi is the ratio of a circle'S circumference to its diameter.

11. Write 10 -843 X 10^7 in scientific notation
18
288 (8 9 4)
3
1.0843 X 10^11

12. To convert a decimal to a percent...
4725
...multiply by 100.
87.5%
62.5%

13. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
2
67 - 71 - 73
x(x - y + 1)
When the function is not defined for all real numbers -; only a subset of the real numbers.

14. Can you subtract 3sqrt4 from sqrt4?
A reflection about the axis.
4a^2(b)
Yes - like radicals can be added/subtracted.
61 - 67

15. Can you simplify sqrt72?
75:11
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
90
18

16. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
90pi
y = 2x^2 - 3
1:1:sqrt2
A reflection about the axis.

17. How to find the circumference of a circle which circumscribes a square?
(b + c)
(base*height) / 2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(a - b)(a + b)

18. Max and Min lengths for a side of a triangle?
N! / (k!)(n-k)!
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...
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The third side is greater than the difference and less than the sum.

19. Legs 6 - 8. Hypotenuse?
The overlapping sections.
The steeper the slope.
10
2

20. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
...multiply by 100.
28. n = 8 - k = 2. n! / k!(n-k)!
3
The point of intersection of the systems.

21. Describe the relationship between the graphs of x^2 and (1/2)x^2
x^(6-3) = x^3
12! / 5!7! = 792
The direction of the inequality is reversed.
The second graph is less steep.

22. Which is greater? 27^(-4) or 9^(-8)
1:1:sqrt2
Yes - like radicals can be added/subtracted.
27^(-4)
9 : 25

23. Number of degrees in a triangle
The two xes after factoring.
180 degrees
An arc is a portion of a circumference of a circle.
180

24. What is a subset?
A grouping of the members within a set based on a shared characteristic.
Its last two digits are divisible by 4.
12! / 5!7! = 792
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

25. Legs 5 - 12. Hypotenuse?
180
28. n = 8 - k = 2. n! / k!(n-k)!
13
F(x + c)

26. 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
(a + b)^2
1 & 37/132
Yes - like radicals can be added/subtracted.

27. a^2 - b^2
(a - b)(a + b)
Cd
y = (x + 5)/2
The set of output values for a function.

28. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
83.333%
The curve opens downward and the vertex is the maximum point on the graph.

29. 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?
10
2.592 kg
F(x) - c
When the function is not defined for all real numbers -; only a subset of the real numbers.

30. Simplify the expression (p^2 - q^2)/ -5(q - p)
$3 -500 in the 9% and $2 -500 in the 7%.
441000 = 1 10 10 10 21 * 21
(p + q)/5
The overlapping sections.

31. What percent of 40 is 22?
Angle/360 x (pi)r^2
55%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
0

32. Area of a triangle?
(base*height) / 2
(a - b)^2
The union of A and B.
The two xes after factoring.

33. Volume for a cylinder?
1
8
Area of the base X height = (pi)hr^2
An angle which is supplementary to an interior angle.

34. What is the name for a grouping of the members within a set based on a shared characteristic?
10
A subset.
No - the input value has exactly one output.
13pi / 2

35. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
Ax^2 + bx + c where a -b and c are constants and a /=0
0
75:11
The two xes after factoring.

36. 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?
441000 = 1 10 10 10 21 * 21
6
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 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

37. 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?
31 - 37
55%
52
1

38. Which is greater? 200x^295 or 10x^294?
Relationship cannot be determined (what if x is negative?)
4.25 - 6 - 22
The direction of the inequality is reversed.
(a + b)^2

39. Formula for the area of a circle?
Two angles whose sum is 180.
A = pi(r^2)
y = (x + 5)/2
4a^2(b)

40. Formula to find a circle'S circumference from its diameter?
C = (pi)d
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
3/2 - 5/3
A reflection about the origin.

41. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
3
1
75:11
Triangles with same measure and same side lengths.

42. The ratio of the areas of two similar polygons is ...
F(x-c)
... the square of the ratios of the corresponding sides.
The steeper the slope.
(a - b)(a + b)

43. What is the 'Range' of a function?
Ax^2 + bx + c where a -b and c are constants and a /=0
The set of output values for a function.
500
Undefined

44. When does a function automatically have a restricted domain (2)?
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
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

45. 30< all primes<40
31 - 37
Ax^2 + bx + c where a -b and c are constants and a /=0
Part = Percent X Whole
70

46. Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Undefined - because we can'T divide by 0.
1/a^6
12! / 5!7! = 792

47. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
500
2 & 3/7
18
1:1:sqrt2

48. What are the roots of the quadrinomial x^2 + 2x + 1?
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...
0
The direction of the inequality is reversed.
The two xes after factoring.

49. When the 'a' in a parabola is positive....
An arc is a portion of a circumference of a circle.
The curve opens upward and the vertex is the minimal point on the graph.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
10! / 3!(10-3)! = 120

50. When the 'a' in the parabola is negative...
130pi
The curve opens downward and the vertex is the maximum point on the graph.
Indeterminable.
2 & 3/7