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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 is the side length of an equilateral triangle with altitude 6?
16.6666%
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...
Yes - like radicals can be added/subtracted.
1:1:sqrt2

2. 5x^2 - 35x -55 = 0
72
C = (pi)d
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
A set with a number of elements which can be counted.

3. Can you simplify sqrt72?
The curve opens downward and the vertex is the maximum point on the graph.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
F(x-c)
Sector area = (n/360) X (pi)r^2

4. The perimeter of a square is 48 inches. The length of its diagonal is:
2 & 3/7
6
12sqrt2
Yes. [i.e. f(x) = x^2 - 1

5. a^0 =
1
An isosceles right triangle.
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
F(x) + c

6. What is a central angle?
Area of the base X height = (pi)hr^2
A central angle is an angle formed by 2 radii.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
0

7. The objects in a set are called two names:
Yes. [i.e. f(x) = x^2 - 1
N! / (n-k)!
Members or elements
6 : 1 : 2

8. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
2 & 3/7
4a^2(b)
23 - 29
13pi / 2

9. Write 10 -843 X 10^7 in scientific notation
27^(-4)
1.0843 X 10^11
A reflection about the axis.
(a - b)(a + b)

10. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
8
A circle centered on the origin with radius 8.
N! / (n-k)!
4:5

11. A number is divisible by 6 if...
Two angles whose sum is 180.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Its divisible by 2 and by 3.
Area of the base X height = (pi)hr^2

12. (6sqrt3) x (2sqrt5) =
6
No - only like radicals can be added.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
(amount of decrease/original price) x 100%

13. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
5 OR -5
3
2.592 kg

14. 413.03 x 10^(-4) =
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(amount of decrease/original price) x 100%
Pi is the ratio of a circle'S circumference to its diameter.
413.03 / 10^4 (move the decimal point 4 places to the left)

15. Simplify 9^(1/2) X 4^3 X 2^(-6)?
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)
An angle which is supplementary to an interior angle.
3
70

16. What is the 'Restricted domain of a function'?
When the function is not defined for all real numbers -; only a subset of the real numbers.
0
The overlapping sections.
F(x) + c

17. Simplify the expression [(b^2 - c^2) / (b - c)]
13pi / 2
(b + c)
10! / (10-3)! = 720
9 & 6/7

18. (a^-1)/a^5
The steeper the slope.
1/a^6
16.6666%
Undefined - because we can'T divide by 0.

19. How many multiples does a given number have?
Even
(amount of decrease/original price) x 100%
Infinite.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.

20. Volume for a cylinder?
Triangles with same measure and same side lengths.
Area of the base X height = (pi)hr^2
0
Even

21. 8.84 / 5.2
4:5
1.7
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)

22. a^2 - b^2
IV
N! / (n-k)!
(a - b)(a + b)
90

23. Formula of rectangle where l increases by 20% and w decreases by 20%
F(x) - c
A = I (1 + rt)
Undefined
x= (1.2)(.8)lw

24. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
1
(a - b)(a + b)
13pi / 2
Factors are few - multiples are many.

25. Can the output value of a function have more than one input value?
13pi / 2
$11 -448
Yes. [i.e. f(x) = x^2 - 1
x^(2(4)) =x^8 = (x^4)^2

26. What is an arc of a circle?
The longest arc between points A and B on a circle'S diameter.
1
72
An arc is a portion of a circumference of a circle.

27. What is the order of operations?
A = I (1 + rt)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
83.333%
10

28. What is the 'Range' of a function?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(amount of increase/original price) x 100%
The set of output values for a function.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

29. a^2 - b^2 =
37.5%
6 : 1 : 2
(a - b)(a + b)
4a^2(b)

30. 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)?
The sum of its digits is divisible by 3.
III
Even
y = (x + 5)/2

31. What are the integers?
9 & 6/7
All numbers multiples of 1.
1
2.592 kg

32. 1/6 in percent?
The interesection of A and B.
The steeper the slope.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
16.6666%

33. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
Part = Percent X Whole
$11 -448
1
10! / 3!(10-3)! = 120

34. Find the surface area of a cylinder with radius 3 and height 12.
11 - 13 - 17 - 19
90pi
(a + b)^2
23 - 29

35. 3/8 in percent?
The overlapping sections.
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
37.5%
F(x) - c

36. When does a function automatically have a restricted domain (2)?
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...
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

37. Define an 'expression'.
C = 2(pi)r
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)
7 / 1000
1

38. Formula for the area of a sector of a circle?
Its divisible by 2 and by 3.
Sector area = (n/360) X (pi)r^2
... the square of the ratios of the corresponding sides.
N! / (n-k)!

39. What are the irrational numbers?

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40. 1/2 divided by 3/7 is the same as
$3 -500 in the 9% and $2 -500 in the 7%.
A subset.
1:sqrt3:2
1/2 times 7/3

41. Simplify the expression (p^2 - q^2)/ -5(q - p)
61 - 67
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
An arc is a portion of a circumference of a circle.
(p + q)/5

42. What does the graph x^2 + y^2 = 64 look like?
7 / 1000
4.25 - 6 - 22
28. n = 8 - k = 2. n! / k!(n-k)!
A circle centered on the origin with radius 8.

43. What is the slope of a horizontal line?
1:sqrt3:2
3
0
The set of elements found in both A and B.

44. Formula to find a circle'S circumference from its diameter?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Lies opposite the greater angle
C = (pi)d
1:1:sqrt2

45. How to find the diagonal of a rectangular solid?
2.592 kg
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
An expression with just one term (-6x - 2a^2)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

46. 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?
Undefined - because we can'T divide by 0.
75:11
3/2 - 5/3
0

47. What is the 'Solution' for a set of inequalities.
The overlapping sections.
6
Area of the base X height = (pi)hr^2
(a + b)^2

48. 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?
$11 -448
Undefined - because we can'T divide by 0.
441000 = 1 10 10 10 21 * 21
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

49. Evaluate 4/11 + 11/12
20.5
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
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)
1 & 37/132

50. 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?
10! / (10-3)! = 720
1
A = pi(r^2)
9 & 6/7