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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. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
12.5%
Angle/360 x 2(pi)r
A = I (1 + rt)

2. Simplify the expression (p^2 - q^2)/ -5(q - p)
1
6 : 1 : 2
48
(p + q)/5

3. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
1.0843 X 10^11
55%
10! / 3!(10-3)! = 120
Triangles with same measure and same side lengths.

4. Formula to calculate arc length?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
72
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Part = Percent X Whole

5. 10<all primes<20
1
(base*height) / 2
11 - 13 - 17 - 19
288 (8 9 4)

6. (x^2)^4
Sqrt 12
x^(2(4)) =x^8 = (x^4)^2
C = 2(pi)r
Diameter(Pi)

7. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
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...
4a^2(b)
True

8. What is the ratio of the sides of a 30-60-90 triangle?
x(x - y + 1)
(b + c)
1:sqrt3:2
$11 -448

9. What is a parabola?
Its negative reciprocal. (-b/a)
Pi is the ratio of a circle'S circumference to its diameter.
Ax^2 + bx + c where a -b and c are constants and a /=0
5 OR -5

10. 1/8 in percent?
1
y = (x + 5)/2
12.5%
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

11. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
F(x) - c
87.5%
20.5
2 & 3/7

12. What is the empty set?
x^(6-3) = x^3
83.333%
A set with no members - denoted by a circle with a diagonal through it.
x^(4+7) = x^11

13. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
2 & 3/7
A 30-60-90 triangle.
53 - 59

14. 10^6 has how many zeroes?
Undefined - because we can'T divide by 0.
6
87.5%
y = 2x^2 - 3

15. Solve the quadratic equation ax^2 + bx + c= 0
A tangent is a line that only touches one point on the circumference of a circle.
10! / (10-3)! = 720
Divide by 100.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

16. What are complementary angles?
The empty set - denoted by a circle with a diagonal through it.
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)
A reflection about the origin.
Two angles whose sum is 90.

17. sqrt 2(sqrt 6)=
90pi
A central angle is an angle formed by 2 radii.
Sqrt 12
90

18. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
61 - 67
A circle centered on the origin with radius 8.
62.5%

19. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
Yes. [i.e. f(x) = x^2 - 1
The sum of its digits is divisible by 3.
70
83.333%

20. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
6
(b + c)
A circle centered at -2 - -2 with radius 3.

21. 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?
Pi is the ratio of a circle'S circumference to its diameter.
31 - 37
75:11
Yes. [i.e. f(x) = x^2 - 1

22. What is the graph of f(x) shifted downward c units or spaces?
$11 -448
Angle/360 x 2(pi)r
28. n = 8 - k = 2. n! / k!(n-k)!
F(x) - c

23. Can you subtract 3sqrt4 from sqrt4?
Angle/360 x 2(pi)r
Yes - like radicals can be added/subtracted.
13pi / 2
3/2 - 5/3

24. What are the smallest three prime numbers greater than 65?
1
The set of elements which can be found in either A or B.
67 - 71 - 73
72

25. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
An isosceles right triangle.
12.5%
The curve opens upward and the vertex is the minimal point on the graph.
28. n = 8 - k = 2. n! / k!(n-k)!

26. Formula to find a circle'S circumference from its radius?
A tangent is a line that only touches one point on the circumference of a circle.
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.
C = 2(pi)r
Area of the base X height = (pi)hr^2

27. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
180
The sum of digits is divisible by 9.
0

28. Formula for the area of a sector of a circle?
A reflection about the axis.
3/2 - 5/3
Undefined
Sector area = (n/360) X (pi)r^2

29. 70 < all primes< 80
71 - 73 - 79
4.25 - 6 - 22
II
A chord is a line segment joining two points on a circle.

30. 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))?
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)
A tangent is a line that only touches one point on the circumference of a circle.
A central angle is an angle formed by 2 radii.
20.5

31. 30< all primes<40
Factors are few - multiples are many.
31 - 37
C = 2(pi)r
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

32. Hector invested $6000. Part was invested in account with 9% simple annual interest - and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments - how much did he invest in each account?
A set with a number of elements which can be counted.
16.6666%
A = I (1 + rt)
$3 -500 in the 9% and $2 -500 in the 7%.

33. What are the irrational numbers?

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34. 60 < all primes <70
53 - 59
A reflection about the axis.
(a - b)^2
61 - 67

35. How to find the diagonal of a rectangular solid?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
All numbers multiples of 1.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

36. To convert a decimal to a percent...
...multiply by 100.
3/2 - 5/3
(a + b)^2
Even

37. Which is greater? 64^5 or 16^8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
7 / 1000
62.5%
(a - b)(a + b)

38. What is the side length of an equilateral triangle with altitude 6?
I
3
(n-2) x 180
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...

39. What is the 'union' of A and B?
1:sqrt3:2
The set of elements which can be found in either A or B.
A tangent is a line that only touches one point on the circumference of a circle.
1.0843 X 10^11

40. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
75:11
1
The empty set - denoted by a circle with a diagonal through it.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

41. The larger the absolute value of the slope...
4a^2(b)
A set with no members - denoted by a circle with a diagonal through it.
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 steeper the slope.

42. 5/6 in percent?
52
(n-2) x 180
83.333%
4:5

43. What is the slope of a vertical line?

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44. What is an isoceles triangle?
90 degrees
1
Two equal sides and two equal angles.
18

45. 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.
I
Its last two digits are divisible by 4.
90 degrees
(p + q)/5

46. Formula to find a circle'S circumference from its diameter?
288 (8 9 4)
72
4.25 - 6 - 22
C = (pi)d

47. Define a 'monomial'
52
An expression with just one term (-6x - 2a^2)
Angle/360 x (pi)r^2
9 : 25

48. Factor a^2 + 2ab + b^2
(a + b)^2
The curve opens upward and the vertex is the minimal point on the graph.
Its negative reciprocal. (-b/a)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

49. Describe the relationship between 3x^2 and 3(x - 1)^2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
An infinite set.
Cd
A = I (1 + rt)

50. Which quadrant is the lower left hand?
A circle centered on the origin with radius 8.
6 : 1 : 2
III
A subset.