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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. x^(-y)=
1/(x^y)
Even
The set of output values for a function.
180

2. What is the ratio of the sides of an isosceles right triangle?
Area of the base X height = (pi)hr^2
Infinite.
2 & 3/7
1:1:sqrt2

3. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
A set with no members - denoted by a circle with a diagonal through it.
An isosceles right triangle.
The empty set - denoted by a circle with a diagonal through it.
90pi

4. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
No - the input value has exactly one output.
The curve opens upward and the vertex is the minimal point on the graph.
41 - 43 - 47

5. 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?
Even
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
8
441000 = 1 10 10 10 21 * 21

6. How many sides does a hexagon have?
$11 -448
(base*height) / 2
6
3sqrt4

7. 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)?
71 - 73 - 79
y = (x + 5)/2
(p + q)/5
3

8. a^2 - b^2
True
5
2^9 / 2 = 256
(a - b)(a + b)

9. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
The greatest value minus the smallest.
Pi is the ratio of a circle'S circumference to its diameter.
83.333%

10. What is the 'Range' of a function?
The set of output values for a function.
C = 2(pi)r
2^9 / 2 = 256
The two xes after factoring.

11. x^4 + x^7 =
The steeper the slope.
An isosceles right triangle.
x^(2(4)) =x^8 = (x^4)^2
x^(4+7) = x^11

12. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
A reflection about the origin.
The overlapping sections.
4a^2(b)
True

13. What is the ratio of the sides of a 30-60-90 triangle?
The second graph is less steep.
1:sqrt3:2
6
Area of the base X height = (pi)hr^2

14. What is the set of elements which can be found in either A or B?
1
6
The union of A and B.
The greatest value minus the smallest.

15. (x^2)^4
10! / 3!(10-3)! = 120
x^(2(4)) =x^8 = (x^4)^2
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
2(pi)r^2 + 2(pi)rh

16. 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.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1 & 37/132
The two xes after factoring.

17. Simplify (a^2 + b)^2 - (a^2 - b)^2
23 - 29
4a^2(b)
(a + b)^2
10

18. What is the graph of f(x) shifted downward c units or spaces?
71 - 73 - 79
A 30-60-90 triangle.
$3 -500 in the 9% and $2 -500 in the 7%.
F(x) - c

19. (6sqrt3) x (2sqrt5) =
2(pi)r^2 + 2(pi)rh
3
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
4.25 - 6 - 22

20. Which quadrant is the upper left hand?
y = 2x^2 - 3
The point of intersection of the systems.
II
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

21. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
67 - 71 - 73
Two equal sides and two equal angles.
4:5
2^9 / 2 = 256

22. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
8
2sqrt6
Area of the base X height = (pi)hr^2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

23. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
...multiply by 100.
52
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

24. 60 < all primes <70
Diameter(Pi)
61 - 67
Its negative reciprocal. (-b/a)
10

25. 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
An isosceles right triangle.
Sqrt 12
87.5%

26. 8.84 / 5.2
10! / 3!(10-3)! = 120
1
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
1.7

27. a^2 - 2ab + b^2
7 / 1000
(a - b)^2
500
Undefined - because we can'T divide by 0.

28. 5/6 in percent?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
1
Two angles whose sum is 180.
83.333%

29. What is the 'domain' of a function?
G(x) = {x}
5
2.592 kg
The set of input values for a function.

30. What is a finite set?
180
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A set with a number of elements which can be counted.
The longest arc between points A and B on a circle'S diameter.

31. a^2 - b^2 =
The second graph is less steep.
90 degrees
500
(a - b)(a + b)

32. What is a set with no members called?
23 - 29
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
130pi
The empty set - denoted by a circle with a diagonal through it.

33. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
(a - b)(a + b)
9 & 6/7
The direction of the inequality is reversed.

34. 6w^2 - w - 15 = 0
1:1:sqrt2
N! / (n-k)!
Sector area = (n/360) X (pi)r^2
3/2 - 5/3

35. sqrt 2(sqrt 6)=
1
II
The shortest arc between points A and B on a circle'S diameter.
Sqrt 12

36. What is the measure of an exterior angle of a regular pentagon?
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)
Even
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
72

37. What is a central angle?
A central angle is an angle formed by 2 radii.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
180 degrees
5 OR -5

38. Length of an arc of a circle?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Its negative reciprocal. (-b/a)
3
Angle/360 x 2(pi)r

39. To multiply a number by 10^x
The longest arc between points A and B on a circle'S diameter.
2^9 / 2 = 256
1:1:sqrt2
Move the decimal point to the right x places

40. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
x^(4+7) = x^11
Undefined
2.592 kg

41. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
8
6
$11 -448
72

42. What is the intersection of A and B?
Diameter(Pi)
The set of elements found in both A and B.
N! / (n-k)!
(n-2) x 180

43. What is the area of a regular hexagon with side 6?
28. n = 8 - k = 2. n! / k!(n-k)!
All numbers multiples of 1.
x(x - y + 1)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

44. Which is greater? 64^5 or 16^8
1
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
The sum of digits is divisible by 9.
The second graph is less steep.

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?
0
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(amount of increase/original price) x 100%
N! / (n-k)!

46. Which quandrant is the lower right hand?
23 - 29
IV
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A = I (1 + rt)

47. Formula to find a circle'S circumference from its diameter?
The third side is greater than the difference and less than the sum.
C = (pi)d
The set of input values for a function.
Its negative reciprocal. (-b/a)

48. a^2 + 2ab + b^2
G(x) = {x}
(a + b)^2
$3 -500 in the 9% and $2 -500 in the 7%.
16.6666%

49. P and r are factors of 100. What is greater - pr or 100?
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
2.592 kg
An isosceles right triangle.
Indeterminable.

50. A number is divisible by 4 is...
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
72
Its last two digits are divisible by 4.
3