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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. 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?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
10! / 3!(10-3)! = 120
(a - b)(a + b)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

2. Solve the quadratic equation ax^2 + bx + c= 0
(a - b)(a + b)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
IV
F(x) - c

3. a^2 - b^2 =
A reflection about the axis.
...multiply by 100.
(a - b)(a + b)
The set of output values for a function.

4. What is the 'domain' of a function?
72
$3 -500 in the 9% and $2 -500 in the 7%.
2.592 kg
The set of input values for a function.

5. a^2 - 2ab + b^2
I
(a - b)^2
441000 = 1 10 10 10 21 * 21
13pi / 2

6. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
An infinite set.
The two xes after factoring.
IV

7. What is the formula for computing simple interest?
A = I (1 + rt)
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)
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)
The sum of digits is divisible by 9.

8. What is a parabola?
Ax^2 + bx + c where a -b and c are constants and a /=0
N! / (k!)(n-k)!
1:1:sqrt2
4:5

9. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
The interesection of A and B.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
y = 2x^2 - 3

10. What is a set with no members called?
90pi
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The empty set - denoted by a circle with a diagonal through it.
2sqrt6

11. Find the surface area of a cylinder with radius 3 and height 12.
413.03 / 10^4 (move the decimal point 4 places to the left)
48
90pi
The empty set - denoted by a circle with a diagonal through it.

12. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
The longest arc between points A and B on a circle'S diameter.
5 OR -5
28. n = 8 - k = 2. n! / k!(n-k)!
The objects within a set.

13. When the 'a' in the parabola is negative...
1/a^6
Two angles whose sum is 90.
The curve opens downward and the vertex is the maximum point on the graph.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

14. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
90 degrees
The set of elements found in both A and B.
The union of A and B.
4.25 - 6 - 22

15. Simplify the expression (p^2 - q^2)/ -5(q - p)
(p + q)/5
Relationship cannot be determined (what if x is negative?)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
72

16. Can you subtract 3sqrt4 from sqrt4?
III
Yes - like radicals can be added/subtracted.
Part = Percent X Whole
C = 2(pi)r

17. Which is greater? 64^5 or 16^8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
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
130pi
4725

18. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4:5
The sum of digits is divisible by 9.
6 : 1 : 2
Undefined

19. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(a + b)^2
(a + b)^2
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
16.6666%

20. 5/8 in percent?
A grouping of the members within a set based on a shared characteristic.
62.5%
N! / (n-k)!
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

21. Circumference of a circle?
1
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Undefined
Diameter(Pi)

22. What is the slope of a horizontal line?
72
...multiply by 100.
0
The shortest arc between points A and B on a circle'S diameter.

23. What are the rational numbers?
62.5%
2
6
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

24. x^4 + x^7 =
An angle which is supplementary to an interior angle.
1/2 times 7/3
N! / (k!)(n-k)!
x^(4+7) = x^11

25. What is a major arc?

26. (-1)^2 =
A set with no members - denoted by a circle with a diagonal through it.
Cd
288 (8 9 4)
1

27. What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
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.
55%
x= (1.2)(.8)lw

28. Formula for the area of a circle?
x^(4+7) = x^11
A 30-60-90 triangle.
A = pi(r^2)
2.592 kg

29. 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?
An arc is a portion of a circumference of a circle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
N! / (n-k)!
Factors are few - multiples are many.

30. What is the percent formula?
(a + b)^2
Diameter(Pi)
5
Part = Percent X Whole

31. What are the irrational numbers?

32. What is the name for a grouping of the members within a set based on a shared characteristic?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
A subset.
y = (x + 5)/2
F(x) + c

33. What are congruent triangles?
1 & 37/132
$3 -500 in the 9% and $2 -500 in the 7%.
Triangles with same measure and same side lengths.
(b + c)

34. 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))?
True
20.5
The curve opens upward and the vertex is the minimal point on the graph.
13pi / 2

35. 25^(1/2) or sqrt. 25 =
5 OR -5
A circle centered on the origin with radius 8.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
23 - 29

36. (-1)^3 =
62.5%
The longest arc between points A and B on a circle'S diameter.
N! / (k!)(n-k)!
1

37. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
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
1
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
Cd

38. The slope of a line perpendicular to (a/b)?
Its negative reciprocal. (-b/a)
(n-2) x 180
1/(x^y)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

39. 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)]?
True
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)
Sqrt 12
An angle which is supplementary to an interior angle.

40. 30< all primes<40
C = (pi)d
20.5
0
31 - 37

41. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
Undefined - because we can'T divide by 0.
A reflection about the axis.
2(pi)r^2 + 2(pi)rh
0

42. What is the maximum value for the function g(x) = (-2x^2) -1?
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
6 : 1 : 2
...multiply by 100.

43. 10<all primes<20
The shortest arc between points A and B on a circle'S diameter.
18
11 - 13 - 17 - 19
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

44. a^2 + 2ab + b^2
12sqrt2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
(a + b)^2
IV

45. Legs 6 - 8. Hypotenuse?
6 : 1 : 2
10
A tangent is a line that only touches one point on the circumference of a circle.
An infinite set.

46. 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.
3 - -3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
90 degrees

47. Simplify (a^2 + b)^2 - (a^2 - b)^2
52
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
4a^2(b)
The third side is greater than the difference and less than the sum.

48. 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?
27^(-4)
72
1/a^6
$3 -500 in the 9% and $2 -500 in the 7%.

49. When the 'a' in a parabola is positive....
1.0843 X 10^11
11 - 13 - 17 - 19
The curve opens upward and the vertex is the minimal point on the graph.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

50. What is an isoceles triangle?
The curve opens upward and the vertex is the minimal point on the graph.
12.5%
Two equal sides and two equal angles.
6 : 1 : 2