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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. 4.809 X 10^7 =
No - the input value has exactly one output.
.0004809 X 10^11
A 30-60-90 triangle.
A set with no members - denoted by a circle with a diagonal through it.

2. When the 'a' in the parabola is negative...
N! / (k!)(n-k)!
The curve opens downward and the vertex is the maximum point on the graph.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
61 - 67

3. (6sqrt3) x (2sqrt5) =
6 : 1 : 2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
10! / (10-3)! = 720
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

4. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
Angle/360 x (pi)r^2
A tangent is a line that only touches one point on the circumference of a circle.
Cd

5. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
48
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
The curve opens upward and the vertex is the minimal point on the graph.
x= (1.2)(.8)lw

6. Length of an arc of a circle?
48
Angle/360 x 2(pi)r
4096
$3 -500 in the 9% and $2 -500 in the 7%.

7. What is a set with no members called?
An infinite set.
11 - 13 - 17 - 19
Factors are few - multiples are many.
The empty set - denoted by a circle with a diagonal through it.

8. (12sqrt15) / (2sqrt5) =
y = (x + 5)/2
A central angle is an angle formed by 2 radii.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
4.25 - 6 - 22

9. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
The objects within a set.
Yes - like radicals can be added/subtracted.
Its negative reciprocal. (-b/a)
2sqrt6

10. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
An isosceles right triangle.
Yes - like radicals can be added/subtracted.
3/2 - 5/3
A circle centered at -2 - -2 with radius 3.

11. x^6 / x^3
The longest arc between points A and B on a circle'S diameter.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
$11 -448
x^(6-3) = x^3

12. To convert a decimal to a percent...
Two equal sides and two equal angles.
...multiply by 100.
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)
The third side is greater than the difference and less than the sum.

13. What is the surface area of a cylinder with radius 5 and height 8?
4096
130pi
The set of input values for a function.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3

14. a^2 + 2ab + b^2
Sqrt 12
(a + b)^2
A = pi(r^2)
Part = Percent X Whole

15. Which is greater? 27^(-4) or 9^(-8)
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...
9 : 25
27^(-4)
2^9 / 2 = 256

16. Write 10 -843 X 10^7 in scientific notation
2(pi)r^2 + 2(pi)rh
1.0843 X 10^11
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(a + b)^2

17. Can the input value of a function have more than one output value (i.e. x: y - y1)?
2(pi)r^2 + 2(pi)rh
...multiply by 100.
1/2 times 7/3
No - the input value has exactly one output.

18. What are the roots of the quadrinomial x^2 + 2x + 1?
The two xes after factoring.
10! / (10-3)! = 720
Diameter(Pi)
A central angle is an angle formed by 2 radii.

19. How to determine percent increase?
(amount of increase/original price) x 100%
A reflection about the origin.
F(x + c)
Yes. [i.e. f(x) = x^2 - 1

20. 413.03 x 10^(-4) =
1:sqrt3:2
413.03 / 10^4 (move the decimal point 4 places to the left)
71 - 73 - 79
12sqrt2

21. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
10
...multiply by 100.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
70

22. 1/6 in percent?
When the function is not defined for all real numbers -; only a subset of the real numbers.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
16.6666%
A = pi(r^2)

23. 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)]?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Divide by 100.
The greatest value minus the smallest.
True

24. What is a major arc?

25. The slope of a line perpendicular to (a/b)?
F(x) + c
Its negative reciprocal. (-b/a)
16.6666%
From northeast - counterclockwise. I - II - III - IV

26. Simplify the expression (p^2 - q^2)/ -5(q - p)
A central angle is an angle formed by 2 radii.
1.7
(p + q)/5
A grouping of the members within a set based on a shared characteristic.

27. 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?
The set of elements which can be found in either A or B.
441000 = 1 10 10 10 21 * 21
Ax^2 + bx + c where a -b and c are constants and a /=0
1

28. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
Triangles with same measure and same side lengths.
10
3sqrt4

29. Evaluate (4^3)^2
Sqrt 12
(a - b)(a + b)
4096
4.25 - 6 - 22

30. Max and Min lengths for a side of a triangle?
The point of intersection of the systems.
Triangles with same measure and same side lengths.
The third side is greater than the difference and less than the sum.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

31. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
90
12! / 5!7! = 792
288 (8 9 4)
16.6666%

32. 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.
(a + b)^2
Angle/360 x 2(pi)r
N! / (n-k)!
90 degrees

33. What is the measure of an exterior angle of a regular pentagon?
The set of elements found in both A and B.
72
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
IV

34. Area of a triangle?
An isosceles right triangle.
The interesection of A and B.
(base*height) / 2
16.6666%

35. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An arc is a portion of a circumference of a circle.
An isosceles right triangle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Arc length = (n/360) x pi(2r) where n is the number of degrees.

36. Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas' ages?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
9 : 25
441000 = 1 10 10 10 21 * 21
Part = Percent X Whole

37. If the 80th percentile of the measurements is 72degrees - about how many measurments are between 69 degrees and 72 degrees? Round your answer to the nearest tenth
Angle/360 x 2(pi)r
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4.25 - 6 - 22
18

38. 6w^2 - w - 15 = 0
6
71 - 73 - 79
3/2 - 5/3
500

39. What percent of 40 is 22?
83.333%
No - only like radicals can be added.
55%
67 - 71 - 73

40. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
28. n = 8 - k = 2. n! / k!(n-k)!
2 & 3/7
16.6666%
N! / (k!)(n-k)!

41. How to find the circumference of a circle which circumscribes a square?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
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 set of elements found in both A and B.
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.

42. Can you simplify sqrt72?
A 30-60-90 triangle.
12! / 5!7! = 792
0
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

43. What is a minor arc?

44. (-1)^3 =
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)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
1
37.5%

45. 25^(1/2) or sqrt. 25 =
(a + b)^2
All numbers multiples of 1.
F(x-c)
5 OR -5

46. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
C = 2(pi)r
The third side is greater than the difference and less than the sum.
(amount of decrease/original price) x 100%

47. Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
6
(a + b)^2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

48. Describe the relationship between the graphs of x^2 and (1/2)x^2
An isosceles right triangle.
The second graph is less steep.
180 degrees
23 - 29

49. 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?
67 - 71 - 73
The empty set - denoted by a circle with a diagonal through it.
$3 -500 in the 9% and $2 -500 in the 7%.
F(x + c)

50. What does the graph x^2 + y^2 = 64 look like?
Lies opposite the greater angle
1
A circle centered on the origin with radius 8.
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...