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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 are the integers?
All numbers multiples of 1.
8
A subset.
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.

2. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
A set with no members - denoted by a circle with a diagonal through it.
(a - b)(a + b)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.

3. What is the slope of a horizontal line?
0
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
10! / (10-3)! = 720
48

4. What are the irrational numbers?

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5. 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.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
(base*height) / 2

6. What percent of 40 is 22?
(a + b)^2
55%
True
12! / 5!7! = 792

7. Which quadrant is the upper right hand?
413.03 / 10^4 (move the decimal point 4 places to the left)
The interesection of A and B.
12.5%
I

8. a^2 - b^2
(a - b)(a + b)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
y = 2x^2 - 3
III

9. To multiply a number by 10^x
Indeterminable.
Move the decimal point to the right x places
Its divisible by 2 and by 3.
61 - 67

10. Which is greater? 200x^295 or 10x^294?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Relationship cannot be determined (what if x is negative?)
2^9 / 2 = 256
Cd

11. 10^6 has how many zeroes?
6
500
An isosceles right triangle.
1

12. What is a subset?
A set with no members - denoted by a circle with a diagonal through it.
441000 = 1 10 10 10 21 * 21
A grouping of the members within a set based on a shared characteristic.
True

13. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
1
A central angle is an angle formed by 2 radii.
N! / (n-k)!
1/2 times 7/3

14. What is a parabola?
4096
500
(base*height) / 2
Ax^2 + bx + c where a -b and c are constants and a /=0

15. Evaluate 4/11 + 11/12
Angle/360 x 2(pi)r
1 & 37/132
$11 -448
3sqrt4

16. (-1)^2 =
From northeast - counterclockwise. I - II - III - IV
x^(2(4)) =x^8 = (x^4)^2
Triangles with same measure and same side lengths.
1

17. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
55%
2^9 / 2 = 256
F(x-c)
A circle centered on the origin with radius 8.

18. 413.03 x 10^(-4) =
13pi / 2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
From northeast - counterclockwise. I - II - III - IV
413.03 / 10^4 (move the decimal point 4 places to the left)

19. What are the members or elements of a set?
72
The union of A and B.
The objects within a set.
.0004809 X 10^11

20. What is an arc of a circle?
y = 2x^2 - 3
5
An arc is a portion of a circumference of a circle.
8

21. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A circle centered at -2 - -2 with radius 3.
20.5
All numbers multiples of 1.
(a + b)^2

22. Which quandrant is the lower right hand?
IV
288 (8 9 4)
2^9 / 2 = 256
1

23. What number between 70 & 75 - inclusive - has the greatest number of factors?
A reflection about the origin.
10
72
N! / (k!)(n-k)!

24. What is a set with no members called?
The empty set - denoted by a circle with a diagonal through it.
A 30-60-90 triangle.
70
An expression with just one term (-6x - 2a^2)

25. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
13pi / 2
70
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
1

26. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
500
Undefined - because we can'T divide by 0.
28. n = 8 - k = 2. n! / k!(n-k)!
A chord is a line segment joining two points on a circle.

27. Define a 'Term' -
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
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)
87.5%
C = 2(pi)r

28. What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
23 - 29
83.333%
10

29. What is the side length of an equilateral triangle with altitude 6?
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...
8
The set of output values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

30. What is the slope of a vertical line?

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31. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
An angle which is supplementary to an interior angle.
The direction of the inequality is reversed.

32. Evaluate (4^3)^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
F(x) - c
G(x) = {x}
4096

33. 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?
A 30-60-90 triangle.
Divide by 100.
180
10! / (10-3)! = 720

34. 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)]?
.0004809 X 10^11
A 30-60-90 triangle.
Infinite.
True

35. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
N! / (k!)(n-k)!
Two angles whose sum is 180.
(b + c)
2 & 3/7

36. What is a central angle?
Yes. [i.e. f(x) = x^2 - 1
F(x + c)
A central angle is an angle formed by 2 radii.
The objects within a set.

37. What is the empty set?
When the function is not defined for all real numbers -; only a subset of the real numbers.
The set of output values for a function.
A set with no members - denoted by a circle with a diagonal through it.
Two equal sides and two equal angles.

38. 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))?
20.5
Even
2(pi)r^2 + 2(pi)rh
(amount of increase/original price) x 100%

39. A number is divisible by 6 if...
1
11 - 13 - 17 - 19
A subset.
Its divisible by 2 and by 3.

40. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
(amount of decrease/original price) x 100%
1 & 37/132
4:5
The third side is greater than the difference and less than the sum.

41. What is the 'Range' of a series of numbers?
... the square of the ratios of the corresponding sides.
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
12.5%
The greatest value minus the smallest.

42. Simplify the expression (p^2 - q^2)/ -5(q - p)
413.03 / 10^4 (move the decimal point 4 places to the left)
The curve opens downward and the vertex is the maximum point on the graph.
1.0843 X 10^11
(p + q)/5

43. The objects in a set are called two names:
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
2
Members or elements
An angle which is supplementary to an interior angle.

44. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
72
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
71 - 73 - 79

45. Pi is a ratio of what to what?

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46. 10<all primes<20
11 - 13 - 17 - 19
18
9 & 6/7
The point of intersection of the systems.

47. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
C = (pi)d
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
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

48. What is the graph of f(x) shifted right c units or spaces?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
F(x-c)
... the square of the ratios of the corresponding sides.
41 - 43 - 47

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?
From northeast - counterclockwise. I - II - III - IV
6 : 1 : 2
$3 -500 in the 9% and $2 -500 in the 7%.
16.6666%

50. Simplify (a^2 + b)^2 - (a^2 - b)^2
12! / 5!7! = 792
The empty set - denoted by a circle with a diagonal through it.
4a^2(b)
When the function is not defined for all real numbers -; only a subset of the real numbers.

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GRE Math: Common Errors

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