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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.
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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. Is 0 even or odd?
13pi / 2
Its divisible by 2 and by 3.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Even

2. a^0 =
1
83.333%
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The sum of its digits is divisible by 3.

3. 4.809 X 10^7 =
.0004809 X 10^11
2 & 3/7
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

4. 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?
37.5%
$3 -500 in the 9% and $2 -500 in the 7%.
1
1/2 times 7/3

5. What is the order of operations?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Infinite.
x^(6-3) = x^3
A = I (1 + rt)

6. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
.0004809 X 10^11
The direction of the inequality is reversed.
4:5

7. 10<all primes<20
A central angle is an angle formed by 2 radii.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
11 - 13 - 17 - 19
6

8. Describe the relationship between the graphs of x^2 and (1/2)x^2
The second graph is less steep.
6
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1/(x^y)

9. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
F(x) - c
A subset.
Two equal sides and two equal angles.

10. Describe the relationship between 3x^2 and 3(x - 1)^2
A circle centered at -2 - -2 with radius 3.
28. n = 8 - k = 2. n! / k!(n-k)!
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

11. Which is greater? 27^(-4) or 9^(-8)
4725
(base*height) / 2
27^(-4)
Infinite.

12. a^2 - 2ab + b^2
No - the input value has exactly one output.
Pi is the ratio of a circle'S circumference to its diameter.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
(a - b)^2

13. Reduce: 4.8 : 0.8 : 1.6
x^(4+7) = x^11
2^9 / 2 = 256
180 degrees
6 : 1 : 2

14. 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)?
y = (x + 5)/2
A circle centered on the origin with radius 8.
The point of intersection of the systems.
7 / 1000

15. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
A = I (1 + rt)
A reflection about the axis.
1:sqrt3:2

16. 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))?
Sector area = (n/360) X (pi)r^2
20.5
The greatest value minus the smallest.
90

17. Factor a^2 + 2ab + b^2
(a - b)(a + b)
12.5%
(a + b)^2
4.25 - 6 - 22

18. 5x^2 - 35x -55 = 0
71 - 73 - 79
90 degrees
... the square of the ratios of the corresponding sides.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

19. 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?
9 : 25
10
4.25 - 6 - 22
4:5

20. If an inequality is multiplied or divided by a negative number....
53 - 59
The direction of the inequality is reversed.
A circle centered at -2 - -2 with radius 3.
The shortest arc between points A and B on a circle'S diameter.

21. 25^(1/2) or sqrt. 25 =
Lies opposite the greater angle
Two angles whose sum is 180.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
5 OR -5

22. A number is divisible by 9 if...
2sqrt6
The sum of digits is divisible by 9.
3
(p + q)/5

23. What is the set of elements which can be found in either A or B?
y = (x + 5)/2
The union of A and B.
A circle centered at -2 - -2 with radius 3.
y = 2x^2 - 3

24. To convert a decimal to a percent...
A chord is a line segment joining two points on a circle.
The overlapping sections.
...multiply by 100.
90pi

25. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
A grouping of the members within a set based on a shared characteristic.
1:1:sqrt2
0
70

26. x^4 + x^7 =
The two xes after factoring.
x^(4+7) = x^11
Relationship cannot be determined (what if x is negative?)
1:sqrt3:2

27. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
288 (8 9 4)
2.592 kg
1
A circle centered at -2 - -2 with radius 3.

28. Formula for the area of a sector of a circle?
The steeper the slope.
9 : 25
1.7
Sector area = (n/360) X (pi)r^2

29. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
F(x-c)
12sqrt2

30. What is the name of set with a number of elements which cannot be counted?
The set of elements found in both A and B.
53 - 59
500
An infinite set.

31. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
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)
90
4.25 - 6 - 22
3sqrt4

32. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
A set with a number of elements which can be counted.
2 & 3/7
1 & 37/132

33. Can you add sqrt 3 and sqrt 5?
75:11
Infinite.
(base*height) / 2
No - only like radicals can be added.

34. A number is divisible by 6 if...
The union of A and B.
Its divisible by 2 and by 3.
A 30-60-90 triangle.
A tangent is a line that only touches one point on the circumference of a circle.

35. Convert 0.7% to a fraction.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
7 / 1000
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

36. What are the rational numbers?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
2.592 kg
Move the decimal point to the right x places

37. What are the integers?
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
II
All numbers multiples of 1.
90

38. What are the smallest three prime numbers greater than 65?
The direction of the inequality is reversed.
67 - 71 - 73
Diameter(Pi)
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

39. Which quadrant is the upper right hand?
I
90
72
67 - 71 - 73

40. 8.84 / 5.2
An expression with just one term (-6x - 2a^2)
Two equal sides and two equal angles.
The objects within a set.
1.7

41. Legs 5 - 12. Hypotenuse?
13
II
2 & 3/7
Members or elements

42. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A circle centered at -2 - -2 with radius 3.
27^(-4)
Its negative reciprocal. (-b/a)
F(x) - c

43. Which quandrant is the lower right hand?
The third side is greater than the difference and less than the sum.
IV
4a^2(b)
An angle which is supplementary to an interior angle.

44. What is the 'Solution' for a set of inequalities.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(a + b)^2
The overlapping sections.
(n-2) x 180

45. 6w^2 - w - 15 = 0
A circle centered at -2 - -2 with radius 3.
18
Relationship cannot be determined (what if x is negative?)
3/2 - 5/3

46. Number of degrees in a triangle
180
1
288 (8 9 4)
8

47. 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)]?
The overlapping sections.
True
The set of input values for a function.
87.5%

48. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
2sqrt6
G(x) = {x}
A subset.

49. 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
Factors are few - multiples are many.
True
18
The two xes after factoring.

50. Can the output value of a function have more than one input value?
2(pi)r^2 + 2(pi)rh
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
C = (pi)d
Yes. [i.e. f(x) = x^2 - 1

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GRE Math: Common Errors

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