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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. The slope of a line perpendicular to (a/b)?
Its negative reciprocal. (-b/a)
3
(n-2) x 180
1/a^6

2. What is an isoceles triangle?
An infinite set.
A reflection about the origin.
Two equal sides and two equal angles.
41 - 43 - 47

3. Factor a^2 + 2ab + b^2
(a + b)^2
A circle centered on the origin with radius 8.
A chord is a line segment joining two points on a circle.
48

4. What is the intersection of A and B?
Lies opposite the greater angle
The set of elements found in both A and B.
A set with no members - denoted by a circle with a diagonal through it.
28. n = 8 - k = 2. n! / k!(n-k)!

5. 10<all primes<20
(a + b)^2
71 - 73 - 79
6
11 - 13 - 17 - 19

6. What is the name for a grouping of the members within a set based on a shared characteristic?
7 / 1000
3
A subset.
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)

7. When does a function automatically have a restricted domain (2)?
F(x + c)
x^(4+7) = x^11
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
True

8. If the two sides of a triangle are unequal then the longer side...
III
(a + b)^2
Lies opposite the greater angle
N! / (k!)(n-k)!

9. a^2 - b^2
(a - b)(a + b)
3
$3 -500 in the 9% and $2 -500 in the 7%.
The point of intersection of the systems.

10. Which quadrant is the upper right hand?
I
Sqrt 12
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
3sqrt4

11. 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
5 OR -5
18
C = 2(pi)r
90pi

12. Can you subtract 3sqrt4 from sqrt4?
The set of elements which can be found in either A or B.
(base*height) / 2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Yes - like radicals can be added/subtracted.

13. a^2 + 2ab + b^2
(a + b)^2
Yes - like radicals can be added/subtracted.
5
Divide by 100.

14. 6w^2 - w - 15 = 0
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
87.5%
1
3/2 - 5/3

15. What is the 'Solution' for a system of linear equations?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
True
2 & 3/7
The point of intersection of the systems.

16. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
Yes. [i.e. f(x) = x^2 - 1
1.7
(amount of increase/original price) x 100%
2

17. Legs 6 - 8. Hypotenuse?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
10
$11 -448
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

18. 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?
Yes - like radicals can be added/subtracted.
500
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
7 / 1000

19. sqrt 2(sqrt 6)=
II
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
Sqrt 12

20. 1/8 in percent?
10! / 3!(10-3)! = 120
12.5%
1
5

21. 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?
2.592 kg
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
1

22. Formula to find a circle'S circumference from its diameter?
An arc is a portion of a circumference of a circle.
A = pi(r^2)
41 - 43 - 47
C = (pi)d

23. The objects in a set are called two names:
An isosceles right triangle.
Members or elements
55%
10

24. What is the formula for compounded interest?
Part = Percent X Whole
4a^2(b)
4725
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.

25. Area of a triangle?
(base*height) / 2
$3 -500 in the 9% and $2 -500 in the 7%.
18
12sqrt2

26. 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)?
180
An infinite set.
y = (x + 5)/2
(amount of decrease/original price) x 100%

27. To multiply a number by 10^x
Move the decimal point to the right x places
Sqrt 12
N! / (k!)(n-k)!
1

28. 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
2(pi)r^2 + 2(pi)rh
Sqrt 12
Cd

29. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
12! / 5!7! = 792
A reflection about the origin.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
G(x) = {x}

30. What are complementary angles?
7 / 1000
Two angles whose sum is 90.
Ax^2 + bx + c where a -b and c are constants and a /=0
II

31. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
Its negative reciprocal. (-b/a)
...multiply by 100.
52
The set of elements which can be found in either A or B.

32. x^2 = 9. What is the value of x?
4725
52
3 - -3
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

33. 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?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
10! / (10-3)! = 720
$3 -500 in the 9% and $2 -500 in the 7%.
Infinite.

34. 50 < all primes< 60
53 - 59
500
(base*height) / 2
1.7

35. 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?
Sector area = (n/360) X (pi)r^2
83.333%
441000 = 1 10 10 10 21 * 21
No - the input value has exactly one output.

36. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
All numbers multiples of 1.
A circle centered at -2 - -2 with radius 3.
1:sqrt3:2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

37. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
F(x-c)
.0004809 X 10^11
From northeast - counterclockwise. I - II - III - IV
3

38. What is the ratio of the sides of a 30-60-90 triangle?
Two equal sides and two equal angles.
True
... the square of the ratios of the corresponding sides.
1:sqrt3:2

39. 0^0
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The direction of the inequality is reversed.
Its negative reciprocal. (-b/a)
Undefined

40. What is the graph of f(x) shifted right c units or spaces?
x^(4+7) = x^11
An isosceles right triangle.
The curve opens downward and the vertex is the maximum point on the graph.
F(x-c)

41. Number of degrees in a triangle
Two angles whose sum is 180.
180
83.333%
2 & 3/7

42. A number is divisible by 4 is...
Yes. [i.e. f(x) = x^2 - 1
37.5%
Its last two digits are divisible by 4.
2 & 3/7

43. What does the graph x^2 + y^2 = 64 look like?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
3 - -3
28. n = 8 - k = 2. n! / k!(n-k)!
A circle centered on the origin with radius 8.

44. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
Angle/360 x (pi)r^2
An angle which is supplementary to an interior angle.
Two angles whose sum is 90.

45. What are congruent triangles?
The shortest arc between points A and B on a circle'S diameter.
3
The set of output values for a function.
Triangles with same measure and same side lengths.

46. 8.84 / 5.2
1.7
$3 -500 in the 9% and $2 -500 in the 7%.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
55%

47. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
3/2 - 5/3
$3 -500 in the 9% and $2 -500 in the 7%.
Angle/360 x 2(pi)r

48. Order of quadrants:
A = pi(r^2)
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.
From northeast - counterclockwise. I - II - III - IV
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.

49. What is the order of operations?
180 degrees
Divide by 100.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
27^(-4)

50. To convert a percent to a fraction....
3/2 - 5/3
Yes - like radicals can be added/subtracted.
1 & 37/132
Divide by 100.

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GRE Math: Common Errors

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