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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. 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?
11 - 13 - 17 - 19
4a^2(b)
(b + c)
$3 -500 in the 9% and $2 -500 in the 7%.

2. (x^2)^4
1
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
x^(2(4)) =x^8 = (x^4)^2
10! / 3!(10-3)! = 120

3. 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)?
The curve opens downward and the vertex is the maximum point on the graph.
Part = Percent X Whole
(n-2) x 180
y = (x + 5)/2

4. How to find the circumference of a circle which circumscribes a square?
x^(2(4)) =x^8 = (x^4)^2
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
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
An infinite set.

5. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Its last two digits are divisible by 4.

6. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
1
1 & 37/132
Two angles whose sum is 90.
A subset.

7. A number is divisible by 9 if...
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
An angle which is supplementary to an interior angle.
The sum of digits is divisible by 9.
(p + q)/5

8. What is the 'Range' of a function?
37.5%
13pi / 2
The set of output values for a function.
No - only like radicals can be added.

9. Formula for the area of a circle?
72
180 degrees
Lies opposite the greater angle
A = pi(r^2)

10. What is an arc of a circle?
All numbers multiples of 1.
Yes - like radicals can be added/subtracted.
Angle/360 x (pi)r^2
An arc is a portion of a circumference of a circle.

11. Simplify the expression (p^2 - q^2)/ -5(q - p)
The greatest value minus the smallest.
An angle which is supplementary to an interior angle.
(p + q)/5
A grouping of the members within a set based on a shared characteristic.

12. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
The union of A and B.
3
83.333%
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...

13. The slope of a line perpendicular to (a/b)?
Its negative reciprocal. (-b/a)
Triangles with same measure and same side lengths.
The curve opens downward and the vertex is the maximum point on the graph.
An expression with just one term (-6x - 2a^2)

14. 0^0
An arc is a portion of a circumference of a circle.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Undefined
83.333%

15. 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
A set with a number of elements which can be counted.
3/2 - 5/3
18
4096

16. What is the 'domain' of a function?
The set of input values for a function.
52
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.
Even

17. Circumference of a circle?
$3 -500 in the 9% and $2 -500 in the 7%.
2^9 / 2 = 256
Diameter(Pi)
The direction of the inequality is reversed.

18. What is the side length of an equilateral triangle with altitude 6?
C = (pi)d
N! / (n-k)!
A central angle is an angle formed by 2 radii.
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...

19. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
C = 2(pi)r
(a + b)^2
(p + q)/5

20. Factor a^2 + 2ab + b^2
441000 = 1 10 10 10 21 * 21
x= (1.2)(.8)lw
(a + b)^2
N! / (k!)(n-k)!

21. 4.809 X 10^7 =
53 - 59
.0004809 X 10^11
27^(-4)
4:5

22. Formula for the area of a sector of a circle?
Its last two digits are divisible by 4.
Its divisible by 2 and by 3.
Sector area = (n/360) X (pi)r^2
Factors are few - multiples are many.

23. Factor x^2 - xy + x.
x(x - y + 1)
87.5%
4a^2(b)
Its negative reciprocal. (-b/a)

24. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
2 & 3/7
(a + b)^2
0
1

25. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Lies opposite the greater angle
13pi / 2
70

26. Convert 0.7% to a fraction.
8
27^(-4)
10
7 / 1000

27. (12sqrt15) / (2sqrt5) =
13
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
y = 2x^2 - 3
6 : 1 : 2

28. Which is greater? 64^5 or 16^8
52
72
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
A = pi(r^2)

29. What is the graph of f(x) shifted right c units or spaces?
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)
F(x-c)
A chord is a line segment joining two points on a circle.
F(x + c)

30. Whats the difference between factors and multiples?
A central angle is an angle formed by 2 radii.
2 & 3/7
Factors are few - multiples are many.
Its last two digits are divisible by 4.

31. What does scientific notation mean?
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)
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...
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The point of intersection of the systems.

32. What is the intersection of A and B?
3/2 - 5/3
4a^2(b)
F(x) + c
The set of elements found in both A and B.

33. Which quadrant is the upper left hand?
72
II
Two equal sides and two equal angles.
x^(2(4)) =x^8 = (x^4)^2

34. 10<all primes<20
1
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)
x^(4+7) = x^11
11 - 13 - 17 - 19

35. How to find the diagonal of a rectangular solid?
8
An infinite set.
2sqrt6
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

36. 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?
441000 = 1 10 10 10 21 * 21
N! / (k!)(n-k)!
The objects within a set.
4.25 - 6 - 22

37. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
The direction of the inequality is reversed.
Its divisible by 2 and by 3.
2^9 / 2 = 256
Two angles whose sum is 90.

38. When the 'a' in a parabola is positive....
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
F(x + c)
The curve opens upward and the vertex is the minimal point on the graph.
Area of the base X height = (pi)hr^2

39. What is the set of elements which can be found in either A or B?
The set of input values for a function.
No - only like radicals can be added.
The union of A and B.
83.333%

40. (-1)^2 =
1
Its negative reciprocal. (-b/a)
Relationship cannot be determined (what if x is negative?)
No - the input value has exactly one output.

41. How to determine percent decrease?
(amount of decrease/original price) x 100%
Sqrt 12
A chord is a line segment joining two points on a circle.
53 - 59

42. 50 < all primes< 60
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)
53 - 59
83.333%
8

43. What is the surface area of a cylinder with radius 5 and height 8?
3
The second graph is less steep.
The curve opens downward and the vertex is the maximum point on the graph.
130pi

44. Legs: 3 - 4. Hypotenuse?
5
2(pi)r^2 + 2(pi)rh
413.03 / 10^4 (move the decimal point 4 places to the left)
5 OR -5

45. 25^(1/2) or sqrt. 25 =
(amount of increase/original price) x 100%
5 OR -5
III
The greatest value minus the smallest.

46. What percent of 40 is 22?
180
6 : 1 : 2
55%
(a + b)^2

47. 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?
Infinite.
3/2 - 5/3
10! / 3!(10-3)! = 120
20.5

48. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
Lies opposite the greater angle
2sqrt6
10! / 3!(10-3)! = 120
9 : 25

49. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
Cd
Members or elements
11 - 13 - 17 - 19

50. Area of a triangle?
0
3 - -3
(base*height) / 2
1

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GRE Math: Common Errors

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