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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. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
52
4.25 - 6 - 22
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
2sqrt6

2. (-1)^2 =
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
1
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Its last two digits are divisible by 4.

3. What are the roots of the quadrinomial x^2 + 2x + 1?
(a - b)^2
13
The two xes after factoring.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

4. What is a parabola?
9 & 6/7
1/a^6
Ax^2 + bx + c where a -b and c are constants and a /=0
A set with no members - denoted by a circle with a diagonal through it.

5. What is the intersection of A and B?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
413.03 / 10^4 (move the decimal point 4 places to the left)
The set of elements found in both A and B.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

6. What is the name of set with a number of elements which cannot be counted?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Sqrt 12
An infinite set.
II

7. When the 'a' in a parabola is positive....
Yes - like radicals can be added/subtracted.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The curve opens upward and the vertex is the minimal point on the graph.
2(pi)r^2 + 2(pi)rh

8. Volume for a cylinder?
II
The two xes after factoring.
Area of the base X height = (pi)hr^2
441000 = 1 10 10 10 21 * 21

9. Surface area for a cylinder?
(a - b)(a + b)
1/a^6
2(pi)r^2 + 2(pi)rh
413.03 / 10^4 (move the decimal point 4 places to the left)

10. The ratio of the areas of two similar polygons is ...
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
... the square of the ratios of the corresponding sides.
A set with a number of elements which can be counted.
A chord is a line segment joining two points on a circle.

11. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
0
The set of input values for a function.
71 - 73 - 79
180

12. What is the maximum value for the function g(x) = (-2x^2) -1?
1
1:sqrt3:2
4.25 - 6 - 22
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. How to find the area of a sector?
The second graph is less steep.
Its negative reciprocal. (-b/a)
Angle/360 x (pi)r^2
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)

14. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
... the square of the ratios of the corresponding sides.
Lies opposite the greater angle
2sqrt6
37.5%

15. What is a central angle?
A central angle is an angle formed by 2 radii.
II
.0004809 X 10^11
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

16. What are complementary angles?
130pi
Two angles whose sum is 90.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
F(x + c)

17. x^(-y)=
18
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)
A circle centered on the origin with radius 8.
1/(x^y)

18. Whats the difference between factors and multiples?
9 : 25
Factors are few - multiples are many.
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 longest arc between points A and B on a circle'S diameter.

19. What is the formula for computing simple interest?
90pi
An angle which is supplementary to an interior angle.
10! / (10-3)! = 720
A = I (1 + rt)

20. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
12sqrt2
Yes - like radicals can be added/subtracted.
An isosceles right triangle.
No - only like radicals can be added.

21. Evaluate (4^3)^2
4725
4096
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
55%

22. 3/8 in percent?
37.5%
The objects within a set.
The curve opens upward and the vertex is the minimal point on the graph.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

23. What are congruent triangles?
Triangles with same measure and same side lengths.
Its last two digits are divisible by 4.
4.25 - 6 - 22
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)

24. x^6 / x^3
x^(6-3) = x^3
(a - b)^2
$3 -500 in the 9% and $2 -500 in the 7%.
441000 = 1 10 10 10 21 * 21

25. 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 angle intersecting the circumference is always the largest angle - and is always 90 degrees.
True
The curve opens upward and the vertex is the minimal point on the graph.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

26. Formula to calculate arc length?
1:1:sqrt2
1 & 37/132
Arc length = (n/360) x pi(2r) where n is the number of degrees.
Indeterminable.

27. When the 'a' in the parabola is negative...
1:sqrt3:2
Its divisible by 2 and by 3.
The curve opens downward and the vertex is the maximum point on the graph.
83.333%

28. Which quadrant is the upper right hand?
I
Arc length = (n/360) x pi(2r) where n is the number of degrees.
x= (1.2)(.8)lw
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).

29. What is the absolute value function?
9 & 6/7
Area of the base X height = (pi)hr^2
No - the input value has exactly one output.
G(x) = {x}

30. What is the empty set?
16.6666%
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.
A set with no members - denoted by a circle with a diagonal through it.
The curve opens downward and the vertex is the maximum point on the graph.

31. 25^(1/2) or sqrt. 25 =
(b + c)
A set with no members - denoted by a circle with a diagonal through it.
5 OR -5
0

32. What is the sum of the angles of a triangle?
180 degrees
III
(a - b)^2
The curve opens downward and the vertex is the maximum point on the graph.

33. Which quandrant is the lower right hand?
...multiply by 100.
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.
90 degrees
IV

34. What is the 'union' of A and B?
The set of elements which can be found in either A or B.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Yes - like radicals can be added/subtracted.
A subset.

35. What is the 'domain' of a function?
71 - 73 - 79
The set of input values for a function.
...multiply by 100.
The sum of its digits is divisible by 3.

36. What are the integers?
1 & 37/132
Undefined - because we can'T divide by 0.
Factors are few - multiples are many.
All numbers multiples of 1.

37. 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
4096
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.
The set of elements which can be found in either A or B.

38. What is the ratio of the sides of an isosceles right triangle?
62.5%
An expression with just one term (-6x - 2a^2)
1:1:sqrt2
90 degrees

39. 50 < all primes< 60
F(x) - c
53 - 59
4a^2(b)
72

40. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
288 (8 9 4)
(a + b)^2
12sqrt2

41. Length of an arc of a circle?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
1
Angle/360 x 2(pi)r
71 - 73 - 79

42. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
413.03 / 10^4 (move the decimal point 4 places to the left)
4725
2^9 / 2 = 256
Lies opposite the greater angle

43. 2sqrt4 + sqrt4 =
2^9 / 2 = 256
(a - b)(a + b)
...multiply by 100.
3sqrt4

44. What is the graph of f(x) shifted left c units or spaces?
III
A reflection about the origin.
Two angles whose sum is 90.
F(x + c)

45. Which is greater? 64^5 or 16^8
(p + q)/5
1
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
55%

46. Solve the quadratic equation ax^2 + bx + c= 0
2sqrt6
Even
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
10! / (10-3)! = 720

47. What is the 'Range' of a function?
Move the decimal point to the right x places
2
The set of output values for a function.
Ax^2 + bx + c where a -b and c are constants and a /=0

48. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
x^(6-3) = x^3
C = (pi)d
(b + c)

49. 7/8 in percent?
A 30-60-90 triangle.
1.0843 X 10^11
The direction of the inequality is reversed.
87.5%

50. Can you simplify sqrt72?
The shortest arc between points A and B on a circle'S diameter.
Sqrt 12
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A 30-60-90 triangle.

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GRE Math: Common Errors

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