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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. What is a piecewise equation?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Divide by 100.
7 / 1000
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. To multiply a number by 10^x
The point of intersection of the systems.
53 - 59
Move the decimal point to the right x places
Its divisible by 2 and by 3.

3. The slope of a line perpendicular to (a/b)?
1
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Its negative reciprocal. (-b/a)
Area of the base X height = (pi)hr^2

4. How to find the circumference of a circle which circumscribes a square?
3sqrt4
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The overlapping sections.
3/2 - 5/3

5. Surface area for a cylinder?
F(x-c)
27^(-4)
The empty set - denoted by a circle with a diagonal through it.
2(pi)r^2 + 2(pi)rh

6. What are the integers?
An expression with just one term (-6x - 2a^2)
All numbers multiples of 1.
x^(6-3) = x^3
1/2 times 7/3

7. Simplify 9^(1/2) X 4^3 X 2^(-6)?
130pi
3
1
No - only like radicals can be added.

8. What is the graph of f(x) shifted downward c units or spaces?
Infinite.
F(x) - c
(a - b)(a + b)
...multiply by 100.

9. If the two sides of a triangle are unequal then the longer side...
Sqrt 12
Lies opposite the greater angle
2.592 kg
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)

10. Define an 'expression'.
Triangles with same measure and same side lengths.
No - only like radicals can be added.
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)
When the function is not defined for all real numbers -; only a subset of the real numbers.

11. Can you simplify sqrt72?
F(x) + c
The curve opens downward and the vertex is the maximum point on the graph.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The set of elements found in both A and B.

12. How many sides does a hexagon have?
6
6 : 1 : 2
13pi / 2
5 OR -5

13. What is the name for a grouping of the members within a set based on a shared characteristic?
C = 2(pi)r
0
A subset.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15

14. 40 < all primes<50
Pi is the ratio of a circle'S circumference to its diameter.
41 - 43 - 47
4096
31 - 37

15. Solve the quadratic equation ax^2 + bx + c= 0
Its last two digits are divisible by 4.
The two xes after factoring.
N! / (k!)(n-k)!
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

16. What is the ratio of the sides of a 30-60-90 triangle?
F(x) + c
1:sqrt3:2
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 set of elements found in both A and B.

17. 1/8 in percent?
6
Its last two digits are divisible by 4.
12.5%
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16

18. a^2 - b^2 =
27^(-4)
(a - b)(a + b)
The set of input values for a function.
Sqrt 12

19. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
Yes. [i.e. f(x) = x^2 - 1
Undefined
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.

20. x^6 / x^3
55%
x^(6-3) = x^3
441000 = 1 10 10 10 21 * 21
The two xes after factoring.

21. Whats the difference between factors and multiples?
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)
Factors are few - multiples are many.
1/(x^y)
A set with a number of elements which can be counted.

22. What are complementary angles?
67 - 71 - 73
A reflection about the origin.
Part = Percent X Whole
Two angles whose sum is 90.

23. Formula for the area of a circle?
1
61 - 67
288 (8 9 4)
A = pi(r^2)

24. a^2 - b^2
II
(a - b)(a + b)
.0004809 X 10^11
130pi

25. A number is divisible by 4 is...
Angle/360 x (pi)r^2
Its last two digits are divisible by 4.
Factors are few - multiples are many.
The curve opens upward and the vertex is the minimal point on the graph.

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?
The set of input values for a function.
4:5
Its last two digits are divisible by 4.
500

27. What is the 'Solution' for a set of inequalities.
G(x) = {x}
10
Factors are few - multiples are many.
The overlapping sections.

28. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
3
1
F(x) + c
N! / (n-k)!

29. Which is greater? 200x^295 or 10x^294?
(base*height) / 2
The sum of its digits is divisible by 3.
180 degrees
Relationship cannot be determined (what if x is negative?)

30. 413.03 x 10^(-4) =
1 & 37/132
Lies opposite the greater angle
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
413.03 / 10^4 (move the decimal point 4 places to the left)

31. 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?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
70
90pi
10! / 3!(10-3)! = 120

32. What are congruent triangles?
True
130pi
Triangles with same measure and same side lengths.
72

33. 5/8 in percent?
1/a^6
1
The union of A and B.
62.5%

34. 7/8 in percent?
x^(4+7) = x^11
87.5%
x(x - y + 1)
1

35. The objects in a set are called two names:
Members or elements
11 - 13 - 17 - 19
Infinite.
Area of the base X height = (pi)hr^2

36. 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
The sum of digits is divisible by 9.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1:1:sqrt2

37. 1/6 in percent?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
61 - 67
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
16.6666%

38. What is the graph of f(x) shifted upward c units or spaces?
C = 2(pi)r
18
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
F(x) + c

39. Describe the relationship between the graphs of x^2 and (1/2)x^2
180
Yes. [i.e. f(x) = x^2 - 1
Triangles with same measure and same side lengths.
The second graph is less steep.

40. 30< all primes<40
5
3sqrt4
31 - 37
A circle centered on the origin with radius 8.

41. Simplify the expression (p^2 - q^2)/ -5(q - p)
1.0843 X 10^11
True
Yes - like radicals can be added/subtracted.
(p + q)/5

42. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
A subset.
(a - b)(a + b)

43. What are the smallest three prime numbers greater than 65?
71 - 73 - 79
N! / (n-k)!
67 - 71 - 73
180

44. a^0 =
Two angles whose sum is 90.
10! / 3!(10-3)! = 120
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
1

45. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
An isosceles right triangle.
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)
48
2

46. 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))?
Pi is the ratio of a circle'S circumference to its diameter.
13
20.5
31 - 37

47. (12sqrt15) / (2sqrt5) =
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
4:5
5 OR -5
3 - -3

48. The four angles around a point measure y - 2y - 35 and 55 respectively. What is the value of y?
Factors are few - multiples are many.
1.7
Indeterminable.
90

49. What percent of 40 is 22?
Its negative reciprocal. (-b/a)
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
55%
A subset.

50. To convert a decimal to a percent...
...multiply by 100.
Its last two digits are divisible by 4.
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)
Members or elements

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GRE Math: Common Errors

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