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GRE Math: Common Errors

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. (12sqrt15) / (2sqrt5) =
x(x - y + 1)
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
13
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

2. a^2 - b^2 =
1
12.5%
(a - b)(a + b)
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.

3. Which quandrant is the lower right hand?
IV
16.6666%
II
2sqrt6

4. To multiply a number by 10^x
Move the decimal point to the right x places
20.5
Yes - like radicals can be added/subtracted.
The set of output values for a function.

5. Define an 'expression'.
(a + b)^2
An expression with just one term (-6x - 2a^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)
A central angle is an angle formed by 2 radii.

6. Legs: 3 - 4. Hypotenuse?
F(x) - c
16.6666%
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
5

7. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
x^(4+7) = x^11
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
13

8. x^6 / x^3
4:5
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
.0004809 X 10^11
x^(6-3) = x^3

9. Describe the relationship between 3x^2 and 3(x - 1)^2
87.5%
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
(amount of increase/original price) x 100%
2

10. What is the name of set with a number of elements which cannot be counted?
Its negative reciprocal. (-b/a)
An expression with just one term (-6x - 2a^2)
An infinite set.
A reflection about the axis.

11. How to find the diagonal of a rectangular solid?
3
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The set of output values for a function.

12. 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)
4.25 - 6 - 22
(a + b)^2
70
A circle centered at -2 - -2 with radius 3.

13. What is the slope of a horizontal line?
72
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
0
Area of the base X height = (pi)hr^2

14. x^(-y)=
1/(x^y)
5 OR -5
A reflection about the origin.
90

15. What is the set of elements which can be found in either A or B?
The union of A and B.
x^(6-3) = x^3
The set of elements which can be found in either A or B.
The curve opens downward and the vertex is the maximum point on the graph.

16. Which quadrant is the lower left hand?
1:sqrt3:2
III
27^(-4)
130pi

17. What is the intersection of A and B?
The set of elements found in both A and B.
8
1
Lies opposite the greater angle

18. Solve the quadratic equation ax^2 + bx + c= 0
Factors are few - multiples are many.
...multiply by 100.
... the square of the ratios of the corresponding sides.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

19. A number is divisible by 4 is...
Its last two digits are divisible by 4.
3/2 - 5/3
The curve opens downward and the vertex is the maximum point on the graph.
9 : 25

20. A number is divisible by 3 if ...
7 / 1000
The steeper the slope.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
The sum of its digits is divisible by 3.

21. 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?
Sector area = (n/360) X (pi)r^2
1
1:1:sqrt2
$3 -500 in the 9% and $2 -500 in the 7%.

22. How to find the circumference of a circle which circumscribes a square?
x(x - y + 1)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
10! / 3!(10-3)! = 120
(a + b)^2

23. If the two sides of a triangle are unequal then the longer side...
6
Lies opposite the greater angle
The set of input values for a function.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.

24. What is the side length of an equilateral triangle with altitude 6?
True
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
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...
F(x + c)

25. 2sqrt4 + sqrt4 =
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...
1/2 times 7/3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3sqrt4

26. Which quadrant is the upper right hand?
The overlapping sections.
I
C = 2(pi)r
12! / 5!7! = 792

27. The larger the absolute value of the slope...
61 - 67
7 / 1000
2 & 3/7
The steeper the slope.

28. A number is divisible by 6 if...
(p + q)/5
The direction of the inequality is reversed.
Its divisible by 2 and by 3.
2.592 kg

29. 5/8 in percent?
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
62.5%
True
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

30. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
(base*height) / 2
70
180 degrees
1:sqrt3:2

31. What is the 'Solution' for a system of linear equations?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The point of intersection of the systems.
3/2 - 5/3
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

32. What are the smallest three prime numbers greater than 65?
5
75:11
67 - 71 - 73
The set of elements found in both A and B.

33. 10<all primes<20
7 / 1000
72
11 - 13 - 17 - 19
5 OR -5

34. 6w^2 - w - 15 = 0
37.5%
y = 2x^2 - 3
3/2 - 5/3
Lies opposite the greater angle

35. What is an exterior angle?
An angle which is supplementary to an interior angle.
(amount of decrease/original price) x 100%
The empty set - denoted by a circle with a diagonal through it.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]

36. 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 greatest value minus the smallest.
2 & 3/7
F(x) + c
True

37. What is the order of operations?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
1.7
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x^(6-3) = x^3

38. Can you add sqrt 3 and sqrt 5?
Two angles whose sum is 180.
12! / 5!7! = 792
No - only like radicals can be added.
Members or elements

39. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
(a + b)^2
13pi / 2
(amount of increase/original price) x 100%
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

40. Simplify the expression (p^2 - q^2)/ -5(q - p)
1 & 37/132
(p + q)/5
A = I (1 + rt)
4725

41. Length of an arc of a circle?
2 & 3/7
53 - 59
Diameter(Pi)
Angle/360 x 2(pi)r

42. What is a subset?
Ax^2 + bx + c where a -b and c are constants and a /=0
A tangent is a line that only touches one point on the circumference of a circle.
A grouping of the members within a set based on a shared characteristic.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.

43. What is an isoceles triangle?
Its last two digits are divisible by 4.
Members or elements
Two equal sides and two equal angles.
18

44. What does the graph x^2 + y^2 = 64 look like?
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...
Two equal sides and two equal angles.
F(x + c)
A circle centered on the origin with radius 8.

45. Simplify (a^2 + b)^2 - (a^2 - b)^2
1/(x^y)
The direction of the inequality is reversed.
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)
4a^2(b)

46. What is the set of elements found in both A and B?
1
441000 = 1 10 10 10 21 * 21
1.0843 X 10^11
The interesection of A and B.

47. Factor a^2 + 2ab + b^2
1
A set with no members - denoted by a circle with a diagonal through it.
(a + b)^2
(b + c)

48. Find the surface area of a cylinder with radius 3 and height 12.
90pi
71 - 73 - 79
2 & 3/7
Pi is the ratio of a circle'S circumference to its diameter.

49. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
A 30-60-90 triangle.
Angle/360 x 2(pi)r
2
11 - 13 - 17 - 19

50. 60 < all primes <70
The empty set - denoted by a circle with a diagonal through it.
F(x) - c
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
61 - 67