Test your basic knowledge |

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. Which quandrant is the lower right hand?
Diameter(Pi)
An arc is a portion of a circumference of a circle.
IV
(base*height) / 2

2. If you have a set of n objects - but you only want to order k of them - what formula do you use to determine the number of permutations?
N! / (n-k)!
4096
F(x) - c
Undefined - because we can'T divide by 0.

3. (-1)^3 =
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1
(b + c)
Area of the base X height = (pi)hr^2

4. Which quadrant is the upper left hand?
Lies opposite the greater angle
II
The set of elements found in both A and B.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

5. Can the output value of a function have more than one input value?
5
Yes. [i.e. f(x) = x^2 - 1
The set of elements found in both A and B.
1

6. The ratio of the areas of two similar polygons is ...
1 & 37/132
90
... the square of the ratios of the corresponding sides.
True

7. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
The greatest value minus the smallest.
No - only like radicals can be added.
A circle centered at -2 - -2 with radius 3.
4096

8. 40 < all primes<50
41 - 43 - 47
Triangles with same measure and same side lengths.
Yes - like radicals can be added/subtracted.
Arc length = (n/360) x pi(2r) where n is the number of degrees.

9. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
Undefined - because we can'T divide by 0.
2sqrt6
From northeast - counterclockwise. I - II - III - IV

10. Which quadrant is the lower left hand?
Members or elements
III
N! / (k!)(n-k)!
2(pi)r^2 + 2(pi)rh

11. A number is divisible by 9 if...
Divide by 100.
Its divisible by 2 and by 3.
1
The sum of digits is divisible by 9.

12. 5/8 in percent?
Even
62.5%
A set with a number of elements which can be counted.
The sum of digits is divisible by 9.

13. (6sqrt3) x (2sqrt5) =
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
180
2^9 / 2 = 256
Triangles with same measure and same side lengths.

14. Reduce: 4.8 : 0.8 : 1.6
62.5%
2^9 / 2 = 256
6 : 1 : 2
No - the input value has exactly one output.

15. Suppose you have a set of n objects - and you want to select k of them - but the order doesn'T matter. What formula do you use to determine the number of combinations of n objects taken k at a time?
The steeper the slope.
(base*height) / 2
18
N! / (k!)(n-k)!

16. What are 'Supplementary angles?'
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Divide by 100.
Two angles whose sum is 180.
9 : 25

17. What is the area of a regular hexagon with side 6?
.0004809 X 10^11
An isosceles right triangle.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
413.03 / 10^4 (move the decimal point 4 places to the left)

18. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
Factors are few - multiples are many.
4a^2(b)
An arc is a portion of a circumference of a circle.
75:11

19. What is the surface area of a cylinder with radius 5 and height 8?
130pi
16.6666%
I
y = (x + 5)/2

20. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
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)
90 degrees
(amount of decrease/original price) x 100%
A reflection about the axis.

21. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
No - only like radicals can be added.
27^(-4)
28. n = 8 - k = 2. n! / k!(n-k)!
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)

22. What is the absolute value function?
Ax^2 + bx + c where a -b and c are constants and a /=0
5 OR -5
G(x) = {x}
Relationship cannot be determined (what if x is negative?)

23. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
3/2 - 5/3
2^9 / 2 = 256
Even
53 - 59

24. What is the side length of an equilateral triangle with altitude 6?
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...
500
Indeterminable.
4a^2(b)

25. What is the 'Range' of a function?
The set of output values for a function.
130pi
75:11
1

26. Legs: 3 - 4. Hypotenuse?
Two equal sides and two equal angles.
Factors are few - multiples are many.
5
9 : 25

27. (a^-1)/a^5
(b + c)
(a + b)^2
1/a^6
The longest arc between points A and B on a circle'S diameter.

28. When the 'a' in the parabola is negative...
The interesection of A and B.
Yes. [i.e. f(x) = x^2 - 1
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
The curve opens downward and the vertex is the maximum point on the graph.

29. Evaluate 4/11 + 11/12
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x^(6-3) = x^3
1 & 37/132
18

30. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An isosceles right triangle.
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
28. n = 8 - k = 2. n! / k!(n-k)!
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)

31. Solve the quadratic equation ax^2 + bx + c= 0
3
90pi
The shortest arc between points A and B on a circle'S diameter.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a

32. sqrt 2(sqrt 6)=
Sqrt 12
3 - -3
The sum of its digits is divisible by 3.
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)

33. If an inequality is multiplied or divided by a negative number....
8
The direction of the inequality is reversed.
Sqrt 12
9 : 25

34. x^4 + x^7 =
x^(4+7) = x^11
An infinite set.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
An expression with just one term (-6x - 2a^2)

35. Can the input value of a function have more than one output value (i.e. x: y - y1)?
71 - 73 - 79
(b + c)
No - the input value has exactly one output.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

36. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
The longest arc between points A and B on a circle'S diameter.
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

37. In a triangle where the two legs are 4 and 3 - what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?
12sqrt2
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
C = (pi)d
10! / (10-3)! = 720

38. Simplify 9^(1/2) X 4^3 X 2^(-6)?
1:sqrt3:2
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
(a + b)^2
3

39. A number is divisible by 3 if ...
(a + b)^2
Indeterminable.
The sum of its digits is divisible by 3.
A 30-60-90 triangle.

40. What is the slope of a horizontal line?
0
90 degrees
A set with a number of elements which can be counted.
9 : 25

41. a^2 + 2ab + b^2
(a + b)^2
N! / (n-k)!
The direction of the inequality is reversed.
2 & 3/7

42. Simplify the expression (p^2 - q^2)/ -5(q - p)
Two angles whose sum is 180.
90
(p + q)/5
Factors are few - multiples are many.

43. Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week - how many did each work?
Infinite.
48
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
41 - 43 - 47

44. Area of a triangle?
52
(base*height) / 2
6
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).

45. 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?
90 degrees
0
$3 -500 in the 9% and $2 -500 in the 7%.
12sqrt2

46. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
The set of elements which can be found in either A or B.
True
28. n = 8 - k = 2. n! / k!(n-k)!
13pi / 2

47. What is the maximum value for the function g(x) = (-2x^2) -1?
55%
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
1.7
1

48. What is the formula for compounded interest?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Two angles whose sum is 90.
90pi
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.

49. What are the integers?
Indeterminable.
All numbers multiples of 1.
52
8

50. What is the graph of f(x) shifted upward c units or spaces?
The shortest arc between points A and B on a circle'S diameter.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
Undefined
F(x) + c