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Test your basic knowledge |
GRE Math: Common Errors
Start Test
Study First
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. What is the slope of a horizontal line?
A set with a number of elements which can be counted.
0
A = pi(r^2)
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
2. 25^(1/2) or sqrt. 25 =
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
A circle centered at -2 - -2 with radius 3.
5 OR -5
61 - 67
3. 4.809 X 10^7 =
.0004809 X 10^11
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
55%
72
4. What is the name for a grouping of the members within a set based on a shared characteristic?
62.5%
Area of the base X height = (pi)hr^2
A subset.
48
5. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Two angles whose sum is 180.
1 & 37/132
Cd
3sqrt4
6. 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?
1
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
10! / 3!(10-3)! = 120
A circle centered on the origin with radius 8.
7. To convert a percent to a fraction....
Divide by 100.
71 - 73 - 79
3 - -3
288 (8 9 4)
8. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
$11 -448
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
An arc is a portion of a circumference of a circle.
2 & 3/7
9. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
87.5%
3/2 - 5/3
10. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
2sqrt6
27^(-4)
Sector area = (n/360) X (pi)r^2
11. What is a piecewise equation?
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
71 - 73 - 79
Angle/360 x 2(pi)r
x^(4+7) = x^11
12. Evaluate (4^3)^2
II
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
4096
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
13. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
Relationship cannot be determined (what if x is negative?)
An isosceles right triangle.
4096
27^(-4)
14. In a regular polygon with n sides - the formula for the sum of interior angles
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...
(n-2) x 180
The curve opens upward and the vertex is the minimal point on the graph.
71 - 73 - 79
15. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
An isosceles right triangle.
8
90pi
Infinite.
16. 10<all primes<20
11 - 13 - 17 - 19
$11 -448
The interesection of A and B.
1
17. What is the absolute value function?
A circle centered at -2 - -2 with radius 3.
0
G(x) = {x}
72
18. Describe the relationship between the graphs of x^2 and (1/2)x^2
Undefined
The set of output values for a function.
18
The second graph is less steep.
19. The perimeter of a square is 48 inches. The length of its diagonal is:
12sqrt2
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
48
The set of input values for a function.
20. To convert a decimal to a percent...
IV
...multiply by 100.
II
x^(2(4)) =x^8 = (x^4)^2
21. What does scientific notation mean?
Move the decimal point to the right x places
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
The empty set - denoted by a circle with a diagonal through it.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
22. Whats the difference between factors and multiples?
90pi
4.25 - 6 - 22
IV
Factors are few - multiples are many.
23. What are the roots of the quadrinomial x^2 + 2x + 1?
A reflection about the axis.
The two xes after factoring.
(a - b)(a + b)
130pi
24. Order of quadrants:
From northeast - counterclockwise. I - II - III - IV
x^(2(4)) =x^8 = (x^4)^2
52
413.03 / 10^4 (move the decimal point 4 places to the left)
25. What is an exterior angle?
(base*height) / 2
An angle which is supplementary to an interior angle.
10! / 3!(10-3)! = 120
The third side is greater than the difference and less than the sum.
26. Area of a triangle?
The shortest arc between points A and B on a circle'S diameter.
(base*height) / 2
52
10! / 3!(10-3)! = 120
27. P and r are factors of 100. What is greater - pr or 100?
The sum of its digits is divisible by 3.
Undefined - because we can'T divide by 0.
Indeterminable.
13
28. Legs: 3 - 4. Hypotenuse?
5
...multiply by 100.
Cd
Two angles whose sum is 180.
29. What is a major arc?
30. 70 < all primes< 80
71 - 73 - 79
2(pi)r^2 + 2(pi)rh
3sqrt4
...multiply by 100.
31. Simplify the expression [(b^2 - c^2) / (b - c)]
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(b + c)
27^(-4)
Arc length = (n/360) x pi(2r) where n is the number of degrees.
32. 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?
I
N! / (k!)(n-k)!
Its divisible by 2 and by 3.
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)
33. How to find the diagonal of a rectangular solid?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
(amount of increase/original price) x 100%
The second graph is less steep.
413.03 / 10^4 (move the decimal point 4 places to the left)
34. What is a minor arc?
35. What is the graph of f(x) shifted downward c units or spaces?
13
441000 = 1 10 10 10 21 * 21
70
F(x) - c
36. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
2sqrt6
55%
2
37. Evaluate 4/11 + 11/12
True
1 & 37/132
C = 2(pi)r
3/2 - 5/3
38. How to find the area of a sector?
A circle centered at -2 - -2 with radius 3.
Angle/360 x (pi)r^2
x= (1.2)(.8)lw
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
39. 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
Factors are few - multiples are many.
18
x^(4+7) = x^11
1 & 37/132
40. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?
A = I (1 + rt)
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
All numbers multiples of 1.
10! / (10-3)! = 720
41. Which quadrant is the lower left hand?
II
C = (pi)d
x^(4+7) = x^11
III
42. Which is greater? 27^(-4) or 9^(-8)
27^(-4)
G(x) = {x}
53 - 59
x(x - y + 1)
43. 50 < all primes< 60
53 - 59
A 30-60-90 triangle.
2
The interesection of A and B.
44. What is a set with no members called?
62.5%
(p + q)/5
The empty set - denoted by a circle with a diagonal through it.
The set of elements which can be found in either A or B.
45. Factor a^2 + 2ab + b^2
(a + b)^2
Even
Relationship cannot be determined (what if x is negative?)
28. n = 8 - k = 2. n! / k!(n-k)!
46. What is the 'domain' of a function?
0
Even
The set of input values for a function.
1/2 times 7/3
47. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
When the function is not defined for all real numbers -; only a subset of the real numbers.
Two angles whose sum is 90.
70
75:11
48. x^(-y)=
A grouping of the members within a set based on a shared characteristic.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
6
1/(x^y)
49. What is an arc of a circle?
52
Ax^2 + bx + c where a -b and c are constants and a /=0
The longest arc between points A and B on a circle'S diameter.
An arc is a portion of a circumference of a circle.
50. Length of an arc of a circle?
Undefined - because we can'T divide by 0.
Sector area = (n/360) X (pi)r^2
9 & 6/7
Angle/360 x 2(pi)r