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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. The larger the absolute value of the slope...
An expression with just one term (-6x - 2a^2)
3 - -3
II
The steeper the slope.
2. (-1)^2 =
(a + b)^2
13
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
1
3. What is the measure of an exterior angle of a regular pentagon?
The direction of the inequality is reversed.
Yes - like radicals can be added/subtracted.
72
The empty set - denoted by a circle with a diagonal through it.
4. What are the integers?
All numbers multiples of 1.
7 / 1000
10! / (10-3)! = 720
A circle centered on the origin with radius 8.
5. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
90pi
A reflection about the origin.
A circle centered at -2 - -2 with radius 3.
7 / 1000
6. What is the formula for computing simple interest?
A = I (1 + rt)
The steeper the slope.
N! / (n-k)!
x= (1.2)(.8)lw
7. What is the area of a regular hexagon with side 6?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
90 degrees
8. What are the members or elements of a set?
130pi
Cd
F(x + c)
The objects within a set.
9. How many multiples does a given number have?
9 & 6/7
2^9 / 2 = 256
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Infinite.
10. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
x= (1.2)(.8)lw
8
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
C = 2(pi)r
11. Which is greater? 200x^295 or 10x^294?
83.333%
(p + q)/5
Relationship cannot be determined (what if x is negative?)
Sqrt 12
12. The perimeter of a square is 48 inches. The length of its diagonal is:
The third side is greater than the difference and less than the sum.
0
13
12sqrt2
13. 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?
When the function is not defined for all real numbers -; only a subset of the real numbers.
9 : 25
$11 -448
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
14. Which is greater? 64^5 or 16^8
A grouping of the members within a set based on a shared characteristic.
10! / (10-3)! = 720
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
Lies opposite the greater angle
15. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
$11 -448
48
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.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
16. A number is divisible by 9 if...
70
A 30-60-90 triangle.
The sum of digits is divisible by 9.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
17. 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)
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)
4.25 - 6 - 22
The curve opens upward and the vertex is the minimal point on the graph.
Part = Percent X Whole
18. 3/8 in percent?
1
37.5%
An infinite set.
62.5%
19. (x^2)^4
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
The sum of digits is divisible by 9.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
x^(2(4)) =x^8 = (x^4)^2
20. What is the absolute value function?
6 : 1 : 2
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
500
G(x) = {x}
21. 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?
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
N! / (k!)(n-k)!
1
180 degrees
22. To convert a decimal to a percent...
The greatest value minus the smallest.
...multiply by 100.
2
4a^2(b)
23. Legs 5 - 12. Hypotenuse?
Area of the base X height = (pi)hr^2
Cd
13
The curve opens upward and the vertex is the minimal point on the graph.
24. Whats the difference between factors and multiples?
10
A circle centered at -2 - -2 with radius 3.
(amount of decrease/original price) x 100%
Factors are few - multiples are many.
25. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
The set of elements found in both A and B.
No - the input value has exactly one output.
Indeterminable.
26. What is the 'domain' of a function?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
4725
The set of input values for a function.
5
27. Formula to calculate arc length?
Arc length = (n/360) x pi(2r) where n is the number of degrees.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1
x= (1.2)(.8)lw
28. Which quandrant is the lower right hand?
6
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
IV
83.333%
29. Number of degrees in a triangle
An infinite set.
12sqrt2
(a + b)^2
180
30. 50 < all primes< 60
53 - 59
5
Angle/360 x (pi)r^2
The union of A and B.
31. Simplify (a^2 + b)^2 - (a^2 - b)^2
The set of elements which can be found in either A or B.
4a^2(b)
The point of intersection of the systems.
1
32. 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?
48
The empty set - denoted by a circle with a diagonal through it.
The two xes after factoring.
C = 2(pi)r
33. Surface area for a cylinder?
III
1:sqrt3:2
2(pi)r^2 + 2(pi)rh
G(x) = {x}
34. Which quadrant is the upper right hand?
The overlapping sections.
I
Members or elements
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
35. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
Sector area = (n/360) X (pi)r^2
... the square of the ratios of the corresponding sides.
The set of elements found in both A and B.
36. What is the sum of the angles of a triangle?
180 degrees
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
12sqrt2
(p + q)/5
37. 0^0
Undefined
From northeast - counterclockwise. I - II - III - IV
1
The objects within a set.
38. What is the surface area of a cylinder with radius 5 and height 8?
Two equal sides and two equal angles.
2.592 kg
The interesection of A and B.
130pi
39. What is the 'union' of A and B?
Area of the base X height = (pi)hr^2
No - the input value has exactly one output.
(p + q)/5
The set of elements which can be found in either A or B.
40. What is a chord of a circle?
A tangent is a line that only touches one point on the circumference of a circle.
70
A central angle is an angle formed by 2 radii.
A chord is a line segment joining two points on a circle.
41. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
20.5
G(x) = {x}
.0004809 X 10^11
42. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
F(x) - c
0
Cd
4:5
43. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
A 30-60-90 triangle.
x^(6-3) = x^3
A central angle is an angle formed by 2 radii.
A = pi(r^2)
44. Formula for the area of a circle?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
I
1.7
A = pi(r^2)
45. 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?
10
The set of elements found in both A and B.
A central angle is an angle formed by 2 radii.
N! / (n-k)!
46. Which quadrant is the upper left hand?
y = (x + 5)/2
A subset.
I
II
47. 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?
$3 -500 in the 9% and $2 -500 in the 7%.
II
61 - 67
Factors are few - multiples are many.
48. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Two equal sides and two equal angles.
1.7
C = 2(pi)r
49. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
All numbers multiples of 1.
2^9 / 2 = 256
A reflection about the origin.
Two angles whose sum is 180.
50. a^2 - b^2 =
3/2 - 5/3
The curve opens upward and the vertex is the minimal point on the graph.
6
(a - b)(a + b)