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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 name for a grouping of the members within a set based on a shared characteristic?
I
Its negative reciprocal. (-b/a)
The longest arc between points A and B on a circle'S diameter.
A subset.
2. What is a minor arc?
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183
3. What is the empty set?
A = I (1 + rt)
Relationship cannot be determined (what if x is negative?)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A set with no members - denoted by a circle with a diagonal through it.
4. Can you add sqrt 3 and sqrt 5?
.0004809 X 10^11
Yes. [i.e. f(x) = x^2 - 1
70
No - only like radicals can be added.
5. What is the 'domain' of a function?
The set of input values for a function.
No - only like radicals can be added.
IV
31 - 37
6. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
(b + c)
.0004809 X 10^11
18
1
7. 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?
N! / (k!)(n-k)!
9 : 25
2 & 3/7
The set of elements which can be found in either A or B.
8. The perimeter of a square is 48 inches. The length of its diagonal is:
Move the decimal point to the right x places
x= (1.2)(.8)lw
12sqrt2
Arc length = (n/360) x pi(2r) where n is the number of degrees.
9. 25^(1/2) or sqrt. 25 =
The sum of digits is divisible by 9.
48
5 OR -5
Undefined
10. 8.84 / 5.2
A circle centered at -2 - -2 with radius 3.
x= (1.2)(.8)lw
71 - 73 - 79
1.7
11. Solve the quadratic equation ax^2 + bx + c= 0
10! / 3!(10-3)! = 120
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
A set with a number of elements which can be counted.
The curve opens downward and the vertex is the maximum point on the graph.
12. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
x^(6-3) = x^3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
x= (1.2)(.8)lw
III
13. Simplify 9^(1/2) X 4^3 X 2^(-6)?
The interesection of A and B.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
3
13pi / 2
14. What is a set with no members called?
The curve opens upward and the vertex is the minimal point on the graph.
The empty set - denoted by a circle with a diagonal through it.
A set with no members - denoted by a circle with a diagonal through it.
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)
15. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
x^(2(4)) =x^8 = (x^4)^2
41 - 43 - 47
1/(x^y)
16. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
(a - b)(a + b)
Yes. [i.e. f(x) = x^2 - 1
Two angles whose sum is 90.
17. Volume for a cylinder?
52
Area of the base X height = (pi)hr^2
4096
F(x-c)
18. What is the graph of f(x) shifted upward c units or spaces?
.0004809 X 10^11
A reflection about the axis.
F(x) + c
62.5%
19. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
4725
12.5%
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(amount of increase/original price) x 100%
20. Reduce: 4.8 : 0.8 : 1.6
F(x-c)
The set of elements which can be found in either A or B.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
6 : 1 : 2
21. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
1:1:sqrt2
C = (pi)d
Two equal sides and two equal angles.
22. Can you simplify sqrt72?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
13
1/2 times 7/3
23. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
1
1
Cd
A reflection about the axis.
24. Define an 'expression'.
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)
70
The objects within a set.
F(x-c)
25. What is the ratio of the sides of a 30-60-90 triangle?
37.5%
$11 -448
Two angles whose sum is 90.
1:sqrt3:2
26. (6sqrt3) x (2sqrt5) =
Cd
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
27. 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?
10! / 3!(10-3)! = 120
A central angle is an angle formed by 2 radii.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Its last two digits are divisible by 4.
28. To convert a percent to a fraction....
The curve opens downward and the vertex is the maximum point on the graph.
x^(6-3) = x^3
Divide by 100.
5 OR -5
29. What does scientific notation mean?
A circle centered at -2 - -2 with radius 3.
Sqrt 12
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
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
30. 60 < all primes <70
II
The second graph is less steep.
The union of A and B.
61 - 67
31. What is a central angle?
A central angle is an angle formed by 2 radii.
Sqrt 12
1
Sector area = (n/360) X (pi)r^2
32. Max and Min lengths for a side of a triangle?
The third side is greater than the difference and less than the sum.
An isosceles right triangle.
The set of elements which can be found in either A or B.
Sector area = (n/360) X (pi)r^2
33. 7/8 in percent?
2 & 3/7
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
87.5%
Members or elements
34. In a regular polygon with n sides - the formula for the sum of interior angles
4a^2(b)
Angle/360 x 2(pi)r
(n-2) x 180
1/(x^y)
35. How to determine percent increase?
10! / 3!(10-3)! = 120
$11 -448
(amount of increase/original price) x 100%
75:11
36. What is the 'union' of A and B?
52
The set of elements which can be found in either A or B.
4096
1
37. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
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.
4.25 - 6 - 22
(a + b)^2
38. What are the smallest three prime numbers greater than 65?
9 & 6/7
(a + b)^2
Pi is the ratio of a circle'S circumference to its diameter.
67 - 71 - 73
39. x^6 / x^3
Ax^2 + bx + c where a -b and c are constants and a /=0
4096
x^(6-3) = x^3
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
40. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
No - only like radicals can be added.
A circle centered at -2 - -2 with radius 3.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
41. Formula to find a circle'S circumference from its radius?
6
C = 2(pi)r
83.333%
Divide by 100.
42. What is the maximum value for the function g(x) = (-2x^2) -1?
x(x - y + 1)
True
(a + b)^2
1
43. What is the graph of f(x) shifted left c units or spaces?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
Ax^2 + bx + c where a -b and c are constants and a /=0
F(x + c)
True
44. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
20.5
53 - 59
1
2sqrt6
45. To convert a decimal to a percent...
...multiply by 100.
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
$3 -500 in the 9% and $2 -500 in the 7%.
Even
46. Simplify the expression (p^2 - q^2)/ -5(q - p)
23 - 29
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
(p + q)/5
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
47. Is 0 even or odd?
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)
Even
3
Factors are few - multiples are many.
48. 6w^2 - w - 15 = 0
41 - 43 - 47
3/2 - 5/3
1
Relationship cannot be determined (what if x is negative?)
49. 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))?
20.5
y = 2x^2 - 3
The longest arc between points A and B on a circle'S diameter.
A set with a number of elements which can be counted.
50. Evaluate 3& 2/7 / 1/3
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
10! / (10-3)! = 720
9 & 6/7