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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 are the irrational numbers?
2. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
A tangent is a line that only touches one point on the circumference of a circle.
1
Lies opposite the greater angle
18
3. 70 < all primes< 80
71 - 73 - 79
$3 -500 in the 9% and $2 -500 in the 7%.
Diameter(Pi)
41 - 43 - 47
4. Pi is a ratio of what to what?
5. What are congruent triangles?
18
(b + c)
A set with no members - denoted by a circle with a diagonal through it.
Triangles with same measure and same side lengths.
6. When does a function automatically have a restricted domain (2)?
An isosceles right triangle.
Relationship cannot be determined (what if x is negative?)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Yes. [i.e. f(x) = x^2 - 1
7. What is the slope of a vertical line?
8. x^4 + x^7 =
3 - -3
1.0843 X 10^11
10! / 3!(10-3)! = 120
x^(4+7) = x^11
9. 413.03 x 10^(-4) =
413.03 / 10^4 (move the decimal point 4 places to the left)
10! / 3!(10-3)! = 120
Infinite.
2
10. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
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.
True
11. Describe the relationship between the graphs of x^2 and (1/2)x^2
10
75:11
The second graph is less steep.
(a - b)^2
12. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
The third side is greater than the difference and less than the sum.
2
Yes - like radicals can be added/subtracted.
1.0843 X 10^11
13. What is the maximum value for the function g(x) = (-2x^2) -1?
4a^2(b)
0
III
1
14. What is a central angle?
87.5%
A circle centered at -2 - -2 with radius 3.
A central angle is an angle formed by 2 radii.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
15. Can you add sqrt 3 and sqrt 5?
1 & 37/132
No - only like radicals can be added.
Diameter(Pi)
The direction of the inequality is reversed.
16. Find the surface area of a cylinder with radius 3 and height 12.
413.03 / 10^4 (move the decimal point 4 places to the left)
500
An expression with just one term (-6x - 2a^2)
90pi
17. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
3 - -3
(amount of decrease/original price) x 100%
8
1/a^6
18. Formula to find a circle'S circumference from its diameter?
16.6666%
Angle/360 x (pi)r^2
441000 = 1 10 10 10 21 * 21
C = (pi)d
19. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3
IV
The steeper the slope.
20. 1/2 divided by 3/7 is the same as
Two angles whose sum is 180.
18
1/2 times 7/3
The greatest value minus the smallest.
21. To convert a percent to a fraction....
Divide by 100.
90
The sum of digits is divisible by 9.
1/(x^y)
22. What number between 70 & 75 - inclusive - has the greatest number of factors?
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
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
72
23. 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
x^(6-3) = x^3
87.5%
(a + b)^2
18
24. 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?
An angle which is supplementary to an interior angle.
3
Sector area = (n/360) X (pi)r^2
10! / (10-3)! = 720
25. Is 0 even or odd?
A central angle is an angle formed by 2 radii.
2sqrt6
Even
6
26. 1/6 in percent?
A subset.
16.6666%
180 degrees
y = 2x^2 - 3
27. Describe the relationship between 3x^2 and 3(x - 1)^2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
The point of intersection of the systems.
1
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
28. What are the rational numbers?
87.5%
Yes. [i.e. f(x) = x^2 - 1
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
29. What are the roots of the quadrinomial x^2 + 2x + 1?
A set with a number of elements which can be counted.
1
3
The two xes after factoring.
30. Simplify the expression (p^2 - q^2)/ -5(q - p)
Undefined
6 : 1 : 2
An infinite set.
(p + q)/5
31. Evaluate 3& 2/7 / 1/3
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
9 & 6/7
Factors are few - multiples are many.
N! / (n-k)!
32. Factor x^2 - xy + x.
C = 2(pi)r
I
A central angle is an angle formed by 2 radii.
x(x - y + 1)
33. A number is divisible by 4 is...
Angle/360 x 2(pi)r
The set of elements found in both A and B.
Its last two digits are divisible by 4.
A reflection about the origin.
34. What is the slope of a horizontal line?
9 & 6/7
x^(4+7) = x^11
Sqrt 12
0
35. Formula for the area of a sector of a circle?
...multiply by 100.
Sector area = (n/360) X (pi)r^2
90
x^(4+7) = x^11
36. What is a set with no members called?
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)
The empty set - denoted by a circle with a diagonal through it.
Factors are few - multiples are many.
The shortest arc between points A and B on a circle'S diameter.
37. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
The sum of digits is divisible by 9.
The steeper the slope.
III
A reflection about the origin.
38. sqrt 2(sqrt 6)=
(a - b)(a + b)
x= (1.2)(.8)lw
Sqrt 12
12! / 5!7! = 792
39. (6sqrt3) x (2sqrt5) =
N! / (k!)(n-k)!
The empty set - denoted by a circle with a diagonal through it.
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Diameter(Pi)
40. Surface area for a cylinder?
5 OR -5
x^(6-3) = x^3
2(pi)r^2 + 2(pi)rh
12.5%
41. 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?
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
Divide by 100.
The sum of its digits is divisible by 3.
From northeast - counterclockwise. I - II - III - IV
42. What are the members or elements of a set?
The objects within a set.
Angle/360 x (pi)r^2
.0004809 X 10^11
90 degrees
43. What are the real numbers?
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)
When the function is not defined for all real numbers -; only a subset of the real numbers.
Sqrt 12
75:11
44. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
2.592 kg
III
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(b + c)
45. To multiply a number by 10^x
x^(4+7) = x^11
Yes. [i.e. f(x) = x^2 - 1
Move the decimal point to the right x places
27^(-4)
46. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
A subset.
$11 -448
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
3
47. A company places a 6-symbol code on each product. The code consists of the letter T - followed by 3 numerical digits - and then 2 consonants (Y is a conson). How many codes are possible?
Move the decimal point to the right x places
The interesection of A and B.
20.5
441000 = 1 10 10 10 21 * 21
48. What is the graph of f(x) shifted right c units or spaces?
Cd
F(x-c)
(n-2) x 180
12.5%
49. To convert a decimal to a percent...
16.6666%
...multiply by 100.
3/2 - 5/3
90 degrees
50. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
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
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
62.5%