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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. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
20.5
A circle centered at -2 - -2 with radius 3.
5
2^9 / 2 = 256
2. What are the members or elements of a set?
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
I
The objects within a set.
18
3. To convert a decimal to a percent...
Undefined - because we can'T divide by 0.
...multiply by 100.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
20.5
4. How many multiples does a given number have?
90
Infinite.
Its last two digits are divisible by 4.
61 - 67
5. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
9 & 6/7
When the function is not defined for all real numbers -; only a subset of the real numbers.
2sqrt6
6. What is the ratio of the sides of a 30-60-90 triangle?
Pi is the ratio of a circle'S circumference to its diameter.
III
2
1:sqrt3:2
7. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
(a - b)(a + b)
(p + q)/5
0
8. What is the 'Restricted domain of a function'?
Angle/360 x (pi)r^2
When the function is not defined for all real numbers -; only a subset of the real numbers.
41 - 43 - 47
A chord is a line segment joining two points on a circle.
9. 413.03 x 10^(-4) =
Undefined - because we can'T divide by 0.
3/2 - 5/3
413.03 / 10^4 (move the decimal point 4 places to the left)
7 / 1000
10. a^2 + 2ab + b^2
No - the input value has exactly one output.
16.6666%
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
(a + b)^2
11. What are the rational numbers?
I
90pi
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
413.03 / 10^4 (move the decimal point 4 places to the left)
12. The ratio of the areas of two similar polygons is ...
Move the decimal point to the right x places
Ax^2 + bx + c where a -b and c are constants and a /=0
4725
... the square of the ratios of the corresponding sides.
13. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
70
An isosceles right triangle.
12.5%
41 - 43 - 47
14. The objects in a set are called two names:
An expression with just one term (-6x - 2a^2)
0
Members or elements
x(x - y + 1)
15. Formula for the area of a circle?
Ax^2 + bx + c where a -b and c are constants and a /=0
An expression with just one term (-6x - 2a^2)
A = pi(r^2)
72
16. 30< all primes<40
1
31 - 37
72
500
17. Whats the difference between factors and multiples?
Cd
The empty set - denoted by a circle with a diagonal through it.
Factors are few - multiples are many.
The greatest value minus the smallest.
18. Define a 'monomial'
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
An expression with just one term (-6x - 2a^2)
6 : 1 : 2
A circle centered at -2 - -2 with radius 3.
19. How many 3-digit positive integers are even and do not contain the digit 4?
288 (8 9 4)
y = (x + 5)/2
6
All numbers multiples of 1.
20. 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
F(x + c)
1:1:sqrt2
An arc is a portion of a circumference of a circle.
21. 0^0
Undefined
An angle which is supplementary to an interior angle.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
A circle centered on the origin with radius 8.
22. What is the formula for compounded interest?
10
A circle centered on the origin with radius 8.
(b + c)
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.
23. Which is greater? 64^5 or 16^8
No - the input value has exactly one output.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
62.5%
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
24. When does a function automatically have a restricted domain (2)?
Indeterminable.
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Angle/360 x 2(pi)r
1
25. 1/6 in percent?
1
16.6666%
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)
7 / 1000
26. Describe the relationship between the graphs of x^2 and (1/2)x^2
(a - b)^2
The second graph is less steep.
Indeterminable.
2 & 3/7
27. Find the surface area of a cylinder with radius 3 and height 12.
90pi
C = (pi)d
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
10
28. What is the absolute value function?
8
2(pi)r^2 + 2(pi)rh
The overlapping sections.
G(x) = {x}
29. 6w^2 - w - 15 = 0
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...
A chord is a line segment joining two points on a circle.
3/2 - 5/3
The set of elements which can be found in either A or B.
30. 40 < all primes<50
6
Two equal sides and two equal angles.
41 - 43 - 47
2sqrt6
31. What is the intersection of A and B?
The set of elements found in both A and B.
1.0843 X 10^11
When the function is not defined for all real numbers -; only a subset of the real numbers.
87.5%
32. What are the real numbers?
1
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)
70
The second graph is less steep.
33. 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 curve opens downward and the vertex is the maximum point on the graph.
6 : 1 : 2
N! / (k!)(n-k)!
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
34. 5x^2 - 35x -55 = 0
Lies opposite the greater angle
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
90
413.03 / 10^4 (move the decimal point 4 places to the left)
35. Define a 'Term' -
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)
4a^2(b)
2sqrt6
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
36. 5/8 in percent?
F(x + c)
The curve opens downward and the vertex is the maximum point on the graph.
75:11
62.5%
37. Legs 5 - 12. Hypotenuse?
x^(2(4)) =x^8 = (x^4)^2
37.5%
13
11 - 13 - 17 - 19
38. Can you subtract 3sqrt4 from sqrt4?
90pi
II
F(x) - c
Yes - like radicals can be added/subtracted.
39. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
70
90pi
83.333%
40. What is an exterior angle?
1:sqrt3:2
An angle which is supplementary to an interior angle.
9 & 6/7
41 - 43 - 47
41. What is the graph of f(x) shifted upward c units or spaces?
A central angle is an angle formed by 2 radii.
52
F(x) + c
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)
42. (x^2)^4
The sum of its digits is divisible by 3.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
The interesection of A and B.
x^(2(4)) =x^8 = (x^4)^2
43. 4.809 X 10^7 =
6
The curve opens downward and the vertex is the maximum point on the graph.
A set with no members - denoted by a circle with a diagonal through it.
.0004809 X 10^11
44. What is the name of set with a number of elements which cannot be counted?
An infinite set.
180 degrees
23 - 29
A chord is a line segment joining two points on a circle.
45. Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?
y = 2x^2 - 3
A chord is a line segment joining two points on a circle.
67 - 71 - 73
The overlapping sections.
46. What is an arc of a circle?
An arc is a portion of a circumference of a circle.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
No - only like radicals can be added.
The set of elements found in both A and B.
47. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
3/2 - 5/3
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Factors are few - multiples are many.
48. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
13pi / 2
27^(-4)
(amount of decrease/original price) x 100%
49. Which quadrant is the upper right hand?
Even
F(x-c)
I
N! / (n-k)!
50. x^6 / x^3
x^(6-3) = x^3
31 - 37
C = 2(pi)r
(a - b)^2