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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. 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).
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
The set of input values for a function.
Ax^2 + bx + c where a -b and c are constants and a /=0
2. Can the output value of a function have more than one input value?
Two angles whose sum is 180.
When the function is not defined for all real numbers -; only a subset of the real numbers.
441000 = 1 10 10 10 21 * 21
Yes. [i.e. f(x) = x^2 - 1
3. Legs: 3 - 4. Hypotenuse?
Undefined
IV
1/2 times 7/3
5
4. Convert 0.7% to a fraction.
$3 -500 in the 9% and $2 -500 in the 7%.
7 / 1000
The point of intersection of the systems.
Yes. [i.e. f(x) = x^2 - 1
5. 30< all primes<40
31 - 37
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
6
6. Is 0 even or odd?
Even
Indeterminable.
The point of intersection of the systems.
1.7
7. What is the graph of f(x) shifted downward c units or spaces?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
1 & 37/132
F(x) - c
2.592 kg
8. x^2 = 9. What is the value of x?
The third side is greater than the difference and less than the sum.
An expression with just one term (-6x - 2a^2)
3 - -3
The sum of its digits is divisible by 3.
9. Solve the quadratic equation ax^2 + bx + c= 0
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
288 (8 9 4)
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
55%
10. What is the 'domain' of a function?
The set of input values for a function.
An expression with just one term (-6x - 2a^2)
Two angles whose sum is 180.
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)
11. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
10! / 3!(10-3)! = 120
0
Sqrt 12
x^(6-3) = x^3
12. What are the smallest three prime numbers greater than 65?
87.5%
When the function is not defined for all real numbers -; only a subset of the real numbers.
67 - 71 - 73
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
13. Circumference of a circle?
Diameter(Pi)
62.5%
The overlapping sections.
No - only like radicals can be added.
14. Area of a triangle?
Move the decimal point to the right x places
(base*height) / 2
12.5%
IV
15. What is the 'union' of A and B?
x^(6-3) = x^3
The set of elements which can be found in either A or B.
A subset.
All numbers multiples of 1.
16. How to find the area of a sector?
The second graph is less steep.
Angle/360 x (pi)r^2
12sqrt2
Pi is the ratio of a circle'S circumference to its diameter.
17. 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?
A circle centered on the origin with radius 8.
The empty set - denoted by a circle with a diagonal through it.
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)
y = 2x^2 - 3
18. Whats the difference between factors and multiples?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Factors are few - multiples are many.
61 - 67
23 - 29
19. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
16.6666%
A reflection about the origin.
71 - 73 - 79
y = (x + 5)/2
20. sqrt 2(sqrt 6)=
F(x-c)
No - the input value has exactly one output.
Sqrt 12
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
21. Define a 'monomial'
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.
3 - -3
Sector area = (n/360) X (pi)r^2
An expression with just one term (-6x - 2a^2)
22. How many sides does a hexagon have?
The steeper the slope.
6
A set with a number of elements which can be counted.
The objects within a set.
23. Which quadrant is the upper left hand?
II
Its divisible by 2 and by 3.
500
52
24. To convert a decimal to a percent...
...multiply by 100.
1:1:sqrt2
The overlapping sections.
180 degrees
25. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
Infinite.
4:5
10! / 3!(10-3)! = 120
IV
26. The number of degrees in the largest angle of a triangle inscribed in a circle - in which the diameter of the circle is one side of the triangle.
90 degrees
67 - 71 - 73
13
Angle/360 x 2(pi)r
27. What is a set with no members called?
A chord is a line segment joining two points on a circle.
2sqrt6
The empty set - denoted by a circle with a diagonal through it.
9 : 25
28. To multiply a number by 10^x
All numbers multiples of 1.
3sqrt4
N! / (n-k)!
Move the decimal point to the right x places
29. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
3/2 - 5/3
13pi / 2
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
The objects within a set.
30. 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?
N! / (n-k)!
180
When the function is not defined for all real numbers -; only a subset of the real numbers.
1/2 times 7/3
31. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
9 & 6/7
2
The steeper the slope.
32. Can you add sqrt 3 and sqrt 5?
No - only like radicals can be added.
Two angles whose sum is 90.
1.7
71 - 73 - 79
33. When does a function automatically have a restricted domain (2)?
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Divide by 100.
53 - 59
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
34. x^(-y)=
y = 2x^2 - 3
1/(x^y)
83.333%
31 - 37
35. What are the real numbers?
90
I
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)
1
36. 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?
Yes. [i.e. f(x) = x^2 - 1
9 & 6/7
48
The set of output values for a function.
37. What are the roots of the quadrinomial x^2 + 2x + 1?
A grouping of the members within a set based on a shared characteristic.
The two xes after factoring.
y = 2x^2 - 3
72
38. 4.809 X 10^7 =
No - the input value has exactly one output.
.0004809 X 10^11
Its last two digits are divisible by 4.
130pi
39. Length of an arc of a circle?
Angle/360 x 2(pi)r
N! / (k!)(n-k)!
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
1
40. The perimeter of a square is 48 inches. The length of its diagonal is:
(amount of increase/original price) x 100%
A circle centered at -2 - -2 with radius 3.
Pi is the ratio of a circle'S circumference to its diameter.
12sqrt2
41. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
The greatest value minus the smallest.
Cd
II
9 : 25
42. Which is greater? 27^(-4) or 9^(-8)
31 - 37
A central angle is an angle formed by 2 radii.
27^(-4)
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
43. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
75:11
23 - 29
3
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
44. Write 10 -843 X 10^7 in scientific notation
1.0843 X 10^11
Arc length = (n/360) x pi(2r) where n is the number of degrees.
90
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)
45. 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
10! / 3!(10-3)! = 120
Two equal sides and two equal angles.
$3 -500 in the 9% and $2 -500 in the 7%.
46. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
9 : 25
A reflection about the axis.
16.6666%
47. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
4:5
70
2^9 / 2 = 256
48. Formula to find a circle'S circumference from its radius?
(a + b)^2
C = 2(pi)r
Pi is the ratio of a circle'S circumference to its diameter.
Yes - like radicals can be added/subtracted.
49. A cylinder has a surface area of 22pi. If the cylinder has a height of 10 - what is the radius?
3 - -3
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1
0
50. 8.84 / 5.2
3sqrt4
41 - 43 - 47
1.7
Diameter(Pi)