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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. Simplify 9^(1/2) X 4^3 X 2^(-6)?
3
Relationship cannot be determined (what if x is negative?)
4725
...multiply by 100.
2. What are the integers?
Two angles whose sum is 180.
Angle/360 x (pi)r^2
All numbers multiples of 1.
Undefined
3. What is the side length of an equilateral triangle with altitude 6?
(amount of increase/original price) x 100%
F(x + c)
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...
The sum of its digits is divisible by 3.
4. What is the ratio of the sides of a 30-60-90 triangle?
Its negative reciprocal. (-b/a)
1:sqrt3:2
Infinite.
... the square of the ratios of the corresponding sides.
5. 5/8 in percent?
C = 2(pi)r
62.5%
The interesection of A and B.
0
6. What is an exterior angle?
(base*height) / 2
1
The steeper the slope.
An angle which is supplementary to an interior angle.
7. a^2 - b^2 =
18
(a - b)(a + b)
Its divisible by 2 and by 3.
180 degrees
8. 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))?
Lies opposite the greater angle
(base*height) / 2
20.5
Triangles with same measure and same side lengths.
9. Describe the relationship between the graphs of x^2 and (1/2)x^2
6
Its negative reciprocal. (-b/a)
The second graph is less steep.
No - the input value has exactly one output.
10. Define a 'monomial'
An expression with just one term (-6x - 2a^2)
500
F(x) - c
A set with a number of elements which can be counted.
11. a^2 + 2ab + b^2
130pi
C = (pi)d
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 + b)^2
12. The perimeter of a square is 48 inches. The length of its diagonal is:
1/a^6
12sqrt2
Divide by 100.
Relationship cannot be determined (what if x is negative?)
13. A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12 - 18 - and 30. What is the weight of the second brick?
F(x-c)
1.0843 X 10^11
2.592 kg
3
14. What are the members or elements of a set?
1
18
The objects within a set.
1/(x^y)
15. What is the 'domain' of a function?
37.5%
The set of input values for a function.
130pi
Move the decimal point to the right x places
16. Is 0 even or odd?
Even
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
1.7
The steeper the slope.
17. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
2sqrt6
The empty set - denoted by a circle with a diagonal through it.
An angle which is supplementary to an interior angle.
Two equal sides and two equal angles.
18. What is the graph of f(x) shifted downward c units or spaces?
When the function is not defined for all real numbers -; only a subset of the real numbers.
An expression with just one term (-6x - 2a^2)
F(x) - c
180 degrees
19. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
The shortest arc between points A and B on a circle'S diameter.
1 & 37/132
70
5
20. What is a subset?
1/(x^y)
8
F(x) + c
A grouping of the members within a set based on a shared characteristic.
21. (12sqrt15) / (2sqrt5) =
1
3/2 - 5/3
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
Its negative reciprocal. (-b/a)
22. Evaluate 4/11 + 11/12
2 & 3/7
1 & 37/132
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)
41 - 43 - 47
23. Factor a^2 + 2ab + b^2
(n-2) x 180
(a + b)^2
6
12sqrt2
24. Length of an arc of a circle?
413.03 / 10^4 (move the decimal point 4 places to the left)
The sum of digits is divisible by 9.
Angle/360 x 2(pi)r
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)
25. When does a function automatically have a restricted domain (2)?
52
y = (x + 5)/2
4a^2(b)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
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.
Two equal sides and two equal angles.
27^(-4)
90 degrees
18
27. 40 < all primes<50
441000 = 1 10 10 10 21 * 21
71 - 73 - 79
41 - 43 - 47
1.7
28. What percent of 40 is 22?
55%
Angle/360 x (pi)r^2
Divide by 100.
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
29. Solve the quadratic equation ax^2 + bx + c= 0
The curve opens downward and the vertex is the maximum point on the graph.
F(x + c)
x^(4+7) = x^11
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
30. What is a tangent?
III
A tangent is a line that only touches one point on the circumference of a circle.
The interesection of A and B.
(a - b)(a + b)
31. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
An infinite set.
71 - 73 - 79
180 degrees
32. What are complementary angles?
The steeper the slope.
1
Two angles whose sum is 90.
6
33. Describe the relationship between 3x^2 and 3(x - 1)^2
Its divisible by 2 and by 3.
A set with a number of elements which can be counted.
6
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
34. What is a central angle?
x(x - y + 1)
A central angle is an angle formed by 2 radii.
y = 2x^2 - 3
N! / (k!)(n-k)!
35. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
N! / (k!)(n-k)!
18
F(x-c)
36. A number is divisible by 9 if...
180 degrees
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
The sum of digits is divisible by 9.
The two xes after factoring.
37. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
61 - 67
An isosceles right triangle.
12.5%
2
38. Which is greater? 64^5 or 16^8
A circle centered on the origin with radius 8.
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
90
3
39. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(b + c)
4725
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
1/2 times 7/3
40. Which quadrant is the upper left hand?
1
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
II
(b + c)
41. 1/2 divided by 3/7 is the same as
A circle centered on the origin with radius 8.
(amount of decrease/original price) x 100%
1/2 times 7/3
31 - 37
42. x^(-y)=
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.
1.0843 X 10^11
1/(x^y)
1
43. Formula to calculate arc length?
13pi / 2
A central angle is an angle formed by 2 radii.
Arc length = (n/360) x pi(2r) where n is the number of degrees.
The set of elements which can be found in either A or B.
44. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
Move the decimal point to the right x places
Cd
Area of the base X height = (pi)hr^2
12.5%
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?
(b + c)
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
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
N! / (n-k)!
46. Pi is a ratio of what to what?
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47. How many multiples does a given number have?
Undefined - because we can'T divide by 0.
11 - 13 - 17 - 19
Infinite.
62.5%
48. Convert 0.7% to a fraction.
An arc is a portion of a circumference of a circle.
2
7 / 1000
Its last two digits are divisible by 4.
49. 30< all primes<40
4a^2(b)
6
The overlapping sections.
31 - 37
50. What is a chord of a circle?
1.0843 X 10^11
A chord is a line segment joining two points on a circle.
The second graph is less steep.
Its negative reciprocal. (-b/a)