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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)?
The union of A and B.
1
True
3
2. 10<all primes<20
y = 2x^2 - 3
11 - 13 - 17 - 19
7 / 1000
The two xes after factoring.
3. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
3 - -3
75:11
The overlapping sections.
4. How to find the area of a sector?
Sector area = (n/360) X (pi)r^2
Two angles whose sum is 90.
10! / 3!(10-3)! = 120
Angle/360 x (pi)r^2
5. Legs 5 - 12. Hypotenuse?
13
3
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...
2(pi)r^2 + 2(pi)rh
6. Which is greater? 27^(-4) or 9^(-8)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
10! / 3!(10-3)! = 120
27^(-4)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
7. The objects in a set are called two names:
The curve opens upward and the vertex is the minimal point on the graph.
The union of A and B.
Members or elements
Two angles whose sum is 180.
8. How to find the diagonal of a rectangular solid?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
3sqrt4
2^9 / 2 = 256
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
9. Which quadrant is the upper left hand?
The third side is greater than the difference and less than the sum.
II
The two xes after factoring.
x= (1.2)(.8)lw
10. 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?
The shortest arc between points A and B on a circle'S diameter.
1.7
Infinite.
48
11. What is a parabola?
Ax^2 + bx + c where a -b and c are constants and a /=0
1
(a + b)^2
1
12. The larger the absolute value of the slope...
2sqrt6
(a + b)^2
1
The steeper the slope.
13. What is a tangent?
20.5
A tangent is a line that only touches one point on the circumference of a circle.
An arc is a portion of a circumference of a circle.
F(x) + c
14. What are the real numbers?
...multiply by 100.
83.333%
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)
12.5%
15. 6w^2 - w - 15 = 0
1:1:sqrt2
F(x + c)
3/2 - 5/3
A circle centered on the origin with radius 8.
16. What is the graph of f(x) shifted downward c units or spaces?
1/(x^y)
F(x) - c
67 - 71 - 73
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
17. Evaluate 4/11 + 11/12
... the square of the ratios of the corresponding sides.
1 & 37/132
55%
72
18. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
A circle centered at -2 - -2 with radius 3.
180
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
19. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
18
0
Its negative reciprocal. (-b/a)
Indeterminable.
20. Simplify the expression [(b^2 - c^2) / (b - c)]
6 : 1 : 2
(amount of increase/original price) x 100%
(b + c)
An expression with just one term (-6x - 2a^2)
21. 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)
11 - 13 - 17 - 19
The set of elements which can be found in either A or B.
0
22. What is the ratio of the sides of an isosceles right triangle?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Cd
Undefined - because we can'T divide by 0.
1:1:sqrt2
23. Legs 6 - 8. Hypotenuse?
90
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
True
10
24. (x^2)^4
x^(2(4)) =x^8 = (x^4)^2
1
The direction of the inequality is reversed.
No - the input value has exactly one output.
25. x^4 + x^7 =
x^(4+7) = x^11
When the function is not defined for all real numbers -; only a subset of the real numbers.
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)
Lies opposite the greater angle
26. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
The direction of the inequality is reversed.
2(pi)r^2 + 2(pi)rh
3
72
27. Define an 'expression'.
37.5%
y = (x + 5)/2
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)
1
28. What is the maximum value for the function g(x) = (-2x^2) -1?
5
1
11 - 13 - 17 - 19
52
29. 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
18
5
Two angles whose sum is 180.
Even
30. Can you subtract 3sqrt4 from sqrt4?
(b + c)
The greatest value minus the smallest.
3
Yes - like radicals can be added/subtracted.
31. What is the 'Restricted domain of a function'?
When the function is not defined for all real numbers -; only a subset of the real numbers.
F(x + c)
16.6666%
10
32. What is the empty set?
1/a^6
41 - 43 - 47
N! / (n-k)!
A set with no members - denoted by a circle with a diagonal through it.
33. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
Two equal sides and two equal angles.
28. n = 8 - k = 2. n! / k!(n-k)!
180 degrees
5
34. What is the measure of an exterior angle of a regular pentagon?
Indeterminable.
72
A 30-60-90 triangle.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
35. (-1)^3 =
1
The set of output values for a function.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
4725
36. What is the graph of f(x) shifted right c units or spaces?
F(x-c)
0
Yes - like radicals can be added/subtracted.
180 degrees
37. What is the name of set with a number of elements which cannot be counted?
An infinite set.
N! / (k!)(n-k)!
1
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
38. What is a central angle?
500
28. n = 8 - k = 2. n! / k!(n-k)!
A central angle is an angle formed by 2 radii.
Indeterminable.
39. a^2 + 2ab + b^2
An isosceles right triangle.
A circle centered at -2 - -2 with radius 3.
(a + b)^2
55%
40. Factor x^2 - xy + x.
The shortest arc between points A and B on a circle'S diameter.
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
Even
x(x - y + 1)
41. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
90 degrees
An isosceles right triangle.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
12! / 5!7! = 792
42. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
0
F(x + c)
1
G(x) = {x}
43. 30< all primes<40
C = (pi)d
31 - 37
Undefined
130pi
44. Length of an arc of a circle?
67 - 71 - 73
Infinite.
Angle/360 x 2(pi)r
F(x) - c
45. sqrt 2(sqrt 6)=
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
C = 2(pi)r
Sqrt 12
441000 = 1 10 10 10 21 * 21
46. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
52
70
5
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
47. How to determine percent increase?
1
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...
Triangles with same measure and same side lengths.
(amount of increase/original price) x 100%
48. What is the surface area of a cylinder with radius 5 and height 8?
C = 2(pi)r
3
130pi
61 - 67
49. What does the graph x^2 + y^2 = 64 look like?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
1/2 times 7/3
2 & 3/7
A circle centered on the origin with radius 8.
50. Can you simplify sqrt72?
90pi
6
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
180