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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. Formula for the area of a circle?
2
A = pi(r^2)
23 - 29
413.03 / 10^4 (move the decimal point 4 places to the left)
2. What does the graph (x+2)^2 + (y+2)^2 = 9 look like?
A circle centered at -2 - -2 with radius 3.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
(a - b)^2
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
3. x^2 = 9. What is the value of x?
Cd
3 - -3
1.7
x^(2(4)) =x^8 = (x^4)^2
4. What is an isoceles triangle?
Two equal sides and two equal angles.
13
The overlapping sections.
Diameter(Pi)
5. Pi is a ratio of what to what?
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6. What are the irrational numbers?
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7. 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?
1
A 30-60-90 triangle.
2sqrt6
2.592 kg
8. Formula to calculate arc length?
A grouping of the members within a set based on a shared characteristic.
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
12.5%
Arc length = (n/360) x pi(2r) where n is the number of degrees.
9. 40 < all primes<50
When the function is not defined for all real numbers -; only a subset of the real numbers.
(n-2) x 180
A reflection about the axis.
41 - 43 - 47
10. How to determine percent decrease?
(amount of decrease/original price) x 100%
31 - 37
A reflection about the origin.
Area of the base X height = (pi)hr^2
11. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
75:11
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The longest arc between points A and B on a circle'S diameter.
3
12. What is the absolute value function?
G(x) = {x}
x^(6-3) = x^3
F(x + c)
The direction of the inequality is reversed.
13. (x^2)^4
3
(a - b)(a + b)
x^(2(4)) =x^8 = (x^4)^2
27^(-4)
14. 1/6 in percent?
A circle centered on the origin with radius 8.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
The set of elements found in both A and B.
16.6666%
15. 6w^2 - w - 15 = 0
Cd
61 - 67
3/2 - 5/3
F(x-c)
16. What are 'Supplementary angles?'
(a - b)(a + b)
Two angles whose sum is 180.
Pi is the ratio of a circle'S circumference to its diameter.
The union of A and B.
17. How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]
(p + q)/5
0
62.5%
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)
18. What is the name of set with a number of elements which cannot be counted?
27^(-4)
An infinite set.
13pi / 2
9 : 25
19. If the two sides of a triangle are unequal then the longer side...
x^(2(4)) =x^8 = (x^4)^2
2(pi)r^2 + 2(pi)rh
13pi / 2
Lies opposite the greater angle
20. What is the measure of an exterior angle of a regular pentagon?
Ax^2 + bx + c where a -b and c are constants and a /=0
Even
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
72
21. What is the slope of a vertical line?
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22. Legs 6 - 8. Hypotenuse?
10
The interesection of A and B.
4:5
All numbers multiples of 1.
23. Simplify the expression (p^2 - q^2)/ -5(q - p)
An infinite set.
4a^2(b)
(p + q)/5
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
24. 70 < all primes< 80
3
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
The sum of digits is divisible by 9.
71 - 73 - 79
25. 10^6 has how many zeroes?
(a - b)^2
6
1/a^6
N! / (k!)(n-k)!
26. Evaluate 4/11 + 11/12
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 & 37/132
The empty set - denoted by a circle with a diagonal through it.
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)
27. 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?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
75:11
N! / (k!)(n-k)!
Its negative reciprocal. (-b/a)
28. What are the smallest three prime numbers greater than 65?
67 - 71 - 73
90
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
x(x - y + 1)
29. 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
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
6 : 1 : 2
(a + b)^2
30. What is the set of elements found in both A and B?
The interesection of A and B.
3
90
An arc is a portion of a circumference of a circle.
31. x^6 / x^3
6
x^(6-3) = x^3
A set with no members - denoted by a circle with a diagonal through it.
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
32. 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.
130pi
90 degrees
Its divisible by 2 and by 3.
28. n = 8 - k = 2. n! / k!(n-k)!
33. If 8 schools are in a conference - how many games are played if each team plays each other exactly once?
From northeast - counterclockwise. I - II - III - IV
II
28. n = 8 - k = 2. n! / k!(n-k)!
6 : 1 : 2
34. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
4a^2(b)
12.5%
x= (1.2)(.8)lw
4:5
35. When does a function automatically have a restricted domain (2)?
(amount of increase/original price) x 100%
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
Relationship cannot be determined (what if x is negative?)
G(x) = {x}
36. Which quadrant is the upper right hand?
The greatest value minus the smallest.
The empty set - denoted by a circle with a diagonal through it.
A reflection about the axis.
I
37. Simplify the expression [(b^2 - c^2) / (b - c)]
Factors are few - multiples are many.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
x^(6-3) = x^3
(b + c)
38. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
Ax^2 + bx + c where a -b and c are constants and a /=0
1
12! / 5!7! = 792
0
39. What is the name for a grouping of the members within a set based on a shared characteristic?
41 - 43 - 47
2^9 / 2 = 256
A subset.
0
40. 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?
The point of intersection of the systems.
.0004809 X 10^11
10! / (10-3)! = 720
A grouping of the members within a set based on a shared characteristic.
41. What does the graph x^2 + y^2 = 64 look like?
Sector area = (n/360) X (pi)r^2
The shortest arc between points A and B on a circle'S diameter.
70
A circle centered on the origin with radius 8.
42. x^4 + x^7 =
52
4:5
2sqrt6
x^(4+7) = x^11
43. 60 < all primes <70
Move the decimal point to the right x places
87.5%
A central angle is an angle formed by 2 radii.
61 - 67
44. 5/8 in percent?
The overlapping sections.
62.5%
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1
45. What is the sum of the angles of a triangle?
11 - 13 - 17 - 19
F(x-c)
52
180 degrees
46. What is a chord of a circle?
Cd
A subset.
75:11
A chord is a line segment joining two points on a circle.
47. Simplify 4sqrt21 X 5sqrt2 / 10sqrt7
No - the input value has exactly one output.
The third side is greater than the difference and less than the sum.
10
2sqrt6
48. Describe the relationship between the graphs of x^2 and (1/2)x^2
1
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
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 second graph is less steep.
49. 5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same - what is the average of muffins per bakery sold among the remaining?
500
12! / 5!7! = 792
13
x^(2(4)) =x^8 = (x^4)^2
50. What is an exterior angle?
x^(4+7) = x^11
$3 -500 in the 9% and $2 -500 in the 7%.
An expression with just one term (-6x - 2a^2)
An angle which is supplementary to an interior angle.