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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 determine percent decrease?
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
(amount of decrease/original price) x 100%
9 : 25
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
2. 20<all primes<30
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
4:5
23 - 29
Sqrt 12
3. a^2 - b^2
(a - b)(a + b)
Ax^2 + bx + c where a -b and c are constants and a /=0
413.03 / 10^4 (move the decimal point 4 places to the left)
2(pi)r^2 + 2(pi)rh
4. What is the slope of a horizontal line?
No - only like radicals can be added.
0
2.592 kg
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)
5. What is the name for a grouping of the members within a set based on a shared characteristic?
Angle/360 x (pi)r^2
10! / 3!(10-3)! = 120
12.5%
A subset.
6. a^2 - b^2 =
The curve opens downward and the vertex is the maximum point on the graph.
37.5%
(a - b)(a + b)
4.25 - 6 - 22
7. Formula of rectangle where l increases by 20% and w decreases by 20%
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
288 (8 9 4)
0
x= (1.2)(.8)lw
8. Can the input value of a function have more than one output value (i.e. x: y - y1)?
No - the input value has exactly one output.
67 - 71 - 73
$3 -500 in the 9% and $2 -500 in the 7%.
(amount of increase/original price) x 100%
9. What is the order of operations?
$11 -448
y = 2x^2 - 3
A reflection about the origin.
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
10. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A reflection about the origin.
13pi / 2
No - the input value has exactly one output.
A 30-60-90 triangle.
11. What is the surface area of a cylinder with radius 5 and height 8?
(n-2) x 180
x^(2(4)) =x^8 = (x^4)^2
130pi
The sum of digits is divisible by 9.
12. What is the 'Range' of a function?
Part = Percent X Whole
The set of output values for a function.
10! / 3!(10-3)! = 120
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
13. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
Lies opposite the greater angle
1
2sqrt6
$11 -448
14. Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?
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.
2^9 / 2 = 256
$3 -500 in the 9% and $2 -500 in the 7%.
C = (pi)d
15. (x^2)^4
x^(6-3) = x^3
90 degrees
Cd
x^(2(4)) =x^8 = (x^4)^2
16. 1/8 in percent?
4a^2(b)
1.0843 X 10^11
2 & 3/7
12.5%
17. 5/6 in percent?
83.333%
When the function is not defined for all real numbers -; only a subset of the real numbers.
No - only like radicals can be added.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
18. Can you simplify sqrt72?
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
72
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.
75:11
19. How many multiples does a given number have?
x^(4+7) = x^11
90pi
10! / (10-3)! = 720
Infinite.
20. 1:sqrt3:2 is the ratio of the sides of what kind of triangle?
(a - b)(a + b)
A 30-60-90 triangle.
0
A central angle is an angle formed by 2 radii.
21. Legs 5 - 12. Hypotenuse?
5 OR -5
13
1/2 times 7/3
x^(6-3) = x^3
22. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
1
27^(-4)
N! / (k!)(n-k)!
23. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
9 : 25
The sum of its digits is divisible by 3.
4.25 - 6 - 22
24. There are 10 finalists for the school spelling bee. A first - second - and third place trophy will be awarded. How many different people can get the three prizes?
72
(b + c)
10! / 3!(10-3)! = 120
III
25. What are the real numbers?
12! / 5!7! = 792
(p + q)/5
31 - 37
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)
26. To convert a percent to a fraction....
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1
Divide by 100.
4:5
27. Solve the quadratic equation ax^2 + bx + c= 0
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Lies opposite the greater angle
A grouping of the members within a set based on a shared characteristic.
500
28. What is the empty set?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
A set with no members - denoted by a circle with a diagonal through it.
The two xes after factoring.
The set of elements which can be found in either A or B.
29. Factor x^2 - xy + x.
x(x - y + 1)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
130pi
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
30. 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?
52
(base*height) / 2
The interesection of A and B.
500
31. x^6 / x^3
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
The shortest arc between points A and B on a circle'S diameter.
Yes - like radicals can be added/subtracted.
x^(6-3) = x^3
32. What is the absolute value function?
G(x) = {x}
13pi / 2
3
90 degrees
33. 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?
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
10! / 3!(10-3)! = 120
2.592 kg
The interesection of A and B.
34. Is 0 even or odd?
(amount of increase/original price) x 100%
Even
11 - 13 - 17 - 19
True
35. What percent of 40 is 22?
Its last two digits are divisible by 4.
10! / 3!(10-3)! = 120
3sqrt4
55%
36. What is a major arc?
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37. Legs: 3 - 4. Hypotenuse?
1
Undefined - because we can'T divide by 0.
5
The empty set - denoted by a circle with a diagonal through it.
38. 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?
... the square of the ratios of the corresponding sides.
Its negative reciprocal. (-b/a)
II
$3 -500 in the 9% and $2 -500 in the 7%.
39. For similar triangles - the ratio of their corresponding sides is 2:3. What is the ratio of their areas?
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Cd
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)
Arc length = (n/360) x pi(2r) where n is the number of degrees.
40. To convert a decimal to a percent...
The overlapping sections.
130pi
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)
...multiply by 100.
41. What are the irrational numbers?
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42. What is the 'domain' of a function?
Relationship cannot be determined (what if x is negative?)
A subset.
I
The set of input values for a function.
43. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
G(x) = {x}
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.
67 - 71 - 73
4725
44. 40 < all primes<50
41 - 43 - 47
y = (x + 5)/2
Sqrt 12
55%
45. What are the smallest three prime numbers greater than 65?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
67 - 71 - 73
83.333%
Its negative reciprocal. (-b/a)
46. What is the ratio of the sides of an isosceles right triangle?
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)
Yes. [i.e. f(x) = x^2 - 1
1:1:sqrt2
(a - b)(a + b)
47. What is the percent formula?
x= (1.2)(.8)lw
Part = Percent X Whole
130pi
500
48. What is the set of elements found in both A and B?
441000 = 1 10 10 10 21 * 21
Move the decimal point to the right x places
x^(6-3) = x^3
The interesection of A and B.
49. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
No - only like radicals can be added.
6
F(x) + c
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
50. 10^6 has how many zeroes?
6
The set of elements which can be found in either A or B.
12.5%
28. n = 8 - k = 2. n! / k!(n-k)!