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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. 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?
75:11
N! / (n-k)!
180 degrees
Factors are few - multiples are many.
2. What is the name of set with a number of elements which cannot be counted?
Members or elements
An infinite set.
(a - b)^2
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
3. What is the slope of a vertical line?
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183
4. What is the area of a regular hexagon with side 6?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
Angle/360 x (pi)r^2
x^(2(4)) =x^8 = (x^4)^2
7 / 1000
5. 4.809 X 10^7 =
4725
Arc length = (n/360) x pi(2r) where n is the number of degrees.
37.5%
.0004809 X 10^11
6. What is the graph of f(x) shifted right c units or spaces?
62.5%
1.0843 X 10^11
F(x-c)
No - only like radicals can be added.
7. From a box of 12 candles - you are to remove 5. How many different sets of 5 candles could you remove?
Sector area = (n/360) X (pi)r^2
12! / 5!7! = 792
1.7
130pi
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))?
20.5
The longest arc between points A and B on a circle'S diameter.
12sqrt2
0
9. 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 curve opens downward and the vertex is the maximum point on the graph.
13pi / 2
48
3/2 - 5/3
10. What is the ratio of the sides of an isosceles right triangle?
The sum of digits is divisible by 9.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1:1:sqrt2
The interesection of A and B.
11. What is the graph of f(x) shifted upward c units or spaces?
Members or elements
F(x) + c
6
When the function is not defined for all real numbers -; only a subset of the real numbers.
12. 8.84 / 5.2
The second graph is less steep.
1.7
I
Yes. [i.e. f(x) = x^2 - 1
13. What are congruent triangles?
Triangles with same measure and same side lengths.
1/2 times 7/3
52
4:5
14. 60 < all primes <70
The point of intersection of the systems.
2
A reflection about the origin.
61 - 67
15. What is the 'union' of A and B?
0
The set of elements which can be found in either A or B.
The curve opens upward and the vertex is the minimal point on the graph.
72
16. 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
10! / (10-3)! = 720
18
10
C = 2(pi)r
17. Formula for the area of a sector of a circle?
5
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
Sector area = (n/360) X (pi)r^2
The point of intersection of the systems.
18. A number is divisible by 3 if ...
Ax^2 + bx + c where a -b and c are constants and a /=0
The sum of its digits is divisible by 3.
I
61 - 67
19. What is the 'Solution' for a system of linear equations?
x(x - y + 1)
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)
The sum of its digits is divisible by 3.
The point of intersection of the systems.
20. Solve the quadratic equation ax^2 + bx + c= 0
A chord is a line segment joining two points on a circle.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
23 - 29
21. For what values should the domain be restricted for the function f(x) = sqrt(x + 8)
Triangles with same measure and same side lengths.
8
75:11
The union of A and B.
22. What are the integers?
.0004809 X 10^11
All numbers multiples of 1.
A set with no members - denoted by a circle with a diagonal through it.
Area of the base X height = (pi)hr^2
23. What is a central angle?
A subset.
An arc is a portion of a circumference of a circle.
9 : 25
A central angle is an angle formed by 2 radii.
24. Can the input value of a function have more than one output value (i.e. x: y - y1)?
II
48
12.5%
No - the input value has exactly one output.
25. If 4500 is invested at a simple interest rate of 6% - what is the value of the investment after 10 months?
23 - 29
83.333%
4725
Cd
26. 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?
(amount of decrease/original price) x 100%
20.5
$3 -500 in the 9% and $2 -500 in the 7%.
.0004809 X 10^11
27. 1/6 in percent?
(base*height) / 2
62.5%
1 & 37/132
16.6666%
28. How to find the area of a sector?
An infinite set.
1/(x^y)
Angle/360 x (pi)r^2
(a + b)^2
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 greatest value minus the smallest.
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)
The interesection of A and B.
30. T or F? Given d -e &f =/ 0 - [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?
True
6 : 1 : 2
(6 x 2)(sqrt3 x sqrt5) = 12sqrt15
Factors are few - multiples are many.
31. Convert 0.7% to a fraction.
Divide by 100.
1
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)
7 / 1000
32. What is the 'Solution' for a set of inequalities.
The overlapping sections.
The third side is greater than the difference and less than the sum.
1/2 times 7/3
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
33. (x^2)^4
Its negative reciprocal. (-b/a)
An isosceles right triangle.
x^(2(4)) =x^8 = (x^4)^2
83.333%
34. What is an isoceles triangle?
1
Sector area = (n/360) X (pi)r^2
Two equal sides and two equal angles.
7 / 1000
35. Can you simplify sqrt72?
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.
True
The third side is greater than the difference and less than the sum.
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
36. What does scientific notation mean?
No - only like radicals can be added.
A tangent is a line that only touches one point on the circumference of a circle.
3
Expressing a number as the product of a decimal between 1 and 10 - and a power of 10.
37. What is the set of elements found in both A and B?
20.5
The interesection of A and B.
Divide by 100.
10! / (10-3)! = 720
38. Max and Min lengths for a side of a triangle?
72
The third side is greater than the difference and less than the sum.
x^(6-3) = x^3
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)
39. Simplify the expression [(b^2 - c^2) / (b - c)]
(b + c)
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
180 degrees
Undefined - because we can'T divide by 0.
40. If r - t - s & u are distinct - consecutive prime numbers - less than 31 - which of the following could be an average of them (4 - 4.25 - 6 - 9 - 24 - 22 - 24)
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.
4.25 - 6 - 22
IV
0
41. 6w^2 - w - 15 = 0
(a + b)^2
(a - b)(a + b)
3/2 - 5/3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
42. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
288 (8 9 4)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Two angles whose sum is 180.
2 & 3/7
43. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
3
Pi is the ratio of a circle'S circumference to its diameter.
An isosceles right triangle.
10! / 3!(10-3)! = 120
44. (a^-1)/a^5
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
1
True
1/a^6
45. What is the set of elements which can be found in either A or B?
4a^2(b)
The union of A and B.
The set of input values for a function.
The steeper the slope.
46. What is the formula for computing simple interest?
A = I (1 + rt)
F(x + c)
.0004809 X 10^11
Move the decimal point to the right x places
47. How many sides does a hexagon have?
Diameter(Pi)
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
6
1.0843 X 10^11
48. What are the rational numbers?
10! / (10-3)! = 720
All numbers which can be expressed as a ratio of two integers. (All integers and fractions.) (-2 - 1 - .25 - 1/2)
Its divisible by 2 and by 3.
441000 = 1 10 10 10 21 * 21
49. What is the absolute value function?
C = (pi)d
2(pi)r^2 + 2(pi)rh
G(x) = {x}
From northeast - counterclockwise. I - II - III - IV
50. 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
Cd
Move the decimal point to the right x places
2.592 kg