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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. What is a set with no members called?
10
The sum of digits is divisible by 9.
The empty set - denoted by a circle with a diagonal through it.
18
2. 7/8 in percent?
Infinite.
87.5%
The second graph is less steep.
The curve opens upward and the vertex is the minimal point on the graph.
3. What is a finite set?
1:sqrt3:2
An angle which is supplementary to an interior angle.
4a^2(b)
A set with a number of elements which can be counted.
4. What is the slope of a horizontal line?
6
All numbers multiples of 1.
72
0
5. Max and Min lengths for a side of a triangle?
61 - 67
The third side is greater than the difference and less than the sum.
Even
5
6. What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?
x^(2(4)) =x^8 = (x^4)^2
Cd
1/a^6
The greatest value minus the smallest.
7. Is 0 even or odd?
Divide by 100.
23 - 29
61 - 67
Even
8. Surface area for a cylinder?
2(pi)r^2 + 2(pi)rh
10! / (10-3)! = 720
83.333%
10! / 3!(10-3)! = 120
9. Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?
y = (x + 5)/2
Members or elements
2
(a + b)^2
10. A triangle is inscribed in a semi circle with legs 5 and 12. What is the circumfermence of the semicircle?
61 - 67
52
90 degrees
13pi / 2
11. Formula for the area of a circle?
The shortest arc between points A and B on a circle'S diameter.
Undefined
A = pi(r^2)
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
12. Formula to find a circle'S circumference from its diameter?
13
C = (pi)d
Members or elements
A 30-60-90 triangle.
13. If Madagascar'S exports totaled 1.3 billion in 2009 - and 4% came from China - what was the value in millions of the country'S exports to China?
(amount of increase/original price) x 100%
(a - b)(a + b)
.0004809 X 10^11
52
14. What are the roots of the quadrinomial x^2 + 2x + 1?
Yes. [i.e. f(x) = x^2 - 1
Pi is the ratio of a circle'S circumference to its diameter.
180
The two xes after factoring.
15. What is the name of set with a number of elements which cannot be counted?
61 - 67
An infinite set.
3 - -3
20.5
16. The objects in a set are called two names:
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)
Divide by 100.
Members or elements
Move the decimal point to the right x places
17. Which is greater? 64^5 or 16^8
16^8 - 64^5 = (4^3)^5 = 4^15 - 16^8=(4^2)^8 = 4^16
1 & 37/132
(amount of increase/original price) x 100%
3/2 - 5/3
18. The larger the absolute value of the slope...
Infinite.
When the function is not defined for all real numbers -; only a subset of the real numbers.
55%
The steeper the slope.
19. 1:1:sqrt2 is the ratio of the sides of what kind of triangle?
An arc is a portion of a circumference of a circle.
An isosceles right triangle.
10
A reflection about the axis.
20. Formula of rectangle where l increases by 20% and w decreases by 20%
x^(6-3) = x^3
x= (1.2)(.8)lw
(amount of decrease/original price) x 100%
2 & 3/7
21. 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)
4a^2(b)
1:1:sqrt2
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
22. 1/2 divided by 3/7 is the same as
3
Ax^2 + bx + c where a -b and c are constants and a /=0
1/2 times 7/3
13
23. Define a 'Term' -
(amount of decrease/original price) x 100%
The overlapping sections.
The curve opens upward and the vertex is the minimal point on the graph.
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)
24. In similar hexagons - the ratio of the areas is 16:25. What is the ratio of their corresponding sides?
53 - 59
0
A set with a number of elements which can be counted.
4:5
25. Formula to find a circle'S circumference from its radius?
0
C = 2(pi)r
No - only like radicals can be added.
From northeast - counterclockwise. I - II - III - IV
26. Evaluate 3& 2/7 / 1/3
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
F(x-c)
9 & 6/7
.0004809 X 10^11
27. Define an 'expression'.
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)
The third side is greater than the difference and less than the sum.
2 & 3/7
The greatest value minus the smallest.
28. What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?
87.5%
2
The third side is greater than the difference and less than the sum.
An angle which is supplementary to an interior angle.
29. What is the 'domain' of a function?
The set of input values for a function.
IV
The curve opens downward and the vertex is the maximum point on the graph.
A central angle is an angle formed by 2 radii.
30. Legs 5 - 12. Hypotenuse?
(p + q)/5
13
Its last two digits are divisible by 4.
1
31. Factor a^2 + 2ab + b^2
A = pi(r^2)
Members or elements
(a + b)^2
28. n = 8 - k = 2. n! / k!(n-k)!
32. What is the graph of f(x) shifted right c units or spaces?
N! / (k!)(n-k)!
No - the input value has exactly one output.
...multiply by 100.
F(x-c)
33. 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)
The curve opens downward and the vertex is the maximum point on the graph.
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
4.25 - 6 - 22
x^(4+7) = x^11
34. Whats the difference between factors and multiples?
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)
7 / 1000
Factors are few - multiples are many.
All numbers multiples of 1.
35. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
Use Pythagorean theorem twice. (Once across the surface and then a is the diagonal of surface and b is an edge).
F(x-c)
1 & 37/132
A reflection about the origin.
36. How to find the area of a sector?
3
Angle/360 x (pi)r^2
Sector area = (n/360) X (pi)r^2
12! / 5!7! = 792
37. What is the ratio of the sides of a 30-60-90 triangle?
10
$3 -500 in the 9% and $2 -500 in the 7%.
1
1:sqrt3:2
38. 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?
No - only like radicals can be added.
13
Undefined - because we can'T divide by 0.
N! / (k!)(n-k)!
39. How to determine percent increase?
41 - 43 - 47
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
(amount of increase/original price) x 100%
12.5%
40. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
Its last two digits are divisible by 4.
Sector area = (n/360) X (pi)r^2
$3 -500 in the 9% and $2 -500 in the 7%.
70
41. What is the absolute value function?
90pi
G(x) = {x}
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
130pi
42. A number is divisible by 4 is...
2^9 / 2 = 256
6
Its last two digits are divisible by 4.
Diameter(Pi)
43. What is the 'Solution' for a set of inequalities.
2.592 kg
The overlapping sections.
61 - 67
72
44. To convert a decimal to a percent...
The direction of the inequality is reversed.
4.25 - 6 - 22
...multiply by 100.
(amount of increase/original price) x 100%
45. What are the real numbers?
y = (x + 5)/2
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)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
Lies opposite the greater angle
46. What are the irrational numbers?
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47. Which is greater? 27^(-4) or 9^(-8)
2^9 / 2 = 256
II
27^(-4)
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
48. Simplify (a^2 + b)^2 - (a^2 - b)^2
Diameter(Pi)
2(pi)r^2 + 2(pi)rh
Infinite.
4a^2(b)
49. What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2 - 4 - and 6?
75:11
Factors are few - multiples are many.
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)
G(x) = {x}
50. What is a parabola?
Ax^2 + bx + c where a -b and c are constants and a /=0
1/2 times 7/3
x^(4+7) = x^11
(a - b)^2