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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. The objects in a set are called two names:
The second graph is less steep.
53 - 59
Members or elements
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)
2. Which quadrant is the upper left hand?
F(x) + c
Yes - like radicals can be added/subtracted.
A reflection about the axis.
II
3. What is the surface area of a cylinder with radius 5 and height 8?
130pi
2
C = 2(pi)r
The set of input values for a function.
4. Pi is a ratio of what to what?
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183
5. Area of a triangle?
The interesection of A and B.
10! / (10-3)! = 720
A tangent is a line that only touches one point on the circumference of a circle.
(base*height) / 2
6. Which quadrant is the lower left hand?
6
Lies opposite the greater angle
A circle centered on the origin with radius 8.
III
7. A number is divisible by 9 if...
6
The sum of digits is divisible by 9.
A set with a number of elements which can be counted.
288 (8 9 4)
8. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
The interesection of A and B.
The set of input values for a function.
A grouping of the members within a set based on a shared characteristic.
9. Formula for the area of a circle?
IV
A = pi(r^2)
3
A central angle is an angle formed by 2 radii.
10. 3/8 in percent?
(n-2) x 180
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
37.5%
y = (x + 5)/2
11. What is the side length of an equilateral triangle with altitude 6?
(a - b)(a + b)
Divide by 100.
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 set of elements found in both A and B.
12. 8.84 / 5.2
A set with a number of elements which can be counted.
(base*height) / 2
90 degrees
1.7
13. What is the name of set with a number of elements which cannot be counted?
An infinite set.
The overlapping sections.
.0004809 X 10^11
The sum of its digits is divisible by 3.
14. What are the smallest three prime numbers greater than 65?
The longest arc between points A and B on a circle'S diameter.
67 - 71 - 73
87.5%
1.0843 X 10^11
15. What is a parabola?
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
Ax^2 + bx + c where a -b and c are constants and a /=0
2 & 3/7
72
16. What percent of 40 is 22?
55%
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)
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
Ax^2 + bx + c where a -b and c are constants and a /=0
17. Reduce: 4.8 : 0.8 : 1.6
6 : 1 : 2
37.5%
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
13
18. What is an arc of a circle?
(b + c)
N! / (k!)(n-k)!
A reflection about the axis.
An arc is a portion of a circumference of a circle.
19. What is an exterior angle?
A circle centered on the origin with radius 8.
N! / (n-k)!
An angle which is supplementary to an interior angle.
The point of intersection of the systems.
20. (12sqrt15) / (2sqrt5) =
4.25 - 6 - 22
Relationship cannot be determined (what if x is negative?)
1/2 times 7/3
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
21. What is the ratio of the sides of an isosceles right triangle?
A set with a number of elements which can be counted.
1:1:sqrt2
G(x) = {x}
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.
22. a^2 + 2ab + b^2
41 - 43 - 47
Members or elements
(a + b)^2
130pi
23. Which is greater? 200x^295 or 10x^294?
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)
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
Relationship cannot be determined (what if x is negative?)
The union of A and B.
24. Simplify (a^2 + b)^2 - (a^2 - b)^2
4a^2(b)
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)
4.25 - 6 - 22
The empty set - denoted by a circle with a diagonal through it.
25. A cylinder has surface area 22pi. If the cylinder has a height of 10 - what is its radius?
Angle/360 x 2(pi)r
1
Part = Percent X Whole
The second graph is less steep.
26. What is the intersection of A and B?
F(x + c)
Move the decimal point to the right x places
The set of elements found in both A and B.
Infinite.
27. What is the 'Range' of a series of numbers?
The greatest value minus the smallest.
The curve opens downward and the vertex is the maximum point on the graph.
y = (x + 5)/2
2(pi)r^2 + 2(pi)rh
28. (-1)^3 =
A chord is a line segment joining two points on a circle.
Angle/360 x 2(pi)r
1
(a + b)^2
29. 200 <_ x <_ 300. How many values of x are divisible by 5 & 8?
71 - 73 - 79
A reflection about the axis.
3
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)
30. 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)?
9 & 6/7
(a - b)(a + b)
y = (x + 5)/2
27^(-4)
31. What is a set with no members called?
True
8
71 - 73 - 79
The empty set - denoted by a circle with a diagonal through it.
32. 1/2 divided by 3/7 is the same as
F(x) - c
1/2 times 7/3
An arc is a portion of a circumference of a circle.
When the function is not defined for all real numbers -; only a subset of the real numbers.
33. Factor x^2 - xy + x.
y = 2x^2 - 3
27^(-4)
x(x - y + 1)
10! / 3!(10-3)! = 120
34. 70 < all primes< 80
11 - 13 - 17 - 19
2(pi)r^2 + 2(pi)rh
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)
71 - 73 - 79
35. x^2 = 9. What is the value of x?
3 - -3
72
37.5%
The objects within a set.
36. 5/8 in percent?
1/a^6
62.5%
(amount of decrease/original price) x 100%
When the function is not defined for all real numbers -; only a subset of the real numbers.
37. 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.
2 & 3/7
2
28. n = 8 - k = 2. n! / k!(n-k)!
38. (x^2)^4
Yes - because you can factor out a perfect square (36). Sqrt(36 x 2) = sqrt36 X sqrt2 = 6sqrt2.
No - the input value has exactly one output.
x^(2(4)) =x^8 = (x^4)^2
16.6666%
39. To convert a percent to a fraction....
The steeper the slope.
Divide by 100.
1/(x^y)
x= (1.2)(.8)lw
40. What is the maximum value for the function g(x) = (-2x^2) -1?
1
55%
Pi is the ratio of a circle'S circumference to its diameter.
70
41. 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?
Its negative reciprocal. (-b/a)
The longest arc between points A and B on a circle'S diameter.
62.5%
N! / (k!)(n-k)!
42. What is the graph of f(x) shifted downward c units or spaces?
F(x) - c
y = 2x^2 - 3
4a^2(b)
5 OR -5
43. What is the name for a grouping of the members within a set based on a shared characteristic?
1
A subset.
3
Ax^2 + bx + c where a -b and c are constants and a /=0
44. What is the formula for computing simple interest?
The curve opens upward and the vertex is the minimal point on the graph.
12.5%
A = I (1 + rt)
4:5
45. What is a finite set?
62.5%
12! / 5!7! = 792
A set with a number of elements which can be counted.
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
46. Volume for a cylinder?
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
Area of the base X height = (pi)hr^2
4a^2(b)
1.0843 X 10^11
47. Legs 5 - 12. Hypotenuse?
13
Yes. [i.e. f(x) = x^2 - 1
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
The steeper the slope.
48. Formula for the area of a sector of a circle?
Sector area = (n/360) X (pi)r^2
A chord is a line segment joining two points on a circle.
N! / (k!)(n-k)!
Lies opposite the greater angle
49. What is the ratio of the sides of a 30-60-90 triangle?
1:sqrt3:2
62.5%
Ax^2 + bx + c where a -b and c are constants and a /=0
441000 = 1 10 10 10 21 * 21
50. Formula to find a circle'S circumference from its radius?
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
11 - 13 - 17 - 19
C = 2(pi)r
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a