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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 the side length of an equilateral triangle with altitude 6?
[(7+ sqrt93) /2] - [(7 - sqrt93) / 2]
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...
A reflection about the origin.
12sqrt2
2. What are the integers?
Yes - like radicals can be added/subtracted.
All numbers multiples of 1.
x^(6-3) = x^3
9 : 25
3. 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?
48
180
4a^2(b)
...multiply by 100.
4. What is a chord of a circle?
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)
4096
A chord is a line segment joining two points on a circle.
12sqrt2
5. Can you subtract 3sqrt4 from sqrt4?
x^(2(4)) =x^8 = (x^4)^2
87.5%
Yes - like radicals can be added/subtracted.
11 - 13 - 17 - 19
6. What are the smallest three prime numbers greater than 65?
(b + c)
62.5%
67 - 71 - 73
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
7. What is the 'Solution' for a system of linear equations?
54sqrt3. (divide the hexagon into 6 congruent equilateral triangles.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
53 - 59
The point of intersection of the systems.
8. Evaluate and write as a mixed number: 2/7 - 3/21 + 2 & 4/14
No - the input value has exactly one output.
The overlapping sections.
2 & 3/7
6 : 1 : 2
9. What is the intersection of A and B?
The set of elements found in both A and B.
... the square of the ratios of the corresponding sides.
288 (8 9 4)
Yes. [i.e. f(x) = x^2 - 1
10. What is a major arc?
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183
11. What is the graph of f(x) shifted upward c units or spaces?
F(x) + c
An angle which is supplementary to an interior angle.
0
67 - 71 - 73
12. To multiply a number by 10^x
Move the decimal point to the right x places
Diameter(Pi)
12sqrt2
8
13. Volume for a cylinder?
Area of the base X height = (pi)hr^2
Infinite.
Even
A tangent is a line that only touches one point on the circumference of a circle.
14. What is the percent formula?
48
4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.
A 30-60-90 triangle.
Part = Percent X Whole
15. How many sides does a hexagon have?
A central angle is an angle formed by 2 radii.
6
1
10
16. Find the surface area of a cylinder with radius 3 and height 12.
90pi
0
Indeterminable.
The union of A and B.
17. What is the empty set?
x^(6-3) = x^3
A set with no members - denoted by a circle with a diagonal through it.
3 - -3
C = 2(pi)r
18. Which is greater? 27^(-4) or 9^(-8)
11 - 13 - 17 - 19
27^(-4)
3
A subset.
19. What number between 70 & 75 - inclusive - has the greatest number of factors?
72
The union of A and B.
Infinite.
The point of intersection of the systems.
20. 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?
F(x) + c
180
II
75:11
21. a^0 =
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)
Two angles whose sum is 180.
The sum of its digits is divisible by 3.
1
22. Simplify the expression (p^2 - q^2)/ -5(q - p)
From northeast - counterclockwise. I - II - III - IV
(p + q)/5
F(x) + c
Circumference = Diameter(pi). Use pythagorean theorem to find the diagonal of the square (the diameter).
23. Which is greater? 200x^295 or 10x^294?
x^(2(4)) =x^8 = (x^4)^2
2(pi)r^2 + 2(pi)rh
True
Relationship cannot be determined (what if x is negative?)
24. What are complementary angles?
Two angles whose sum is 90.
x = [(-b)+/- (sqrt b^2 - 4ac)]/2a
23 - 29
Divide by 100.
25. a^2 - b^2 =
(amount of decrease/original price) x 100%
(a - b)(a + b)
An infinite set.
55%
26. What is the third quartile of the following data set: 44 - 58 - 63 - 63 - 68 - 70 - 82
Sector area = (n/360) X (pi)r^2
F(x + c)
Area of the base X height = (pi)hr^2
70
27. Evaluate (4^3)^2
Two angles whose sum is 180.
4096
C = (pi)d
Angle/360 x 2(pi)r
28. How many 3-digit positive integers are even and do not contain the digit 4?
(p + q)/5
Pi is the ratio of a circle'S circumference to its diameter.
1
288 (8 9 4)
29. If 10800 is invested at a simple interest rate of 4% - what is the value of the investment after 18 months?
IV
$11 -448
A = I (1 + rt)
F(x + c)
30. What is the graph of f(x) shifted left c units or spaces?
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...
.0004809 X 10^11
0
F(x + c)
31. What is the name of set with a number of elements which cannot be counted?
y = 2x^2 - 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)
An infinite set.
.0004809 X 10^11
32. When the 'a' in the parabola is negative...
The curve opens downward and the vertex is the maximum point on the graph.
7 / 1000
F(x) - c
F(x + c)
33. A number is divisible by 3 if ...
The sum of its digits is divisible by 3.
Lies opposite the greater angle
Yes. [i.e. f(x) = x^2 - 1
x^(6-3) = x^3
34. What transformation occurs if point C is reflected over the x-axis and then the y-axis?
A reflection about the axis.
All real numbers which can'T be expressed as a ratio of two integers - positive and negative (pi - -sqrt3)
1/a^6
1/2 times 7/3
35. What is it called when a point is reflected to the quadrant opposite it (i.e. I to III or II to IV)?
A = I (1 + rt)
A set with a number of elements which can be counted.
A reflection about the origin.
(12/2) x (sqrt15 / sqrt5) = 6sqrt3
36. When does a function automatically have a restricted domain (2)?
180 degrees
72
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)
When we need to avoid having a zero in the denominator or avoid taking the square root of a number.
37. Can the output value of a function have more than one input value?
2
Yes. [i.e. f(x) = x^2 - 1
8
The second graph is less steep.
38. What is the surface area of a cylinder with radius 5 and height 8?
11 - 13 - 17 - 19
(n-2) x 180
130pi
(a - b)(a + b)
39. What is an isoceles triangle?
$11 -448
Two equal sides and two equal angles.
1
Angle/360 x 2(pi)r
40. Evaluate 4/11 + 11/12
1 & 37/132
A chord is a line segment joining two points on a circle.
10! / 3!(10-3)! = 120
The objects within a set.
41. x^(-y)=
Its last two digits are divisible by 4.
9 & 6/7
1/(x^y)
The longest arc between points A and B on a circle'S diameter.
42. In a triangle inscribed inside a circle - where the diameter is one side of the triangle - which angle is largest?
(a - b)^2
G(x) = {x}
Part = Percent X Whole
The angle intersecting the circumference is always the largest angle - and is always 90 degrees.
43. What is the order of operations?
3
PEMDAS (Parentheses Exponents Multiplication/Division Addition/Subtraction)
.0004809 X 10^11
4725
44. 8.84 / 5.2
The two xes after factoring.
1.7
9 & 6/7
The set of elements which can be found in either A or B.
45. Which quandrant is the lower right hand?
Cd
7 / 1000
IV
Divide by 100.
46. Formula of rectangle where l increases by 20% and w decreases by 20%
N! / (n-k)!
x= (1.2)(.8)lw
6
x^(6-3) = x^3
47. 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?
Sector area = (n/360) X (pi)r^2
The longest arc between points A and B on a circle'S diameter.
N! / (n-k)!
A circle centered on the origin with radius 8.
48. Write 10 -843 X 10^7 in scientific notation
A circle centered at -2 - -2 with radius 3.
(amount of increase/original price) x 100%
Diameter(Pi)
1.0843 X 10^11
49. Describe the relationship between 3x^2 and 3(x - 1)^2
The interesection of A and B.
The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.
Area of the base X height = (pi)hr^2
4a^2(b)
50. The perimeter of a square is 48 inches. The length of its diagonal is:
37.5%
All numbers multiples of 1.
12sqrt2
It is a function defined by more than one equation - where each equation applies to a different part of the domain of the function.