AQR Unit 1-2 Review

GPA and Class Grades

100

What is the average of 3 quizzes, with grades of 82, 79, and 91?

Quiz average = 84

200

Your college professor grades his class with this system:  45% Project and 55% Final Exam.

If you get a 88 on your project and a 92 on your final exam, what is your class grade?  

90.2 or rounded down to 90.

300

Your college professor has the following grading system:  30% for Average of 3 quizzes, 15% Homework, and 55% Final Exam.

If you received an 82 as your 3 quiz average, 78 for Homework, and a 94 on your Final Exam, what was your grade in the class? 

88 is your final grade.

400

An A=4, B=3, C=2, D=1, and F=0.  For the semester, you got a B in a 3-credit Calculus class, a C in a 4-credit English class, and an A in a 3-credit Biology class.

What is your final GPA?

GPA = 2.9

500

Your college professor has a grading system: 

42% of the Class Project and 58% of the Final Exam.

If you got a 84 on the class project, what grade would you need on your final exam, to get a final grade of 92?

97.79 or round-up to a 98.

Matrices-Add/Sub

100

What is 

|3  4|          |4   3|

  |5  6|   +     |2   1|  ?

|7     7|

|7     7|

200

What is

|6    -2|        |4    -3|

   |-2    1|   -   |-2    -1|   ?

|2     1|

|0     2|

300

What is 

|455|           |321|

   |235|    +     |174| ?

|776|

|409|

400

What is 

| 842|              |534|

    |-235|      -      |674|   ?

| 308|

|-909|

500

What is 

|  45    21|

| -31    17|        +       | -15    18     20|

| -11    14|                  |  13    28   - 33|       ?

Cannot be solved.  Dimensions are not compatible.

Matrices-Multiply

100

What is

       | 11          14|

     2 x   | 6            17|     ?

| 22         28|

| 12         34|

200

What is

             | 14 |

1.5   x    | 18 |

                   | 22 |     ?

| 21 |

| 27 |

| 33 |

300

What is

  | 2 |               

                    | 6 |    x      | -10      5 |  ?

| -20   10|

| -60   30| 

400

What is 

| 72 |               | -1 |

| 12 |      x       | -1 |

| 32 |               | -1 |      ?

Cannot multiply matrices with incompatible dimensions.

500

What is

                                        | 72 |

|  -1      -1       -1|      x      | 12 |

                                              | 32 |      ?

| -116 |

Adjacency Matrix

100

If          |  21     23       17       14|

     R =  |  19     15       12       23|

            |  13      20       11      10|

what is R_3,2?

20

200

If         |-17    18    21    29|

    M =  | 56  -32    11     19|

           |  11    9     10     13|

what is M_2,4   ? 

 19

300

If      |  2    1 |

M =   | 1     0 | 

what is M³  ?

|  12     5  |

|    5     2  |

400

If      | 5    12 |

R³ = | 2      5  |

how many edges are we considering in the 5 different paths we can take to get from point A to point A?

3 edges.

500

If     |0     2|

P³ = |4     0|

using 3 edges, how many paths can you get from B to A?

4 Paths

Mixed Bag

100

When we think of Linear Models, we think of what?

Lines

200

What is the slope of the following line:

y = 5x - 3 ?

5

300

What is the y-intercept of the following equation:

5x = y + 3 ?

-3

400

In a Fermi Question, there are 3 things that we must do.

First, we make assumptions.

What is the second thing we do?

List Exceptions.

500

If a triangle, with points (0,0), (3,4) and (6,2) is converted into a matrix and multiplied to the matrix,

| -1     0|                                      | 0    -3    -6 |

| 0       1|, we get a new matrix of  | 0     4     2  |.

What is the transformation of the new triangle?

Reflection over the y-axis.