Quizzes

Mathematics quiz

24 questions from the Mathematics track. Score 80% or higher to unlock a certificate.

1. Why Agents Need Math

   1. What is an embedding, in math?

   • A paragraph of English stored in the prompt
   • A vector: a list of numbers that stands for text (or an image, or a tool)
   • A Python error type
   • A GPU setting

2. Functions and Graphs

   2. Which statement is true of a function f?

   • One input is allowed to produce two different outputs
   • Each input in the domain maps to exactly one output
   • Graphs never appear in agents
   • Temperature is not a function because it is a slider

3. Sums, Products, and Averages

   3. Mean squared error is which mix?

   • A product of absolute errors
   • A sum of squared errors, then divided by the count
   • The maximum error only
   • Entropy of the labels

4. Logs and Exp

   4. Why do we use log of a product of token chances?

   • Logs make the model faster on a GPU
   • A product of small chances hits 0.0; a sum of logs stays a usable number
   • log(0) is 1
   • Exp and log are the same function

5. Min, Max, Percent, and Clip

   5. clip(1.4, 0, 1) returns

   • 1.4
   • 0
   • 1
   • -1

6. Vectors

   6. Which operation needs two vectors of equal dimension?

   • Printing a vector
   • Vector addition (and the difference used for distance)
   • Choosing a learning rate
   • Lowercasing text

7. Dot Product and Cosine Similarity

   7. If two vectors already have length 1, cosine equals which of these?

   • Their distance
   • The product of their lengths
   • Their dot product
   • Always 0

8. Matrices

   8. If W is 2 by 3 and x has length 3, what is the length of W x?

   • 3
   • 5
   • 2
   • 6

9. Linear Maps

   9. You scale only document embeddings by a stretch W, and leave the query untransformed. What happens?

   • Cosine scores stay valid because length is ignored
   • Query and documents no longer live in the same geometry, so ranking is meaningless
   • The map stops being linear
   • Rotation is applied automatically to the query

10. Derivatives

    10. To minimize f when f'(x) is positive, you should

    • Increase x (move with the slope)
    • Decrease x (move against the slope)
    • Set h to 0
    • Multiply x by f'(x)

11. Gradients

    11. The gradient of a scalar function f is

    • A single slope that ignores all but one variable
    • The vector of partial derivatives; it points toward steepest increase of f
    • Always the zero vector
    • A matrix-vector product with no meaning

12. The Chain Rule

    12. Backpropagation is

    • A way to sample tokens with temperature
    • The chain rule applied from the loss backward through nested maps
    • Deleting gradients only to save memory
    • Adding a bias vector

13. Optimization

    13. Gradient descent updates weights by

    • Adding the gradient times the learning rate
    • Subtracting the gradient times the learning rate
    • Setting all weights to zero
    • Multiplying weights by entropy

14. Probability

    14. If two events cannot happen at once, the chance that one or the other happens is

    • Always 1
    • The product of their chances
    • The sum of their chances (they are mutually exclusive)
    • Undefined unless they are independent

15. Bayes' Rule

    15. P(E|H) is

    • The posterior belief in H
    • The prior belief in H
    • The likelihood: chance of the evidence assuming H is true
    • Always equal to P(H|E)

16. Distributions

    16. A Bernoulli(p) random variable

    • Is uniform on the real line
    • Takes value 1 with chance p and 0 otherwise
    • Always has mean 0
    • Cannot model tool success or failure

17. Expectation and Variance

    17. Expected cost of a random step is

    • The most common cost
    • The maximum cost
    • The sum of (chance of each outcome times its cost)
    • Variance times standard deviation

18. Entropy

    18. Entropy of a distribution is highest when

    • One outcome has chance 1
    • Chance is spread as evenly as possible over the outcomes
    • You use a smaller log base
    • The mean is zero

19. Softmax

    19. Why subtract max(z) before exp in softmax?

    • It changes which token wins
    • It stops overflow; the chances stay the same
    • It turns logits into embeddings
    • It makes all chances zero

20. Sampling and Temperature

    20. Raising temperature above 1, with the same logits, generally

    • Makes greedy argmax more likely to change the softmax winner
    • Flattens the chance distribution, increasing entropy of samples
    • Converts logits into embeddings
    • Sets all chances to zero

21. Cross-Entropy, KL, and Perplexity

    21. For a one-hot true token k, cross-entropy is

    • Entropy of a uniform distribution
    • Minus log of the model’s chance on k
    • Always 0
    • The learning rate

22. Weighted Averages and Attention

    22. Attention’s output is

    • Always the value with the biggest key
    • A weighted average of the value vectors, with weights from softmax of scores
    • The raw query vector unchanged
    • A probability that sums to n

23. Embedding Geometry

    23. Why is top-k retrieval alone a risky policy for agents?

    • Cosine similarity cannot be implemented with lists
    • k neighbors are always returned, even if every score is poor, so the model may quote irrelevant memory
    • Embeddings cannot live in 2-d even as a toy
    • Temperature disables nearest neighbors

24. Accuracy, Precision, Recall, F1

    24. Precision is

    • How many tickets you graded
    • Of the times you predicted yes, the fraction that were truly yes
    • Always equal to accuracy
    • 1 minus entropy