Week 1 Checkpoint

A short checkpoint on Week 1: number systems, operator precedence, exponents and logarithms, summation and product notation, argmax, and sets. Aim for 80% or better before moving to Week 2. Each explanation points to the chapter to revisit if you miss it.

  1. 1.

    Which number system does the value −34-\tfrac{3}{4} belong to, but 2\sqrt{2} does not?

  2. 2.

    Evaluate 10−2×3+4210 - 2 \times 3 + 4^2 using correct operator precedence.

  3. 3.

    Using the laws of exponents, simplify a5a2\dfrac{a^5}{a^2} (for a≠0a \neq 0).

  4. 4.

    Which identity is correct for logarithms (base b>0b > 0, b≠1b \neq 1)?

  5. 5.

    Expand the product ∏k=14k\displaystyle\prod_{k=1}^{4} k.

  6. 6.

    Let S={ x∈Z:0≤x<5 }S = \{\,x \in \mathbb{Z} : 0 \le x < 5\,\}. Also let v=[8,3,9,1,7]v = [8, 3, 9, 1, 7] indexed from 00. What is ∣S∣|S|, and what is arg⁡max⁡ivi\arg\max_i v_i?