MATH 130 · Test 2

Test 2 Review

Concepts, worked examples, student practice, and synthesis

55 minutes · Offline capable

Today’s Learning Roadmap

  1. 1

    apply exponential and logarithmic models

  2. 2

    solve angle, arc, and sector problems

  3. 3

    choose area, similarity, and speed strategies

Activate · 0.5 minSource: 1

Predict: apply exponential and logarithmic models

Predict first

Which formula or inverse relationship would you choose first?

Commit to a response before discussion.

Activate · 1.0 minSource: Authored

apply exponential and logarithmic models

Concept
  • Match wording to compound-interest formulas.
  • $\log_b(x)=y\iff b^y=x$.

Explain · 2.5 minSource: 2

Model the Skill: apply exponential and logarithmic models

Find the balance for $2500$ at 5.2% compounded quarterly for 6 years, then convert $\log_2(32)=5$.

  1. $A=2500(1+0.052/4)^{24}\approx3408.53$.
  2. $\log_2(32)=5$ is equivalent to $2^5=32$.
  3. The interest result uses dollars; the logarithmic conversion is dimensionless.

Model · 3.0 minSource: 3

You Try: apply exponential and logarithmic models

Student practice

Find the balance on $4000 at 6% monthly for 10 years and rewrite $\log_3(81)=4$.

Practice · 3.0 minSource: Authored

Check and Diagnose: apply exponential and logarithmic models

Error analysis

Convert rates to decimals and preserve the logarithm base.

Self-check

What evidence confirms the setup, sign, unit, or magnitude?

Feedback · 2.0 minSource: 4

Pacing checkpoint

Make It Stick: apply exponential and logarithmic models

Write the first decision you make in each problem type.

Exit response

Answer in complete mathematical sentences and identify one remaining question.

Synthesize · 0.5 minSource: Authored

Predict: solve angle, arc, and sector problems

Predict first

Which formulas require radians and which accept degrees after conversion?

Commit to a response before discussion.

Activate · 1.0 minSource: Authored

solve angle, arc, and sector problems

Concept
  • Convert angles before applying $s=r\theta$ or $A=\tfrac12r^2\theta$.
  • Use circle theorems only after identifying the intercepted arc.

Explain · 2.5 minSource: 5

Model the Skill: solve angle, arc, and sector problems

Convert $5\pi/6$ to degrees and find arc length for $r=9$, $\theta=2\pi/3$.

  1. $(5\pi/6)(180^\circ/\pi)=150^\circ$.
  2. $s=r\theta=9(2\pi/3)=6\pi$ units.
  3. Radians cancel in the arc-length calculation.

Model · 3.0 minSource: 6

You Try: solve angle, arc, and sector problems

Student practice

Find arc length for $r=12$, $\theta=40^\circ$.

Practice · 3.0 minSource: 10

Check and Diagnose: solve angle, arc, and sector problems

Error analysis
  • Do not mix degrees and radians.
  • Central and inscribed angles obey different rules.
Self-check

What evidence confirms the setup, sign, unit, or magnitude?

Feedback · 2.0 minSource: 11

Pacing checkpoint

Make It Stick: solve angle, arc, and sector problems

State the unit check for an arc or sector answer.

Exit response

Answer in complete mathematical sentences and identify one remaining question.

Synthesize · 0.5 minSource: Authored

Predict: choose area, similarity, and speed strategies

Predict first

What information tells you to use Heron, trapezoid area, similarity, or $v=r\omega$?

Commit to a response before discussion.

Activate · 1.0 minSource: Authored

choose area, similarity, and speed strategies

1

Formula selection depends on the givens, not the picture’s appearance.

2

Write corresponding sides in consistent order.

Explain · 2.5 minSource: 7

Model the Skill: choose area, similarity, and speed strategies

Find a trapezoid area with bases 10 and 16 and height 7, then solve $6/9=x/15$.

  1. $A=\tfrac12(10+16)(7)=91$ square units.
  2. $9x=90$, so $x=10$.
  3. Formula choice follows the given measurements and correspondence.

Model · 3.0 minSource: 8

You Try: choose area, similarity, and speed strategies

Student practice

Solve $6/9=x/15$. Then find the rim speed of a wheel with radius 0.4 m turning at 5 rad/s.

Practice · 3.0 minSource: 9

Check and Diagnose: choose area, similarity, and speed strategies

Most lost points come from setup, units, or mismatched corresponding sides.

    Feedback · 2.0 minSource: 12

    Pacing checkpoint

    Make It Stick: choose area, similarity, and speed strategies

    Name the evidence that selects each geometry strategy.

    Exit response

    Answer in complete mathematical sentences and identify one remaining question.

    Synthesize · 0.5 minSource: Authored

    Session Summary and Exit Ticket

    1. State the most important idea from today without looking at your notes.
    2. Complete one representative setup and identify the step most likely to cause an error.
    3. Write one question that should be answered before the next assessment.
    Exit response

    Answer in complete mathematical sentences and identify one remaining question.

    Synthesize · 1.5 minSource: 13