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Fall 2026 · Prof. Young & Prof. Volk

Math 130 — Test 2 Review

Sections 4.2 and 4.3 (exponential and logarithmic functions) and geometry: angles, polygons, circles, radians, and solids. Dates and deadlines are on the MATH 130 page.

Start here · Unit 2 pathway

Learn → targeted practice → checkpoint

Move from exponentials to logarithms, then polygons and circles. Complete the matching practice before each checkpoint, and save Unit 2E for after the first four steps.

Step 1 · Unit 2A · Quiz 5

Exponential functions and interest

Learn Section 4.2, practice tables, graphs, growth/decay, and interest models, then take the five-question checkpoint.

Learn with 2A
Step 2 · Unit 2B · Quiz 6

Logarithmic functions

Learn Section 4.3 after exponentials: how logarithms undo exponentials, converting between the two forms, evaluating logs, reading their graphs, and solving equations.

Learn with 2B
Step 3 · Unit 2C · Quiz 7

Geometry foundations and polygons

Use the two-session HTML deck for angles, parallel lines, triangles, polygon area, and similarity before the eight-question checkpoint.

Learn with 2C
Step 4 · Unit 2D · Quiz 8

Circles, radians, and solids

Radians, arc length, sectors, speed, and cylinder volume and surface area. Quiz 8 checks converting decimal degrees to degrees, minutes, and seconds.

Learn with 2D Cylinder lesson
Step 5 · Unit 2E · Test 2

Cumulative Test 2 readiness

Mix Units 2A–2D. Correct every miss, then repeat the weakest category before taking another cumulative checkpoint.

Review with 2E

Readiness rule: Aim for at least 80% on the matching checkpoint and be able to explain each corrected error before moving forward.

Deck library and downloadable files

Essential Formulas for Test 2

Prefer a walkthrough? Jump to the study videos.

Section 4.2: Exponentials & Interest

Focus: recognize the two interest formulas printed on Test 2 and know when each model is used.
Provided on Test 2
Compound Interest
$$A = P\left(1+\frac{r}{n}\right)^{nt}$$
Printed on Test 2.
$n$ = compounds per year (1 annually, 12 monthly, 365 daily)
Provided on Test 2
Continuous Compounding
$$A = Pe^{rt}$$
Printed on Test 2.
$e \approx 2.71828$
Useful
Simple Interest
$$A = P(1 + rt)$$
Useful for comparison problems.
$P$ = principal, $r$ = annual rate (decimal), $t$ = years

Section 4.3: Logarithms

Focus: memorize log-to-exponential conversion (including fractional exponents, such as $25^{3/2} = 125 \iff \log_{25} 125 = 3/2$) and inverse log equations. Change of base is printed on Test 2. The log property rules are support only.
Memorize
Log ↔ Exponential Form
$$\log_b(x) = y \iff b^y = x$$
Needed for converting between log and exponential forms.
$\log(x)=\log_{10}(x)$ and $\ln(x)=\log_e(x)$
Memorize
Inverse Log Equations
$$\ln(x)=c \iff x=e^c$$ $$\log(x)=c \iff x=10^c$$
Directly useful when solving basic logarithmic equations on the test
Provided on Test 2
Change of Base
$$\log_b(a)=\frac{\ln(a)}{\ln(b)}$$ $$\log_b(a)=\frac{\log(a)}{\log(b)}$$
Printed on Test 2 (the $\ln$ form). Solve $b^x = c$ as $x = \log_b c = \ln c / \ln b$
Useful
Product Rule
$$\log_b(MN) = \log_b(M) + \log_b(N)$$
Helpful for Section 4.3, but not directly needed on this test
Useful
Quotient Rule
$$\log_b\!\left(\frac{M}{N}\right) = \log_b(M) - \log_b(N)$$
Helpful for Section 4.3, but not directly needed on this test
Useful
Power Rule
$$\log_b(M^k) = k\log_b(M)$$
Helpful for Section 4.3, but not directly needed on this test

Geometry: Polygons & Area

Focus: trapezoid and triangle area, Heron's formula (printed on the test), similar triangles, and angle pairs across parallel lines.
Memorize
Triangle Area
$$A = \frac{1}{2}bh$$
Used when a base and perpendicular height are given
Memorize
Trapezoid Area
$$A = \frac{1}{2}h(b_1 + b_2)$$
$b_1$ and $b_2$ are the parallel sides; $h$ is the perpendicular height, not the slanted side
Provided on Test 2
Heron's Formula
$$A = \sqrt{s(s-a)(s-b)(s-c)}$$ $$s = \frac{a+b+c}{2}$$
Printed on Test 2 for the three-side triangle problem, with the semiperimeter $s$.
Memorize
Parallel Lines / Segment Proportions
$$\frac{AC}{CE} = \frac{BD}{DE}$$
When parallel lines cut transversals, corresponding segments are proportional. Match top-to-top and bottom-to-bottom segments.
Useful
Parallelogram Area
$$A = bh$$
Part of the topic set, but not directly used on this test

Geometry: Angle, Arc, and Circle Relationships

Focus: DMS conversions, radian-degree conversion, arc and sector formulas, circle angle theorems, and linear speed.
Memorize
DMS to Decimal Degrees
$$\text{decimal degrees} = D + \frac{M}{60} + \frac{S}{3600}$$
$D$ = degrees, $M$ = minutes, $S$ = seconds
Memorize
Decimal Degrees to DMS
Step 1$$M=(\text{decimal part})\cdot 60$$
Step 2$$S=(\text{new decimal part})\cdot 60$$
Keep the whole-number degrees. Multiply the decimal part by 60, then repeat once more for seconds.
Memorize
Degree ↔ Radian Conversion
$$\text{radians} = \text{degrees}\cdot\frac{\pi}{180}$$ $$\text{degrees} = \text{radians}\cdot\frac{180}{\pi}$$
Use both directions. Also remember $180^\circ = \pi$ radians.
Memorize
Arc Length
$$s = r\theta$$ $$s = \frac{\theta}{360}(2\pi r)$$
Use $s=r\theta$ when $\theta$ is in radians, or use the degree form directly
Memorize
Sector Area
$$A = \frac{1}{2}r^2\theta$$ $$A = \frac{\theta}{360}\pi r^2$$
Use the radian form when $\theta$ is in radians, or use the degree form directly
Memorize
Central Angle and Arc
$$m(\angle\,\text{central}) = m(\text{intercepted arc})$$
A diameter splits the circle into two semicircles of $180^\circ$ each
Memorize
Inscribed Angle Theorem
$$m(\angle\,\text{inscribed}) = \frac{1}{2}m(\text{intercepted arc})$$
An inscribed angle is half of its intercepted arc
Memorize
Intersecting Chords Angle Theorem
$$m\angle = \frac{1}{2}\big(m(\text{arc }1)+m(\text{arc }2)\big)$$
For angles formed by two chords intersecting inside a circle
Memorize
Angular and Linear Speed
$$v = r\omega$$ $$v = (\text{rpm})(2\pi r)$$
Needed for the wheel speed problem on Test 2 (not printed). In $v = r\omega$, $\omega$ must be in radians per unit of time (1 revolution $=2\pi$ rad), so $\omega = (\text{rpm})(2\pi)$ gives feet per minute. Use the radius, not the diameter.
Useful
Circle Area
$$A = \pi r^2$$
Useful background for sector area problems, but not directly required on this test
Useful
Circumference
$$C = 2\pi r$$
Useful background for arc length and linear speed

Practice Generators

🎯 Test 2 Readiness Check

The 15 question types and point values of Test 2 (200 points), in a random order with new numbers every time: interest (20), logarithms (60), angles and polygons (60), DMS (20) and circles (40). Both interest formulas, change of base and Heron's formula are printed on Test 2; every other formula is from memory.

📝 Mock Quiz & Skill Practice

Quizzes 5 to 9 check each step of Unit 2; Quiz 8 covers converting decimal degrees to DMS only, and Quiz 9 covers circles. Dates are on the MATH 130 page.

Study Videos

Section 4.2: Exponentials

Graphing & Tables Calculator: Decimal Exponents Simple vs Compound Interest Continuous Compounding

Section 4.3: Logarithms

Log ↔ Exp Conversions Evaluating Log Expressions Logarithm Change of Base Solving Exponential Eqns using Logs

Geometry & Circles

Piecewise Rectangular Areas DMS to Decimal Conversion Radians & Degrees Intro Circle Sectors & Arc Length

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