Derivatives — First Principles and the Rules
Differentiate from first principles when asked, apply the power rule everywhere else, and know what a derivative actually tells you about a graph.
Tell arithmetic patterns from quadratic ones using differences, build the general term for each, and read sigma notation without panic.
By the end, you can
identify a pattern from its differences, find its general term and calculate a required term or sum.
Free preview
This is exactly how Arithmetic and Quadratic Number Patterns starts, in your browser or on WhatsApp. Short messages, real examples, one step at a time.
Carry on from here →skillSYMS LearnChat
Arithmetic and Quadratic Number Patterns
Differences give the game away
Every number pattern question starts the same way: take the differences. What they do tells you what kind of pattern it is, and that decides every formula you use afterwards. 🔢
Do this before anything else, every time. Guessing the pattern from the numbers works until it doesn't.
Pass the challenge and it arrives straight away as a PDF. Add it to your CV or LinkedIn, and anyone can check it's real.
Certificate of completion
Your name here
has completed the MicroQuest
Arithmetic and Quadratic Number Patterns
LCA-2026-••••••••
Verify at skillsyms.com/verify
Next on the Mathematics P1 path · step 3 of 11
Cubic Calculus: Turning Points, Inflection and Tangents
14 min · R19
Differentiate from first principles when asked, apply the power rule everywhere else, and know what a derivative actually tells you about a graph.
Choose the right financial formula, handle monthly compounding correctly, and work out loan repayments and outstanding balances without guessing.
Read a parabola or exponential graph properly — intercepts, turning point, asymptotes, domain and range — and find an inverse without guessing.
Work with the common ratio, find any term or sum, and know exactly when an infinite series converges and when it does not.
Turn a word problem into one equation, differentiate it to find the maximum or minimum, and interpret rates of change in real units.
The whole Mathematics P1 path → All High School MicroQuests → Browse all 134 →
Send it to a colleague, a friend or your class group.
For employers, schools and training providers
Toolbox talks, inductions, refreshers and revision that people finish, because each one fits in a tea break and runs on the phone they already carry.
Need a topic we don't have? Request it. The topics people ask for most are the ones we write next.
Your people get a WhatsApp message or an email link and learn on their own phones. No logins to manage.
Print an A4 poster for the canteen, staffroom or site office. A scan opens the MicroQuest.
Every completion has a numbered certificate you can check online, which is useful for toolbox talks and inductions.
skillSYMS clients publish their own MicroQuests (policies, site rules, product knowledge) for their own people.
Arithmetic and Quadratic Number Patterns
R19 · 13 min · certificate