Grade 12 · Math

Grade 12 math

Grade 12 math is the last step before university or college math: advanced functions, logarithms, and for many students calculus or statistics. Here is what the year covers, where students usually get stuck, and one way to help.

What your teen learns this year

Courses differ by province and state, but most grade 12 math covers several of these:

  • Polynomial and rational functions. Their graphs, factors, and behaviour far from the origin.
  • Exponentials and logarithms. Log laws, and solving equations where the unknown is an exponent.
  • Trigonometric functions. Radians, identities, and equations with many solutions.
  • Calculus. Rates of change, derivatives, and their use for maximum and minimum problems; vectors in some courses.
  • Data management. Counting with permutations and combinations, probability, and statistics.

Ontario's grade 12 courses include Advanced Functions (MHF4U), Calculus and Vectors (MCV4U) and Data Management (MDM4U). Other provinces offer Pre-calculus, Foundations and Calculus 12, and US students often take precalculus, calculus or statistics.

Where kids usually get stuck

  1. 1Treating a log like division. log₂ 32 is not 32 ÷ 2. It asks which power of 2 makes 32, and the answer is 5.
  2. 2Splitting a log over a plus sign. log(a + b) is not log a + log b. The law works for a product: log(ab) = log a + log b.
  3. 3Calculator in the wrong mode. Degrees when the question is in radians (or the reverse) gives answers that look reasonable and are wrong.

One of Pip's tricks

Log asks: what power?

Use it when evaluating a log like log₂ 32 or log 1000, or rewriting between log form and exponent form.

  1. Read log_b(a) as a question: b to what power gives a?
  2. Answer that question. log_b(a) = c and b^c = a say the same thing.
  3. No base written means base 10, and ln means base e.

Watch it work. log₂ 32. Ask: 2 to what power gives 32? 2⁵ = 32, so log₂ 32 = 5.

Why it works: a logarithm is defined as an exponent, so every log value is the answer to a “what power?” question and nothing more mysterious.

Try three

Have a go, then tap to see the answer.

  1. 1.log₃ 81 = ?

    Show the answer

    4. 3 to what power gives 81? 3⁴ = 81.

  2. 2.log₅ (1/25) = ?

    Show the answer

    −2. 1/25 is 1/5², which is 5⁻².

  3. 3.In how many ways can a committee of 3 be chosen from 5 students?

    Show the answer

    10. Order doesn't matter in a committee, so it is a combination: (5 × 4 × 3) ÷ (3 × 2 × 1) = 60 ÷ 6 = 10.

How Sparkpip fits in

Pip, Sparkpip's tutor, works through problems like these with your teen one small step at a time, using methods like the one above.

Start freeSee how it works

Your curriculum

Sparkpip is built on the grade 12 math curriculum for your province or state. The official pages:

Also: Grade 11 math · Grade 12 science · Grade 12 English