Grade 11 · Math

Grade 11 math

Grade 11 math is about functions: how one quantity depends on another, and how a graph moves when the equation changes. Exponential growth, trigonometry and finance build on that. 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 11 math covers several of these:

  • Functions. Function notation, domain and range, inverses, and moving and stretching graphs.
  • Exponential growth and decay. Populations, investments and depreciation that change by a percent each step.
  • Trigonometry. The sine and cosine laws, angles beyond 90°, and graphs that repeat.
  • Sequences and series. Patterns that add the same amount or multiply by the same amount.
  • Financial math. Simple and compound interest, loans and annuities.

Ontario's main grade 11 courses are Functions (MCR3U), Functions and Applications (MCF3M) and Foundations (MBF3C). Other provinces split into paths with names like Pre-calculus, Foundations and Workplace, and in much of the US grade 11 is Algebra 2.

Where kids usually get stuck

  1. 1Treating growth as adding the same amount. A car losing 15% a year does not lose the same $3,000 each year: each 15% is of that year's value.
  2. 2Moving a graph the wrong way. y = (x − 3)² is y = x² moved 3 to the right, not left: the change inside the bracket does the opposite of what it looks like.
  3. 3Mixing up f(x + 1) and f(x) + 1. The first changes the input before the function acts; the second adds 1 to the output afterwards.

One of Pip's tricks

Multiply, don't add

Use it when repeated percent growth or decay: a population growing 4% a year, a car losing 15% a year.

  1. Turn the percent into a multiplier: growing by 4% is × 1.04, losing 15% is × 0.85.
  2. Amount = start × multiplier, raised to the number of steps.
  3. Count the steps carefully: years, hours or months.

Watch it work. A $20,000 car loses 15% of its value each year. The multiplier is 1 − 0.15 = 0.85. After 3 years: 20,000 × 0.85³ = 20,000 × 0.614125 = $12,282.50.

Why it works: each year's 15% is 15% of that year's value, not of the original, so the same multiplier is applied again and again instead of the same amount being subtracted.

Try three

Tap a choice, or have a go and then tap to see the answer.

  1. 1.500 bacteria grow by 10% an hour. How many are there after 2 hours?

    Show the answer

    605. The multiplier is 1.1: 500 × 1.1 × 1.1 = 605.

  2. 2.A population of 1000 doubles 3 times. How many is that?

    Show the answer

    8000. Doubling is × 2, three times: 1000 × 2³ = 1000 × 8.

  3. 3.The graph of y = (x − 3)² is the graph of y = x² moved…

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 11 math curriculum for your province or state. The official pages:

Also: Grade 10 math · Grade 12 math · Grade 11 science · Grade 11 English