Pre-calculus 11 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Pre-calculus 11 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
RF09 Students will be expected to analyze arithmetic sequences and series to solve problems.
RF09.01 Identify the assumption(s) made when defining an arithmetic sequence or series.
RF09.02 Provide and justify an example of an arithmetic sequence.
RF09.03 Derive a rule for determining the general term of an arithmetic sequence.
RF09.04 Describe the relationship between arithmetic sequences and linear functions.
RF09.05 Determine t₁, d, n, or tₙ in a problem that involves an arithmetic sequence.
RF09.06 Derive a rule for determining the sum of n terms of an arithmetic series.
RF09.07 Determine t₁, d, n, or Sₙ in a problem that involves an arithmetic series.
RF09.08 Solve a problem that involves an arithmetic sequence or series.
RF10 Students will be expected to analyze geometric sequences and series to solve problems.
RF10.01 Identify assumptions made when identifying a geometric sequence or series.
RF10.02 Provide and justify an example of a geometric sequence.
RF10.03 Derive a rule for determining the general term of a geometric sequence.
RF10.04 Determine t₁, r, n, or tₙ in a problem that involves a geometric sequence.
RF10.05 Derive a rule for determining the sum of n terms of a geometric series.
RF10.06 Determine t₁, r, n, or Sₙ in a problem that involves a geometric series.
RF10.07 Generalize, using inductive reasoning, a rule for determining the sum of an infinite geometric series.
RF10.08 Explain why a geometric series is convergent or divergent.
RF10.09 Solve a problem that involves a geometric sequence or series.
Additional Resources and Activities for RF09 (arithmetic sequences and series):
Picture Perfect Desmos Activity - An activity you might use on the first day of the unit to introduce the idea of arithmetic sequences using a context of hanging pictures evenly spaced on a wall.
Plotting an Arithmetic Sequence using Desmos - A Desmos graph showing how to use a list, sliders and the formula for an arithmetic sequence to plot points.
Expressing Number Patterns Desmos Activity - Expressing an arithmetic number pattern using the context of a theatre with additional seats in each row.
First to Four - A game where each team takes turns capturing numbers from a game board. The first team to be able to make an arithmetic sequence four terms long wins. Here is a Mimio file to play this game with. You could also play this game cooperatively as a class challenge.
Arithmetic Sequences Spiders - This set of 3 "spiders" takes students through generating a sequence from an nth term, to finding the nth term of an arithmetic sequence. The concept is designed to encourage discussion.
Linear Sequence Maths Mystery - Hand out the page of clues to pairs of students. They might wish to cut the clues into cards. Ask student to draw a 3 x 3 grid on their paper. Students then use the clues to create an arithmetic sequence in each of the 9 squares on the grid. All of the info is there on the page.
Arithmetic Sequences Secret Message activity - Students find the 10th term of 26 different arithmetic sequences. This creates a key that can decipher a secret message.
Magic and Arithmetic Series - A class opener to get students curious about a formula for finding the sum of an arithmetic sequence and learning about arithmetic series.
Not One Mention - Another class opener to amaze your students with your mental math prowess... actually a clever use of the arithmetic series formula. Here is a handout for students to go with this activity.
Linear Sequences Activities - Sequences Problems, Join the Dots Sequences, A Linear Sequence, and Who is Correct Sequences.
Arithmetic Series Fill in the Blanks worksheet - Students fill in the missing spaces to complete each row in this practice sheet from Dr. Austin Maths website. Solutions.
Additional Resources and Activities for RF10 (geometric sequences and series):
Doodling to Infinity video on YouTube - A talk about infinite sequences in an artistic way.
Creating Sequences Open Middle Problem - Using the digits 0-9, at most one time each, complete the first three terms of the arithmetic and geometric sequences. What sequences result in the greatest sum of their second terms? (e.g. 3, 5, 7 and 2, 6, 18 would result in a sum of 5 + 6 = 11). What sequences result in the least sum of their second terms?
Arithmetic vs. Geometric Open Middle problem - Which is greater... the common ratio, r, in a geometric sequence with a_2=24 and a_5=1536 OR the common difference, d, in an arithmetic sequence with a_4=16 and a_7=31.
Cross Number Puzzles - Create a puzzle for your student to solve and then ask them to make their own.
A Sequences Puzzle and a Geometric Sequences Puzzle - Crossword puzzle activities from the January 1989 issue of Mathematics Teacher. Here is a review worksheet from these activities.
Geometric Series Formula YouTube video - What is the geometric series formula? When is it valid? How do we derive the formula? All explained by James Tanton, the Mathematician in Residence at the Mathematical Association of America in Washington D.C.
The Paper Master Activity - An introduction to infinite geometric series using a single sheet of paper and groups of three students. A similar activity is found in the Pre-calculus textbook from McGraw-Hill Ryerson, problem #23 (mini-lab) on page 65.
Super Ball Activity - Use a bouncing super ball to model an infinite geometric sequence. Each time the ball bounces, it has 92% of its previous height.
Getting Coins from the Bank - A coin problem. "It takes place on a grid with an infinite number of rows and columns, and it starts with three coins in the top left corner of the grid." "The game has one move. At any moment you can remove any coin, and replace it with two coins, one in the cell immediately below the removed coin, and one in the cell immediately to the right of the removed coin. There’s one more thing. You are only allowed to remove a coin, in the way described above, if the cell below that coin and the cell to the right of that coin are empty. In other words, if a coin has an empty cell below it and an empty cell to its right, then you can remove that coin and replace it with two coins, one immediately below and one immediately to the right of the cell of the removed coin." The square of four cells in the upper left corner are called the 'bank." That’s it. There are no more rules. Let’s redraw the initial grid with a red line separating the four cells in the upper left corner. These four cells are called the ‘bank’. The challenge is to try to remove all of the coins from the bank or prove that it is impossible. There is a great solution to this problem using infinite geometric series.
Infinite Geometric Series proofs without words YouTube video - A selection of animated proofs of infinite geometric series.
Unit 1 Cumulative Review
Odd One Out Arithmetic and Geometric Sequences - A self-checking activity. Eight problems and nine answers. Solve the problems to find out which answer is the "odd one out".
Arithmetic and Geometric Sequences and Series Review Secret Message activity - Students work in pairs. Each student solves 10 questions. This creates part of a key that can decipher a secret message. They can work with a partner to get the other half of the key.
Series Review Scavenger Hunt - A scavenger hunt is a self checking activity where the answer to one question leads to the next question. When students complete all the questions correctly, they will end back at their starting question. You can print these questions out and post them on the walls around the room.
Arithmetic and Geometric Sequences Quizizz - This online formative assessment has a number of questions on arithmetic and geometric sequences and series.
Which is Greater? - An enrichment question for students looking for a bit of a challenge.
A New Arena - *Updated May 2025* Students create a proposal for a design for a seating plan for a new NHL arena. The proposal must include the number of seats in the new arena, the layout of those seats, and the price that should be charged for each seat (from the Alberta Assessment Consortium).