Pre-Calculus 12 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 12 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
PCB01 Students will be expected to apply the fundamental counting principle to solve problems. [C, PS, R, V]
PCB01.01 Count the total number of possible choices that can be made, using graphic organizers such as lists and tree diagrams.
PCB01.02 Explain, using examples, why the total number of possible choices is found by multiplying rather than adding the number of ways the individual choices can be made.
PCB01.03 Solve a simple counting problem by applying the fundamental counting principle.
PCB02 Students will be expected to determine the number of permutations of n elements taken r at a time to solve problems. [C, PS, R, V]
PCB02.01 Count, using graphic organizers such as lists and tree diagrams, the number of ways of arranging the elements of a set in a row.
PCB02.02 Determine, in factorial notation, the number of permutations of n different elements taken n at a time to solve a problem.
PCB02.03 Determine, using a variety of strategies, the number of permutations of n different elements taken r at a time to solve a problem.
PCB02.04 Explain why n must be greater than or equal to r in the notation ₙ Pᵣ .
PCB02.05 Solve an equation that involves ₙ Pᵣ notation.
PCB02.06 Explain, using examples, the effect on the total number of permutations when two or more elements are identical.
PCB03 Students will be expected to determine the number of combinations of n different elements taken r at a time to solve problems. [C, PS, R, V]
PCB03.01 Explain, using examples, the difference between a permutation and a combination.
PCB03.02 Determine the number of ways that a subset of k elements can be selected from a set of n different elements.
PCB03.03 Determine the number of combinations of n different elements taken r at a time to solve a problem.
PCB03.04 Explain why n must be greater than or equal to r in the notation ₙ Cᵣ or (n r).
PCB03.05 Explain, using examples, why n_C_r = n_C_(n-r) or (n r) = (n (n-r)).
PCB03.06 Solve an equation that involves or ₙ Cᵣ or (n r) notation, such as n_C_2 =15 or (n 2) =15.
PCB04 Students will be expected to expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers). [CN, R, V]
PCB04.01 Explain the patterns found in the expanded form of (x + y)ⁿ , n ≤ 4, and n∈ N by multiplying n factors of (x + y).
PCB04.02 Explain how to determine the subsequent row in Pascal’s triangle, given any row.
PCB04.03 Relate the coefficients of the terms in the expansion of (x + y)ⁿ to the (n + 1) row in Pascal’s triangle.
PCB04.04 Explain, using examples, how the coefficients of the terms in the expansion of (x + y)ⁿ are determined by combinations.
PCB04.05 Expand, using the binomial theorem, (x + y )ⁿ.
PCB04.06 Determine a specific term in the expansion of (x + y )ⁿ.
All of the outcomes for this unit have been removed from Pre-calculus 12 curriculum.