Addressing Common Math 30-1 Diploma Difficulties

The Math 30-1 Information Bulletin 2023-2024 includes a “Commentary on the Mathematics 30-1 Diploma Examinations”. Within this commentary, students’ strengths and areas for improvement are identified. It is no doubt a priority for every Math 30-1 teacher to prepare his or her students in the best possible manner. Since these comments are based on the results of thousands of students across the province, paying particular attention to these difficulties, would be prudent in terms of this preparation.

Let’s take a closer look at these areas for improvement. Sometimes a greater awareness and a little extra practice can make all the difference. You will find 9 mini-lessons addressing these difficulties. Each has a video (on average just over 11 min) and a set of about 8 practice questions complete with detailed solutions.

Relations and Functions

• “Stronger students are improving in their ability to represent a transformation using mapping notation, but weaker students still have difficulties using this notation”.
  • Using Mapping Notation to Represent a Transformation
  • https://mathpqjq.com/using-mapping-notation-to-represent-a-transformation/

• “Students continue to have difficulty determining the number of invariant points associated with different transformations”.
  • Number of Invariant Points
  • https://mathpqjq.com/number-of-invariant-points/

• “Students have difficulty restricting the domain of a function so that the inverse will also be a function”.
  • Restricting Domain so Inverse is a Function
  • https://mathpqjq.com/restricting-domain-so-inverse-is-a-function/

• “Students are able to use the power law to simplify a logarithmic expression, but many continue to have difficulty combining multiple logarithm laws to simplify an expression into a single logarithm or to solve a logarithmic equation”.
  • Combining Multiple Logarithmic Laws
  • https://mathpqjq.com/combining-multiple-logarithm-laws/

• “Students continue to have difficulty determining the range of a rational function that contains a point of discontinuity”.
  • Range of a Rational Function With a Point of Discontinuity
  • https://mathpqjq.com/range-of-a-rational-function-with-a-point-of-discontinuity/

• “Students are able to determine the domain and range of a function after a transformation, but many students have difficulty determining the domain after the division of two functions”.
  • Domain After the Division of Two Functions
  • https://mathpqjq.com/domain-after-the-division-of-two-functions/

Trigonometry

• “Students are able to solve second-degree trigonometric equations in a variety of domains, but many students have difficulty solving equations when an identity substitution is required”.
  • Solving a Trig Equation Using Identity Substitution
  • https://mathpqjq.com/solving-a-trig-equation-using-identity-substitution/

Permutations, Combinations and The Binomial Theorem

• “Students are able to solve permutation problems that involve one or two constraints, but many students have difficulty solving problems with multiple cases”.
  • Combinatorics Problems With Cases
  • https://mathpqjq.com/combinatorics-problems-with-cases/

• “Students are able to identify the correct statements about the expansion of a binomial with linear terms; however, many students have difficulty determining specific terms in the expansion of a binomial with non-linear terms”.
  • The Binomial Theorem With Non-Linear Terms
  • https://mathpqjq.com/binomial-theorem-with-non-linear-terms/