 # Level 4 - Math & Problem Solving

SPECIAL NOTE: Our intention is still to offer both in-class and virtual online options for our Fall/Winter programs, so that clients can choose which way they wish to learn.

When we do offer in-class options, we will be following strict protocol for the health and safety of our students and staff, and ensuring we not only adhere to government requirements but exceed safety expectations.

More information on our live online distance learning can be found HERE.

Information on refer-a-friend discounts and virtual discounts is available HERE.

Our Level 4 Math & Problem Solving course targets students in Grades 8 to 10. This level addresses difficult topics in math and applies advanced problem-solving strategies.

Level 4 instruction includes, but is not limited to:

• Polynomials
• Linear equations and systems of linear equations
• Problem solving for linear equations, systems of equations, and for quadratic equations
• Geometry on a plane (axioms, theorems proof, problem solving)
• Introduction to trigonometry: trigo ratios, solving identities, sin and cosine laws, problem solving
• Arithmetic and geometric sets and series
• Mathematical induction
• Fundamental law of combinatorics, permutations, and combinations
• Logic problems – higher level content (see Levels 1 – 3)
• Brain teasers

Prerequisite for Level 4: Completion of Level 3 OR successful completion of assessment interview (for new students).

##### Sample problems

Given trapezoid ABCD. MN is a mid-line of ABCD. MN = 28cm.
Sides AB and CD continued until they meet in point P. APD = 30°.
A circle with diameter MN is drawn with the center O in
the middle of mid-line MN. Points B and C are on the circle. Stephanie and Elizabeth live in houses on the same street. The street is straight and there is a very high transmission antenna between their houses. Stephanie observes from her house the top of the antenna at the angle of elevation 33°, but Elizabeth observes from her house the top of the antenna at the angle of elevation 47°. How high is the top of the antenna from the ground, if Elizabeth’s house is 120 meters nearer to the antenna than Stephanie’s house?

Prove the following trigonometric identity: Prove the following using mathematical induction:
1 + 3 + 5 + 7 + . . . + (2n – 1) = n2