# Level 4 - Math & Problem Solving

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:

- Exponents and radicals
- Polynomials
- Linear equations and systems of linear equations
- Quadratic 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.

- Find length of AD.

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) = n^{2}