Foundations of Math 11 tutor for BC students, live online

Source: BC Foundations of Mathematics 11 curriculum. Big ideas, content and competencies come from the page as downloaded with curl on 23 October 2026. Modern Age Coders works independently of BC’s education ministry and every school district.

The problem. A school garden club grows tomatoes and kale in trays. A tomato tray needs 3 m² of bed space and 2 volunteer hours and yields about 5 kg; a kale tray needs 2 m² and 3 hours and yields about 4 kg. The club has 60 m² of beds and 48 volunteer hours for the season. How many trays of each should it plant to harvest the most?

1. Name the variables. Let t be tomato trays and k be kale trays.
2. Write the constraints. Space: 3t + 2k ≤ 60. Time: 2t + 3k ≤ 48. And t ≥ 0, k ≥ 0, because trays cannot be negative.
3. Write the objective function. Harvest H = 5t + 4k, to be maximized.
4. Graph the feasible region. With graphing technology, shade the region that satisfies all four inequalities. It is a four-sided shape with corners on the axes and one where the two boundary lines cross.
5. Find the crossing corner. Solve 3t + 2k = 60 and 2t + 3k = 48 together. Triple the first and double the second: 9t + 6k = 180 and 4t + 6k = 96. Subtract: 5t = 84, so t = 16.8 and k = 4.8.
6. Test the objective at every corner. The maximum of a linear objective over a region like this occurs at a corner. The program checks all four, then checks every whole-number plan.

# Garden club plan: maximize harvest inside the feasible region (ours)
# Tomato tray: 3 m^2 of bed, 2 volunteer hours, 5 kg. Kale tray: 2 m^2, 3 hours, 4 kg.
# Limits: 60 m^2 of bed space, 48 volunteer hours.

def feasible(t, k):
    return t >= 0 and k >= 0 and 3*t + 2*k <= 60 and 2*t + 3*k <= 48

def harvest(t, k):
    return 5*t + 4*k

# 1. The corners of the region (from solving pairs of boundary lines by hand)
corners = [(0, 0), (20, 0), (0, 16), (16.8, 4.8)]
for t, k in corners:
    print(f"corner ({t}, {k}): harvest {harvest(t, k):.1f} kg")

# 2. Trays come in whole numbers, so test every whole-number plan
top = max(((t, k) for t in range(21) for k in range(17) if feasible(t, k)),
           key=lambda p: harvest(*p))
print("top whole-number plan:", top, "harvest", harvest(*top), "kg")

corner (0, 0): harvest 0.0 kg
corner (20, 0): harvest 100.0 kg
corner (0, 16): harvest 64.0 kg
corner (16.8, 4.8): harvest 103.2 kg
top whole-number plan: (18, 3) harvest 102 kg

1. Deductive proof. Prove that the sum of any two odd integers is even.
2. Counter-example. A student notices that n² + n + 41 is prime for n = 0, 1, 2, 3 and 4, and conjectures it is always prime. Find a counter-example.
3. Game analysis. Two players take turns removing 1, 2 or 3 counters from a pile of 15. Whoever takes the last counter wins. Should you go first, and how many should you take?
4. Parallel lines. A transversal crosses two parallel lines, making alternate interior angles of (3x + 10)° and (5x − 30)°. Find x and the angle.
5. Polygons. Find the sum of the interior angles of a hexagon, and each interior angle of a regular hexagon.
6. Solution region. Is the point (2, 3) in the region defined by y < −x + 6 and y ≥ 2x − 3? Show the test.
7. Quadratic graph. For y = −x² + 6x − 5, give the vertex, the maximum, the axis of symmetry and the intercepts.
8. Linear-quadratic system. Find where y = x² − 4 and y = 2x − 1 meet.
9. z-score. A class test has mean 72 and standard deviation 8. What is the z-score of a mark of 84, and what does it tell you?
10. Confidence interval. A school survey reports that 62% of students walk or cycle to school, accurate within 4 percentage points, 19 times out of 20. State the interval and explain what 19 times out of 20 means.
11. Scale. A 1:200 model of a building is 45 cm tall and its footprint is 0.06 m². Find the real height and footprint.
12. Square-cube law. Every length of a solid is tripled. By what factors do its surface area, volume and surface-to-volume ratio change?

1. Ask how the course is assessed. Tests, a statistics project, presentations, and which graphing tools are allowed.
2. Learn the vocabulary of reasoning. Conjecture, inductive, deductive, counter-example, proof. Write one example of each.
3. Practise proofs in a set format. Statement and reason, line by line, for angle proofs; the teacher’s preferred layout is the one to use.
4. Get fluent with one graphing tool. Inequalities, quadratics and systems are graphed with technology in this course, so speed with the tool matters.
5. For optimization, follow the same five steps every time. Variables, constraints, objective, region, corners. Then ask whether the answer must be a whole number.
6. For statistics, start from the question. Pose it, decide what data answers it, collect, summarise with mean and standard deviation, and answer the question in a sentence.
7. For scale, write units everywhere. Convert before comparing, and square or cube the factor for area or volume.
8. Keep an explanation log. For each topic, one paragraph in your own words explaining why the method works.
9. Do a mixed review every two weeks. Our twelve questions above make a starting set.
10. Before a test, explain three answers out loud to someone who has not taken the course. If they follow, you are ready.