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MCV4U · MDM4U · Ontario — rates of change, vectors, data and money

Grade 12 Math

0 of 230 stars · 0 of 46 lessons done · report card →
Formula pick
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Rearranging
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Setup & units
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Answers
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Rates of Change

  • L1
    Reading the rate
    which number is a rate, which is an amount
    ★★★★★
    Start
  • L2
    Slope is a rate of change
    the secant between two readings, computed
    ★★★★★
    Start
  • L3
    Average velocity
    d = v̄t · the trapezoid under the velocity line
    ★★★★★
    Start
  • L4
    Velocity as the derivative
    v = v₀ + at · the rate of the rate
    ★★★★★
    Start
  • L5
    The position function
    d = v₀t + ½at² · where the half comes from
    ★★★★★
    Start
  • L6
    The no-time shortcut
    v² = v₀² + 2ad · when the clock is missing
    ★★★★★
    Start
  • ★
    The Final Descent
    the boss · no calculator · one runaway cart, line by line
    ★★★★★
    Start

Optimization & the Vertex

  • L8
    Reading the parabola
    which coefficient is which, and where the optimum lives
    ★★★★★
    Start
  • L9
    Finding the turning point
    x = −b/2a · the input that optimizes
    ★★★★★
    Start
  • L10
    The peak value
    k = c − b²/4a · what the optimum is actually worth
    ★★★★★
    Start
  • L11
    Roots and the discriminant
    b² − 4ac decides how many answers exist
    ★★★★★
    Start
  • L12
    What the roots whisper
    sum and product of roots, without solving a thing
    ★★★★★
    Start
  • L13
    The break-even point
    Q = F/(p − v) · optimization in business clothes
    ★★★★★
    Start
  • ★
    The Golden Vertex
    the boss · no calculator · launch it, peak it, land it
    ★★★★★
    Start

Vectors

  • L15
    Reading the vector
    magnitude, component or angle — which is which
    ★★★★★
    Start
  • L16
    How long is the arrow
    |v| = √(vₓ² + v_y²), asked every way
    ★★★★★
    Start
  • L17
    Casting the shadows
    vₓ = |v|cos θ, v_y = |v|sin θ · resolve the vector
    ★★★★★
    Start
  • L18
    The direction angle
    θ = tan⁻¹(v_y / vₓ) · which way it points
    ★★★★★
    Start
  • L19
    Two forces, one resultant
    R = √(A² + B² + 2AB·cos θ) · adding at an angle
    ★★★★★
    Start
  • L20
    The dot product
    a·b two ways — components, or lengths and the angle
    ★★★★★
    Start
  • L21
    The angle between
    cos θ = a·b / |a||b| · rearranged for the angle
    ★★★★★
    Start
  • L22
    The cross product and area
    |a×b| = |a||b|sin θ · the parallelogram it sweeps
    ★★★★★
    Start
  • L23
    Work is a dot product
    W = Fₓdₓ + F_yd_y · only the parallel part pushes
    ★★★★★
    Start
  • ★
    The River Crossing
    the boss · no calculator · current, heading and the true track
    ★★★★★
    Start

Counting & Probability

  • L25
    Reading the odds
    probability, odds or a count — which is which
    ★★★★★
    Start
  • L26
    Favourable over total
    P = f / n, and the other side of it
    ★★★★★
    Start
  • L27
    Either, or, or both
    the addition rules · subtract the overlap once
    ★★★★★
    Start
  • L28
    And then
    multiplication rules · with replacement, without, and given
    ★★★★★
    Start
  • L29
    Counting the ways
    factorials, permutations, combinations — order or not
    ★★★★★
    Start
  • L30
    The binomial distribution
    exactly k successes in n tries
    ★★★★★
    Start
  • L31
    At least one, and what it's worth
    one minus none · the first success · the price of a bet
    ★★★★★
    Start
  • ★
    The Full House
    the boss · no calculator · count it, chance it, price it
    ★★★★★
    Start

Statistics & Data

  • L33
    Reading the data
    centre, spread or position — which is which
    ★★★★★
    Start
  • L34
    Measuring the spread
    variance, standard deviation, range and IQR
    ★★★★★
    Start
  • L35
    How unusual is it
    z = (x − μ)/σ, asked every way
    ★★★★★
    Start
  • L36
    Fences and outliers
    Q₁ − 1.5·IQR and Q₃ + 1.5·IQR — who gets flagged
    ★★★★★
    Start
  • L37
    The line of best fit
    slope from r, intercept through the means, then predict
    ★★★★★
    Start
  • L38
    How good is the fit
    R², percent error, and the honest average
    ★★★★★
    Start
  • ★
    The Data Defence
    the boss · no calculator · one dataset, interrogated line by line
    ★★★★★
    Start

Financial Math

  • L40
    Percent change and simple interest
    I = Prt · money's first formula
    ★★★★★
    Start
  • L41
    Compound growth
    A = P(1 + r/n)ⁿᵗ · interest on the interest
    ★★★★★
    Start
  • L42
    Money travels in time
    PV = FV / (1 + r)ᵗ · what a future amount is worth today
    ★★★★★
    Start
  • L43
    How long to double
    the rule of 72, and solving for the exponent honestly
    ★★★★★
    Start
  • L44
    The annuity
    regular deposits, compounding as they land
    ★★★★★
    Start
  • L45
    Loans and honest rates
    the payment formula, total interest, and the EAR
    ★★★★★
    Start
  • ★
    The Mortgage Final
    the boss · no calculator · one household, one year, every formula
    ★★★★★
    Start

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