MCF3M · Ontario — quadratics, growth and decay, periodic motion, trigonometry, money

Grade 11 Math — Functions & Applications

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Formula pick

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Rearranging

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Setup & units

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Answers

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Quadratic Functions

L1
Reading the parabola
which number is a, b, c — and what each one does
★★★★★
Start
L2
The vertex
locate the turning point with x = −b/2a
★★★★★
Start
L3
Completing the square
half it, square it — and the vertex falls out
★★★★★
Start
L4
The quadratic formula
both roots of ax² + bx + c = 0, on demand
★★★★★
Start
L5
Counting the roots
Δ = b² − 4ac · the crossing count before the crossing
★★★★★
Start
L6
Sum and product of roots
Vieta's five-second audit — check without re-solving
★★★★★
Start
L7
The height of a throw
h = v₀t − ½gt² — the parabola you can throw
★★★★★
Start
★
The Apex
the boss · no calculator · launch to landing, every line feeds the next
★★★★★
Start

Exponential Growth & Decay

L9
Growth or decay
read the base — climbing, or fading?
★★★★★
Start
L10
Percent change
how big was the jump, measured from where you started
★★★★★
Start
L11
Growing by a ratio
A = A₀(1 + r)^t · asked every way
★★★★★
Start
L12
Decay and depreciation
(1 − r)^t · the car, the dose, the write-off
★★★★★
Start
L13
Half-life
count the halvings before you compute
★★★★★
Start
L14
Doubling time
N = N₀·2^(t/T) · and 72 in your head
★★★★★
Start
L15
Solving for time
the unknown is in the exponent — logs bring it down
★★★★★
Start
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The Petri Dish
the boss · no calculator · a culture doubles while its dye halves
★★★★★
Start

Periodic Functions

L17
Reading the cycle
period, frequency, amplitude — by their units
★★★★★
Start
L18
Period and frequency
T = 1/f, asked both ways
★★★★★
Start
L19
The wave equation
v = fλ · Hz times metres is m/s
★★★★★
Start
L20
The pendulum
length and gravity only — the bob never votes
★★★★★
Start
L21
Around the wheel
v = 2πr/T · the circle behind every sinusoid
★★★★★
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L22
A snapshot in time
x = A·cos(2πt/T) at the special angles
★★★★★
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The Metronome
the boss · no calculator · in strict time
★★★★★
Start

Trigonometry Applications

L24
Naming the sides
opposite, adjacent, hypotenuse — relative to WHICH angle?
★★★★★
Start
L25
Choosing the ratio
sine, cosine or tangent — pick the tool before touching a number
★★★★★
Start
L26
Heights and shadows
elevation, depression, and Pythagoras closing the triangle
★★★★★
Start
L27
The sine law
two angles and a side — solve a triangle with no right angle
★★★★★
Start
L28
The cosine law
two sides and the angle between them — find the third
★★★★★
Start
L29
Area without the height
½ab sin C · two sides and the angle they trap
★★★★★
Start
★
The Survey
the boss · no calculator · close the traverse, then state the area
★★★★★
Start

Sequences & Financial Math

L31
Spotting the pattern
adding the same amount, or multiplying by the same ratio?
★★★★★
Start
L32
Arithmetic sequences
tₙ = a + (n − 1)d · the off-by-one lives here
★★★★★
Start
L33
Arithmetic series
Gauss's handshake · n/2 identical pairs
★★★★★
Start
L34
Geometric sequences
tₙ = a·rⁿ⁻¹ · exponents count the steps
★★★★★
Start
L35
Geometric series
the multiplying total · the bridge to the annuity
★★★★★
Start
L36
Simple interest
I = Prt · percent wears a disguise
★★★★★
Start
L37
Compound interest
A = P(1 + i)ⁿ · interest earning interest
★★★★★
Start
L38
Annuities and loans
regular deposits grow, regular payments repay
★★★★★
Start
★
The First Paycheque
the boss · no calculator · three plans, one podium
★★★★★
Start

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