formula.expert
MPM2D-adjacent · Ontario

Grade 10 Math

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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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Proportion & Percent

  • L1
    Reading rates
    which number is the rate, the amount, the total
    ★★★★★
    Start
  • L2
    The better buy
    price per kilogram · make two tags comparable
    ★★★★★
    Start
  • L3
    Scaling the recipe
    Q₂ = Q₁ · S₂/S₁ · every ingredient rides the factor
    ★★★★★
    Start
  • L4
    Reading the map
    d = m·S · the cm-to-km chain
    ★★★★★
    Start
  • L5
    Percent off
    S = L·(1 − d) · and the climb back to the sticker
    ★★★★★
    Start
  • L6
    Adding the tax
    T = P·(1 + r) · the register's one move
    ★★★★★
    Start
  • L7
    Percent change
    c = (new − old)/old · drops are negative
    ★★★★★
    Start
  • ★
    The Checkout
    the boss · no calculator · sticker to till
    ★★★★★
    Start

Linear Relations & Rates

  • L9
    Rise over run
    reading a slope's sign and size
    ★★★★★
    Start
  • L10
    Slope from two points
    m = Δy/Δx · mind the order
    ★★★★★
    Start
  • L11
    y = mx + b
    the line's uniform · y, m or b in turn
    ★★★★★
    Start
  • L12
    Other forms of the line
    standard form, intercepts, point-slope
    ★★★★★
    Start
  • L13
    Speed is a slope
    v = d/t on the distance–time graph
    ★★★★★
    Start
  • L14
    At the pump
    L/100 km · price per litre · range
    ★★★★★
    Start
  • L15
    Midpoint and distance
    halfway points and 3-4-5 spans
    ★★★★★
    Start
  • ★
    The Delivery Run
    the boss · no calculator · one route, every rate
    ★★★★★
    Start

Area & Perimeter

  • L17
    Naming the formula
    which shape wears which formula
    ★★★★★
    Start
  • L18
    Rectangles and parallelograms
    length times width · the slant-side lie
    ★★★★★
    Start
  • L19
    Triangles and trapezoids
    the half, and the average of two sides
    ★★★★★
    Start
  • L20
    Circles
    πr² inside, 2πr around · r is HALF of d
    ★★★★★
    Start
  • L21
    Sectors and arcs
    a slice's fair share of the pie
    ★★★★★
    Start
  • L22
    Area in reverse
    divide back, un-square, recover the side
    ★★★★★
    Start
  • L23
    Composite floors
    cut strange floors into friendly shapes
    ★★★★★
    Start
  • ★
    The Paint Estimate
    the boss · no calculator · paint by numbers
    ★★★★★
    Start

Volume & Surface Area

  • L25
    Prisms
    boxes, cubes and tents — base times length
    ★★★★★
    Start
  • L26
    Cylinders
    V = πr²h · asked every way
    ★★★★★
    Start
  • L27
    The one-third family
    cones and pyramids — never forget the third
    ★★★★★
    Start
  • L28
    Spheres
    the ball, filled and skinned — cubes grow fast
    ★★★★★
    Start
  • L29
    Wrapping the box
    surface area · faces come in pairs
    ★★★★★
    Start
  • L30
    Wrapping the curves
    labels, lids and the slant — πrl needs l first
    ★★★★★
    Start
  • L31
    Litres and cubes
    cm³, L and m³ · the bridge comes cubed
    ★★★★★
    Start
  • L32
    Volume in reverse
    given V, find the edge, radius or height
    ★★★★★
    Start
  • ★
    The Grain Silo
    the boss · no calculator · π rides until the last line
    ★★★★★
    Start

Right-triangle trigonometry

  • L34
    Labelling the sides
    opposite, adjacent, hypotenuse — names that move
    ★★★★★
    Start
  • L35
    Pythagoras
    a² + b² = c² · add for the hypotenuse, subtract for a leg
    ★★★★★
    Start
  • L36
    Choosing the ratio
    SOH CAH TOA · let the sides pick the tool
    ★★★★★
    Start
  • L37
    Finding a side
    multiply or divide by the ratio — the triangle decides
    ★★★★★
    Start
  • L38
    Finding the angle
    sin⁻¹, cos⁻¹, tan⁻¹ · the ratio, run backwards
    ★★★★★
    Start
  • L39
    Elevation and depression
    look up, look down — the tangent measures both
    ★★★★★
    Start
  • L40
    Grades and slopes
    percent grade, n:1 ratio, slope angle — one hill, three costumes
    ★★★★★
    Start
  • ★
    The Ramp Inspection
    the boss · no calculator · one ramp against the code
    ★★★★★
    Start

Money & Interest

  • L42
    Reading the loan
    principal, rate, time, interest — who's who
    ★★★★★
    Start
  • L43
    Simple interest
    I = P·r·t, asked every way
    ★★★★★
    Start
  • L44
    Compound interest
    A = P(1 + r)ᵗ · interest earning interest
    ★★★★★
    Start
  • L45
    Compounding frequency
    the fine print: r/n and n·t, plus the honest rate
    ★★★★★
    Start
  • L46
    The rule of 72
    the doubling clock · no calculator needed
    ★★★★★
    Start
  • L47
    Present value
    PV = FV / (1 + r)ᵗ · growth, run backwards
    ★★★★★
    Start
  • L48
    Simple vs compound
    two paths, one deposit · the gap is the answer
    ★★★★★
    Start
  • ★
    The Savings Ledger
    the boss · no calculator · every line feeds the next
    ★★★★★
    Start

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