Grade 10 Math formula sheet: printable

Math 10-1 Unit Price (Price per Unit Quantity)

p = \frac{C}{m}

Price per unit of quantity, the number that makes two package sizes comparable on a shelf.

Math 10-2 Percent Change

c = \frac{x_{\text{new}} - x_{\text{old}}}{x_{\text{old}}}

Relative change from an old value to a new one, as a fraction of the old value.

Math 10-3 Recipe Scaling (Ingredient for a New Yield)

Q_2 = Q_1 \cdot \frac{S_2}{S_1}

Ingredient quantity rescaled from the yield a recipe was written for to the yield you actually want.

Math 10-4 Map Scale to Real Distance

d = m\,S

Real distance from a map measurement times the scale denominator.

Math 10-5 Discount Price (Percentage Off)

S = L\,(1 - d)

Price after a percentage is taken off the list price, and the discount implied by any pair of list…

Math 10-6 Sales Tax and Total Price

T = P\,(1 + r)

Total payable from a pre-tax price and a tax rate, and the reverse: recovering the pre-tax price…

Math 10-7 Slope Between Two Points

m = \frac{y_2 - y_1}{x_2 - x_1}

Steepness of a line as rise over run between two points.

Math 10-8 Slope-Intercept Form of a Line

y = mx + b

Equation of a straight line from its slope and y-intercept.

Math 10-9 Slope from Standard Form of a Line

m = -\frac{A}{B}

Slope of a line written in standard form Ax + By = C, read straight off the two coefficients…

Math 10-10 x-Intercept of a Line

x_{\text{int}} = -\frac{b}{m}

Where a line in slope-intercept form crosses the x-axis, found by setting y to zero and solving the…

Math 10-11 Point-Slope Form of a Line

y = y_1 + m(x - x_1)

Equation of a straight line through one known point with a known slope, giving the y-value at any x…

Math 10-12 Speed, Distance & Time

v = \tfrac{d}{t}

Average speed from distance travelled and elapsed time.

Math 10-13 Fuel Consumption (L/100 km)

C = \frac{100\,V}{d}

Fuel consumption in litres per hundred kilometres from the fuel burned and the distance covered.

Math 10-14 Miles per Gallon ↔ L/100 km

C = \dfrac{235.215}{M}

The reciprocal relation between litres per hundred kilometres and US miles per gallon: their…

Math 10-15 Midpoint Formula

x_m = \frac{x_1 + x_2}{2}

The coordinate halfway between two endpoints along one axis; apply it to x and again to y for the…

Math 10-16 Distance Formula (2D)

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Straight-line distance between two points in the coordinate plane.

Math 10-17 Pythagorean Theorem

a^{2} + b^{2} = c^{2}

Relates the three sides of a right triangle.

Math 10-18 Rectangle Area

A = l \cdot w

Area of a rectangle as length times width.

Math 10-19 Area of a Triangle

A = \tfrac{1}{2} b h

Area from base and perpendicular height.

Math 10-20 Area of a Circle

A = \pi r^{2}

Area enclosed by a circle of radius r.

Math 10-21 Trapezoid Area

A = \frac{a + b}{2} \cdot h

Area of a trapezoid as the average of its two parallel sides times the perpendicular height.

Math 10-22 Parallelogram Area

A = b \cdot h

Area of a parallelogram from its base and perpendicular height.

Math 10-23 Rectangle Perimeter

P = 2(l + w)

Perimeter of a rectangle from its length and width.

Math 10-24 Square Perimeter

P = 4s

Perimeter of a square as four times its side length.

Math 10-25 Parallelogram Perimeter

P = 2(a + b)

Perimeter of a parallelogram from its two side lengths.

Math 10-26 Triangle Perimeter

P = a + b + c

Perimeter of a triangle as the sum of its three sides.

Math 10-27 Circumference of a Circle

C = 2 \pi r

Distance around a circle of radius r.

Math 10-28 Ellipse Perimeter (Ramanujan Approximation)

P \approx \pi \left[ 3(a+b) - \sqrt{(3a+b)(a+3b)} \right]

Perimeter of an ellipse by Ramanujan's second approximation: accurate to better than one part in a…

Math 10-29 Circular Sector Area

A = \frac{1}{2} r^{2} \theta

Area of a pie-slice sector of a circle from its radius and central angle in radians.

Math 10-30 Arc Length

s = r \theta

Length of a circular arc as radius times central angle in radians.

Math 10-31 Rectangular Prism Volume

V = l \cdot w \cdot h

Volume of a box as the product of its length, width, and height.

Math 10-32 Cube Volume

V = a^{3}

Volume of a cube as its edge length raised to the third power.

Math 10-33 Triangular Prism Volume

V = \tfrac{1}{2} b h_t L

Volume of a triangular prism: the triangular end area times the prism length, from the triangle's…

Math 10-34 Prism Volume (General Cross-Section)

V = B L

Volume of any prism or extrusion whose cross-section does not change along its length:…

Math 10-35 Cylinder Volume

V = \pi r^{2} h

Volume of a right circular cylinder from its radius and height, using π ≈ 3.14159265.

Math 10-36 Cone Volume

V = \frac{1}{3} \pi r^{2} h

Volume of a right circular cone (one-third of the matching cylinder) using π ≈ 3.14159265.

Math 10-37 Pyramid Volume

V = \frac{1}{3} B h

Volume of any pyramid as one-third of its base area times its perpendicular height.

Math 10-38 Sphere Volume

V = \frac{4}{3} \pi r^{3}

Volume enclosed by a sphere of radius r, using π ≈ 3.14159265.

Math 10-39 Sphere Surface Area

S = 4 \pi r^{2}

Surface area of a sphere of radius r, using π ≈ 3.14159265.

Math 10-40 Rectangular Prism Surface Area

A = 2(lw + lh + wh)

Total surface area of a box: three pairs of matching rectangular faces, from length, width and…

Math 10-41 Cube Surface Area

S = 6 a^{2}

Surface area of a cube as six times the area of one square face.

Math 10-42 Cylinder Surface Area

S = 2 \pi r^{2} + 2 \pi r h

Total surface area of a closed cylinder (two end caps plus the wrapped side) using π ≈ 3.14159265.

Math 10-43 Cylinder Lateral Surface Area

A = 2\pi r h

Area of a cylinder's curved wall only, with no end caps: the label on a can, the insulation around…

Math 10-44 Cone Lateral Surface Area

A = \pi r l

Curved surface of a right circular cone from its base radius and slant height, excluding the base…

Math 10-45 Cone Slant Height

l = \sqrt{r^2 + h^2}

Slant height of a right circular cone by Pythagoras on its axial cross-section, from base radius…

Math 10-46 Hemisphere Volume

V = \frac{2}{3}\pi r^3

Volume of half a sphere, exactly half of the full sphere's (4/3)*pi*r^3.

Math 10-47 Hemisphere Total Surface Area

A = 3\pi r^2

Total surface of a solid hemisphere: the curved half-sphere 2*pi*r^2 plus the flat circular base…

Math 10-48 Right-Triangle Sine Ratio (SOH)

\sin\theta = \frac{o}{h}

Relates an acute angle of a right triangle to its opposite side and the hypotenuse.

Math 10-49 Right-Triangle Cosine Ratio (CAH)

\cos\theta = \frac{a}{h}

Relates an acute angle of a right triangle to its adjacent side and the hypotenuse.

Math 10-50 Right-Triangle Tangent Ratio (TOA)

\tan\theta = \frac{o}{a}

Relates an acute angle of a right triangle to the ratio of its opposite and adjacent legs.

Math 10-51 Percent Grade from Rise and Run

G = \frac{100\,\Delta h}{L}

Percent grade is one hundred times the vertical rise divided by the horizontal run, measured level,…

Math 10-52 Grade to Slope Angle

\theta = \arctan\!\left(\frac{G}{100}\right)

Converts a percent grade into the slope angle measured from horizontal, and back again with the…

Math 10-53 Slope Ratio (H:V) to Percent Grade

G = \frac{100}{n}

Converts an embankment slope quoted as n horizontal to one vertical into the equivalent percent…

Math 10-54 Simple Interest

I = P \, r \, t

Interest earned on a principal at a flat rate per period, without compounding.

Math 10-55 Compound Interest (Periodic)

A = P \left( 1 + \frac{r}{n} \right)^{n t}

Amount after t periods when interest compounds n times per period at rate r.

Math 10-56 Effective Annual Rate from a Nominal Rate

\mathit{EAR} = \left(1 + \frac{r}{m}\right)^{m} - 1

What a quoted nominal annual rate really costs or earns once it compounds m times a year: 12%…

Math 10-57 Rule of 72 (Doubling Time)

n \approx \frac{0.72}{i}

Mental-arithmetic estimate of how many periods it takes money to double at rate i: with the rate…

Math 10-58 Present Value

\mathit{PV} = \frac{\mathit{FV}}{(1 + r)^{t}}

Today's value of a future amount, discounted at rate r per period.