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Grade 10 Math — formula sheet

Ratios, lines, shapes, trigonometry and money · 53 formulas · metric edition 1

The full booklet — learning zone, problems, answer key
Unit Price (Price per Unit Quantity)
p=Cmp = \frac{C}{m}
Percent Change
c=xnew−xoldxoldc = \frac{x_{\text{new}} - x_{\text{old}}}{x_{\text{old}}}
Recipe Scaling (Ingredient for a New Yield)
Q2=Q1⋅S2S1Q_2 = Q_1 \cdot \frac{S_2}{S_1}
Map Scale to Real Distance
d=m Sd = m\,S
Discount Price (Percentage Off)
S=L (1−d)S = L\,(1 - d)
Sales Tax and Total Price
T=P (1+r)T = P\,(1 + r)
Slope Between Two Points
m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
Slope-Intercept Form of a Line
y=mx+by = mx + b
Slope from Standard Form of a Line
m=−ABm = -\frac{A}{B}
x-Intercept of a Line
xint=−bmx_{\text{int}} = -\frac{b}{m}
Point-Slope Form of a Line
y=y1+m(x−x1)y = y_1 + m(x - x_1)
Speed, Distance & Time
v=dtv = \tfrac{d}{t}
Fuel Consumption (L/100 km)
C=100 VdC = \frac{100\,V}{d}
Miles per Gallon ↔ L/100 km
C⋅M=235.215C \cdot M = 235.215
Midpoint Formula
xm=x1+x22x_m = \frac{x_1 + x_2}{2}
Distance Formula (2D)
d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Pythagorean Theorem
a2+b2=c2a^{2} + b^{2} = c^{2}
Rectangle Area
A=l⋅wA = l \cdot w
Area of a Triangle
A=12bhA = \tfrac{1}{2} b h
Area of a Circle
A=πr2A = \pi r^{2}
Trapezoid Area
A=a+b2⋅hA = \frac{a + b}{2} \cdot h
Parallelogram Area
A=b⋅hA = b \cdot h
Circumference of a Circle
C=2πrC = 2 \pi r
Circular Sector Area
A=12r2θA = \frac{1}{2} r^{2} \theta
Arc Length
s=rθs = r \theta
Rectangular Prism Volume
V=l⋅w⋅hV = l \cdot w \cdot h
Cube Volume
V=a3V = a^{3}
Triangular Prism Volume
V=12bhtLV = \tfrac{1}{2} b h_t L
Prism Volume (General Cross-Section)
V=BLV = B L
Cylinder Volume
V=πr2hV = \pi r^{2} h
Cone Volume
V=13πr2hV = \frac{1}{3} \pi r^{2} h
Pyramid Volume
V=13BhV = \frac{1}{3} B h
Sphere Volume
V=43πr3V = \frac{4}{3} \pi r^{3}
Sphere Surface Area
S=4πr2S = 4 \pi r^{2}
Rectangular Prism Surface Area
A=2(lw+lh+wh)A = 2(lw + lh + wh)
Cube Surface Area
S=6a2S = 6 a^{2}
Cylinder Surface Area
S=2πr2+2πrhS = 2 \pi r^{2} + 2 \pi r h
Cylinder Lateral Surface Area
A=2πrhA = 2\pi r h
Cone Lateral Surface Area
A=πrlA = \pi r l
Cone Slant Height
l=r2+h2l = \sqrt{r^2 + h^2}
Hemisphere Volume
V=23πr3V = \frac{2}{3}\pi r^3
Hemisphere Total Surface Area
A=3πr2A = 3\pi r^2
Right-Triangle Sine Ratio (SOH)
sin⁡θ=oh\sin\theta = \frac{o}{h}
Right-Triangle Cosine Ratio (CAH)
cos⁡θ=ah\cos\theta = \frac{a}{h}
Right-Triangle Tangent Ratio (TOA)
tan⁡θ=oa\tan\theta = \frac{o}{a}
Percent Grade from Rise and Run
G=100 ΔhLG = \frac{100\,\Delta h}{L}
Grade to Slope Angle
θ=arctan⁡ ⁣(G100)\theta = \arctan\!\left(\frac{G}{100}\right)
Slope Ratio (H:V) to Percent Grade
G=100nG = \frac{100}{n}
Simple Interest
I=P r tI = P \, r \, t
Compound Interest (Periodic)
A=P(1+rn)ntA = P \left( 1 + \frac{r}{n} \right)^{n t}
Effective Annual Rate from a Nominal Rate
EAR=(1+rm)m−1\mathit{EAR} = \left(1 + \frac{r}{m}\right)^{m} - 1
Rule of 72 (Doubling Time)
n≈0.72in \approx \frac{0.72}{i}
Present Value
PV=FV(1+r)t\mathit{PV} = \frac{\mathit{FV}}{(1 + r)^{t}}