NBCC Skill Ready Math 120

Cheatsheet Content

### Numbers and Operations #### Order of Operations (BEDMAS/PEMDAS) - **B/P**rackets/Parentheses - **E**xponents - **D/M**ivision/Multiplication (left to right) - **A/S**ddition/Subtraction (left to right) #### Fractions - **Addition/Subtraction:** Find common denominator. $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ - **Multiplication:** Multiply numerators and denominators. $$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$ - **Division:** Multiply by the reciprocal. $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$$ #### Decimals - **Rounding:** Identify place value, look at next digit. If 5 or greater, round up. #### Percentages - **Percent to Decimal:** Divide by 100 (e.g., 25% = 0.25) - **Decimal to Percent:** Multiply by 100 (e.g., 0.75 = 75%) - **Finding a Percent of a Number:** `Part = Percent (as decimal) x Whole` - **Percent Increase/Decrease:** $$\frac{\text{Change}}{\text{Original}} \times 100\%$$ #### Ratios and Proportions - **Ratio:** Comparison of two quantities (e.g., $a:b$ or $\frac{a}{b}$) - **Proportion:** Two ratios are equal (e.g., $\frac{a}{b} = \frac{c}{d}$) - Cross-multiplication: $ad = bc$ ### Measurement #### Unit Conversions - **Metric System (SI):** Based on powers of 10. - Kilo (k) = 1000 - Hecto (h) = 100 - Deca (da) = 10 - Base Unit (m, L, g) = 1 - Deci (d) = 0.1 - Centi (c) = 0.01 - Milli (m) = 0.001 - **Imperial System:** - Length: 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5280 ft - Weight: 1 lb = 16 oz, 1 ton = 2000 lb - Volume: 1 cup = 8 fl oz, 1 pint = 2 cups, 1 quart = 2 pints, 1 gallon = 4 quarts - **Between Systems:** (Approximate) - 1 inch $\approx$ 2.54 cm - 1 foot $\approx$ 30.48 cm - 1 mile $\approx$ 1.609 km - 1 gallon $\approx$ 3.785 L - 1 kg $\approx$ 2.205 lbs #### Area - **Rectangle:** $A = l \times w$ - **Square:** $A = s^2$ - **Triangle:** $A = \frac{1}{2} b \times h$ - **Circle:** $A = \pi r^2$ ($r$ = radius) - **Trapezoid:** $A = \frac{1}{2} (a+b)h$ ($a, b$ = parallel sides) #### Perimeter and Circumference - **Perimeter of a Polygon:** Sum of all side lengths. - **Circumference of a Circle:** $C = 2 \pi r$ or $C = \pi d$ ($d$ = diameter) #### Volume - **Rectangular Prism:** $V = l \times w \times h$ - **Cube:** $V = s^3$ - **Cylinder:** $V = \pi r^2 h$ - **Cone:** $V = \frac{1}{3} \pi r^2 h$ - **Sphere:** $V = \frac{4}{3} \pi r^3$ #### Surface Area - **Rectangular Prism:** $SA = 2(lw + lh + wh)$ - **Cube:** $SA = 6s^2$ - **Cylinder (closed):** $SA = 2\pi r^2 + 2\pi rh$ ### Geometry #### Pythagorean Theorem - For a right-angled triangle with legs $a, b$ and hypotenuse $c$: $$a^2 + b^2 = c^2$$ #### Angles - **Straight Angle:** $180^\circ$ - **Right Angle:** $90^\circ$ - **Complementary Angles:** Sum to $90^\circ$ - **Supplementary Angles:** Sum to $180^\circ$ - **Angles in a Triangle:** Sum to $180^\circ$ ### Algebra #### Solving Linear Equations - Isolate the variable using inverse operations. - Example: $2x + 5 = 11$ $2x = 11 - 5$ $2x = 6$ $x = \frac{6}{2}$ $x = 3$ #### Formulas - **Rearranging Formulas:** Use inverse operations to solve for a specific variable. - Example: Solve $P = 2l + 2w$ for $l$ $P - 2w = 2l$ $l = \frac{P - 2w}{2}$ #### Graphing Linear Equations - **Slope-Intercept Form:** $y = mx + b$ - $m$ = slope (rise/run) - $b$ = y-intercept (where the line crosses the y-axis) - **Slope Formula:** Given two points $(x_1, y_1)$ and $(x_2, y_2)$: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ ### Data Analysis #### Measures of Central Tendency - **Mean (Average):** Sum of all values divided by the number of values. $$\bar{x} = \frac{\sum x}{n}$$ - **Median:** The middle value when data is ordered from least to greatest. If an even number of values, average the two middle values. - **Mode:** The value that appears most frequently in a data set. #### Probability - **Probability of an Event:** $$P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}$$ - **Probability Range:** $0 \le P(\text{Event}) \le 1$ (or 0% to 100%)