Trades Math Review Flashcards: Formulas, Geometry, Percent, Ratios, Notation, and Error Analysis

A comprehensive set of practice questions covering formulas, geometry, circles, percent, ratios, rates, proportions, scientific notation, and error analysis from the lecture notes.

What is a variable in a formula?

An unknown value represented by a letter.

How can multiplication be written in formulas?

As 2A, 2*A, 2(A), or (2)(A).

How can division be written in formulas?

As 3/B or 3 ÷ B.

Write the cost formula for nails costing $2.42 per pound with $15 shipping, where w is pounds.

C = 2.42w + 15.

Find the total cost for 7 pounds of nails using the nails formula C = 2.42w + 15.

$31.94 (C = 2.42×7 + 15 = 16.94 + 15 = 31.94).

Describe the Uber fare formula.

Fare = Base Fare + (Cost per minute × time in ride) + (Cost per mile × ride distance) + Booking Fee.

Calculate Uber fare with base $6, 0.15/min, 27 minutes, 1.57/mile, 19.8 miles, and $0.55 booking fee.

$41.69 (6 + 0.15×27 + 1.57×19.8 + 0.55 = 6 + 4.05 + 31.086 + 0.55 = 41.686 ≈ $41.69).

If the weather forecast shows 29°C, should you wear a jacket or shorts?

Shorts (29°C is warm).

What is a polygon?

A closed plane figure with three or more angles and three or more straight sides.

How do you find the perimeter of a polygon?

Add the lengths of all its sides.

Define a parallelogram.

Opposite sides are parallel and equal in length.

Define a rectangle.

A parallelogram with all angles equal to 90 degrees.

Define a square.

A rectangle with all sides equal; area A = s^2; perimeter P = 4s.

Define a trapezoid.

A quadrilateral with two parallel sides and two non-parallel sides.

What is a quadrilateral?

A four-sided polygon with no requirement on parallelism.

Rectangle area formula.

A = L × W.

Rectangle perimeter formula.

P = 2L + 2W.

Square area formula.

A = s^2.

Square perimeter formula.

P = 4s.

Parallelogram area formula.

A = b × h.

Parallelogram perimeter formula.

P = 2a + 2b.

Trapezoid area formulas.

A = ((b1 + b2) / 2) × h or A = (h/2) × (b1 + b2).

How do you find the circumference of a circle?

C = πd or C = 2πr.

Relation between diameter and radius.

d = 2r and r = d/2.

If the diameter is 28, what is the circumference approximately?

C ≈ 87.96 (C = πd with d = 28).

What does percent mean in math?

Percent means per hundred; base is the whole.

How do you convert a decimal to a percent?

Multiply the decimal by 100%.

How do you convert a fraction to a percent?

Convert to a decimal, then multiply by 100%.

Convert 0.5 to a percent.

50%.

Convert 0.42 to a percent.

42%.

Convert 0.123 to a percent.

12.3%.

Convert 0.07 to a percent.

7%.

Convert 1/2 to a percent.

50%.

Convert 3/4 to a percent.

75%.

Convert 5/8 to a percent.

62.5%.

Convert 7/16 to a percent.

43.75%.

Convert 23% to decimal.

0.23.

Convert 17% to decimal.

0.17.

Convert 50% to decimal.

0.50.

Convert 62% to decimal.

0.62.

Convert 1/2% to decimal.

0.005.

Convert 7/16% to decimal.

0.004375.

What percent of 90 is 72?

80%.

If $80 is 6% of a number, what is that number?

$1,333.33 (1333 1/3).

If total bill is $128.49 and you tip 17%, how much is the tip?

$21.84.

What is the total after a 17% tip on $128.49?

$150.33.

Percent increase formula concept with a quick example (41% to 43%).

Percent increase ≈ (43−41)/41 ≈ 4.88%.

Percent increase example with weight change from 187 lb to 205 lb.

Percent increase ≈ (205−187)/187 ≈ 9.63%.

Percent decrease formula concept with production drop from 3987 to 2890.

Decrease = 3987−2890 = 1097; percent decrease ≈ 1097/3987 ≈ 27.54%.

Percent decrease example: vaccine shots per day from 298,971 to 228,093.

Decrease ≈ 70,878; percent decrease ≈ 70,878/298,971 ≈ 23.70%.

What is absolute error?

The absolute difference between the measured value and the expected value.

What is relative error?

Absolute error divided by the expected outcome; expressed as a percent.

What is tolerance?

The maximum allowable deviation from the expected outcome.

Highest and lowest measurement within tolerance: outside diameter 10 inches with ±0.125 inches tolerance.

Highest: 10.125 inches; Lowest: 9.875 inches.

Highest and lowest weights for a 5 g bag with ±0.1 g tolerance.

Highest: 5.1 g; Lowest: 4.9 g.

Relative error calculation example 12 (28.89 vs 28.5).

|28.89−28.5| / 28.5 ≈ 0.39/28.5 ≈ 1.37%.

Relative error calculation example 13 (1.978 vs 1.8892).

|1.978−1.8892| / 1.978 ≈ 0.0888/1.978 ≈ 4.49%.

What is engineering notation?

Like scientific notation, but exponents are powers of three; uses prefixes like kilo (10^3), mega (10^6), etc.

What is scientific notation?

A number in the form P × 10^k where 1 ≤ P < 10 and k is an integer.

Convert 1000 to scientific notation.

1.0 × 10^3.

Convert 0.00063 to scientific notation.

6.3 × 10^−4.

Multiply in scientific notation: (1.2 × 10^2)(1.6 × 10^3)

1.92 × 10^5.

Divide in scientific notation: (A × 10^B) ÷ (C × 10^D)

(A/C) × 10^(B−D).

What is a unit price?

A rate with the price in the numerator and a denominator of 1 (e.g., $/lb, $/ft^3).

Unit price for 20 ft of pipe costing $12.82, what is the price per foot?

$12.82 / 20 = $0.641 per foot (about $0.64/ft).

Unit price for a carpet 12 ft by 18 ft costing $686.88, price per square foot?

$686.88 / (12×18) = $686.88 / 216 ≈ $3.18 per ft^2.

Unit price for a 50 lb bag of cement costing $5.92.

$5.92 / 50 ≈ $0.1184 per lb (about $0.12 per lb).

Proportion true/false: 3/8 = 36/96.

True.

Proportion true/false: 5/16 = 15/64.

False.

Solve for n: n/8 = 18/72.

n = 2.

Solve for x: 3/8 = x/128.

x = 48.

Solve for m: 2.7/9.8 = 1.5/m.

m ≈ 5.44.

Round-trip gas estimate: 420 miles, 18.38 gallons, 928 miles away, gas price $2.85/gal.

First compute mpg ≈ 420/18.38 ≈ 22.89; gallons for 928 miles ≈ 928/22.89 ≈ 40.6; cost ≈ 40.6 × 2.85 ≈ $115.71.

Gas cost for Prius round trip: 928 miles, 45.87 mpg, gas $2.85/gal.

Gallons ≈ 928/45.87 ≈ 20.23; cost ≈ 20.23 × 2.85 ≈ $57.66.

What is a rate in math?

The quotient of two quantities with different units; expressed as unit rates when denominator is 1.

What is a unit rate?

A rate with a denominator of 1, e.g., miles per hour, dollars per item.

What is a base in percent problems?

The whole amount or total base to which the percent applies.

What is the standard percent problem equation?

Amount = Rate × Base (A = R × B).