D771 WGU Quantitative Literacy Latest updated version with accurate solutions

What is an equation?

A math statement showing two expressions are equal, connected by an equal sign (=).

What is an expression?

A math phrase without an equal sign.

Example of an equation?

8 + 3 = 11.

Example of an expression?

8 + 3.

How do you solve for an unknown in an equation?

Apply the same operation to both sides until the unknown is isolated.

What is a variable?

A symbol (like x) that represents an unknown value.

What is a constant?

A fixed value that does not change.

What is a coefficient?

A number multiplied by a variable (in 5x, 5 is the coefficient).

How do you multiply fractions?

Multiply numerators together and denominators together.

How do you divide fractions?

Multiply by the reciprocal of the divisor.

How do you add/subtract fractions?

Rewrite with a common denominator, then add/subtract numerators.

What is a reciprocal?

The flipped version of a fraction (e.g., 3/4 → 4/3).

What does percent mean?

Per hundred.

How do you convert a decimal to a percent?

Multiply by 100. (0.25 → 25%).

How do you convert a percent to a decimal?

Divide by 100. (75% → 0.75).

How do you find 10% of a number quickly?

Move the decimal one place to the left.

Example: What is 25% of 200?

200 × 0.25 = 50.

What is a ratio?

A comparison of two numbers (e.g., 2:3).

What is a rate?

A ratio with different units (e.g., miles/hour).

What is a unit rate?

A rate with denominator of 1 (e.g., $2 per slice).

What is a proportion?

An equation showing two ratios are equal.

How do you solve a proportion?

Cross multiply and divide.

Example: 3/4 = x/12. Solve for x.

x = 9.

How do you find the perimeter of a rectangle?

2 × length + 2 × width.

Example: Rectangle 10 ft by 14 ft perimeter?

48 ft.

What is the circumference of a circle?

Distance around a circle.

Formula for circumference using diameter?

C = π × diameter.

Formula for circumference using radius?

C = 2πr.

Approximate value of π?

3.14.

What does ≈ mean?

About equal to.

What is a conversion factor?

A ratio that compares two equivalent values in different units.

How do you convert 150 minutes into hours?

150 × (1 hr / 60 min) = 2.5 hours.

How do you convert inches to feet?

Divide by 12.

What is a function?

A relation where each input has exactly one output.

What is function notation?

y = f(x).

What is a linear function?

A function that forms a straight line, written as y = mx + b.

In y = mx + b, what does m represent?

The slope (rate of change).

In y = mx + b, what does b represent?

The y-intercept (starting value).

Example: $2000 setup fee + $30 per person. Function?

y = 30x + 2000.

What is linear growth?

Increase by the same fixed amount each step.

What is exponential growth?

Increase by the same fixed percentage each step.

Linear growth recursive formula?

Pn = Pn−1 + d.

Linear growth explicit formula?

Pn = P0 + dn.

Exponential growth explicit formula?

Pn = P0(1 + r)^n.

Example of linear growth: 437 bottles + 32/year. Formula?

Pn = 437 + 32n.

Example of exponential growth: $10,000 at 5% interest. Formula?

y = 10,000(1.05)^n.

What are net earnings?

Income after taxes are deducted.

What are expenses?

Money spent on housing, food, transportation, etc.

What is the 80/20 budgeting rule?

Spend 80%, save 20%.

What is good debt?

Student loans or mortgages that build value.

What is bad debt?

High-interest credit card debt.

Formula for retail price with markup?

Retail = Cost × (1 + markup).

Example: Item costs $50, 20% markup. Price?

$60.00.

Formula for sales tax?

Total = Price × (1 + tax rate).

Example: $500 laptop with 8% tax. Price?

$540.00.

How do you calculate discount price?

Price × (1 − discount rate).

Example: $80 item, 25% off. Price?

$60.00.

What is mean?

The average of numbers.

What is median?

The middle value in ordered data.

What is mode?

The most frequent value.

What is range?

Largest value − smallest value.

What is probability?

Chance of an event happening, between 0 and 1.

Example: Coin flip probability of heads?

0.5.

Variable in math

A symbol (often a letter) that represents an unknown value.

Equation

A mathematical statement showing two expressions are equal (e.g., 2x + 3 = 7).

Solve for x in 2x + 3 = 7

Subtract 3 from both sides → 2x = 4 → Divide by 2 → x = 2.

Rearrange y = mx + b to solve for x

x = (y - b) / m.

Ratio

A comparison of two quantities by division (a:b or a/b).

Rate

A ratio comparing two different units (e.g., miles per hour).

Formula for unit rate

Rate = Quantity ÷ Time (or other unit).

Conversion method for units

Multiply by conversion factor (e.g., inches × (1 ft / 12 in) = feet).

Function

A rule that assigns exactly one output (y) to each input (x).

Function notation meaning: f(x)

f(x) = "the output when input is x."

Slope-intercept form of a line

y = mx + b, where m = slope and b = y-intercept.

Exponential function formula

y = a·b^x (a = initial value, b = growth/decay factor).

Formula for percent

Percent = (Part ÷ Whole) × 100.

Formula for finding the part

Part = Percent × Whole.

Sales tax formula

Total Price = Original Price × (1 + Tax Rate).

Markup formula

Selling Price = Cost × (1 + Markup Rate).

Budget

A plan for income and expenses over a set time.

Common fixed expenses

Rent, utilities, insurance.

Common variable expenses

Food, entertainment, gas.

Formula for comparing unit costs

Unit Price = Total Price ÷ Quantity.

Simple Interest Formula

I = P · r · t (P = principal, r = rate, t = time).

Total with Simple Interest

A = P + I = P(1 + rt).

Compound Interest Formula

A = P(1 + r/n)^(n·t).

What does "n" represent in compound interest?

Number of compounding periods per year.

Perimeter of a rectangle

P = 2l + 2w.

Area of a rectangle

A = l × w.

Area of a triangle

A = ½ · b · h.

Volume of a rectangular prism

V = l × w × h.

Volume of a cylinder

V = πr²h.

Estimation purpose in math

To quickly approximate values for practical use.

Rounding rule for estimation

Round to nearest significant digit before multiplying/dividing.

When estimating area/volume, what should you round?

Dimensions (length, width, height, radius) before calculating.

Number of degrees in a triangle

180°.

Complementary angles add up to?

90°.

Supplementary angles add up to?

180°.

Formula for the sum of interior angles of a polygon

(n - 2) × 180°, where n = number of sides.

Strategy if quiz/test score is below 80%

Review notes and meet with an instructor for help.