ParaProfessional / Clerical civil service tests (state & local) Mathematics & Quantitative Reasoning Syllabus

How do you convert the fraction 3/8 to a percent?

Divide 3 by 8 to get 0.375, then multiply by 100: 37.5%.

What is a ratio, and how is the ratio 12 to 8 simplified?

A ratio compares two quantities. 12 to 8 simplifies to 3 to 2 by dividing both terms by their greatest common factor (4).

What defines a proportion, and how do you solve one using cross multiplication?

A proportion states two ratios are equal (a/b = c/d). Cross multiply: a x d = b x c, then solve for the unknown.

Solve the proportion 3/4 = x/20 for x.

x = 15. Cross multiply: 4x = 60, so x = 15.

If 3 pounds of apples cost $6, how much do 7 pounds cost (assuming the same rate)?

$14. The unit rate is $2 per pound, so 7 x $2 = $14.

How do you calculate a simple (arithmetic) average (mean)?

Add all the values together and divide by the number of values.

What is the average of 12, 15, 18, and 23?

17. Sum is 68; 68 / 4 = 17.

What is a weighted average, and when is it used?

An average where each value is multiplied by a weight (its relative importance), the products are summed, and the total is divided by the sum of the weights. Used when values count more than once or unequally, such as grades by credit hours.

A student scores 80 on a test worth 30% and 90 on a test worth 70%. What is the weighted average?

87. (80 x 0.30) + (90 x 0.70) = 24 + 63 = 87.

How do you compute gross pay for an hourly worker, and how is overtime usually calculated?

Gross pay = hourly rate x hours worked. Overtime (over 40 hours/week) is typically paid at 1.5 times the regular rate ('time and a half').

An employee earns $16/hour and works 45 hours with overtime at time-and-a-half over 40. What is the gross pay?

$760. Regular: 40 x $16 = $640; overtime: 5 x $24 = $120; total $760.

What is the difference between gross pay and net pay?

Gross pay is total earnings before deductions; net pay (take-home pay) is what remains after taxes and other deductions are subtracted.

How do you make change for a customer who pays with $20 for a $13.45 purchase?

Subtract the cost from the amount paid: $20.00 - $13.45 = $6.55 in change.

How do you calculate the sale price after a discount?

Multiply the original price by the discount rate to find the discount amount, then subtract it from the original price. Or multiply by (1 - discount rate). Example: $50 at 20% off = $50 x 0.80 = $40.

How do you calculate the final price including sales tax?

Multiply the price by the tax rate to find the tax, then add it to the price. Or multiply by (1 + tax rate). Example: $40 with 6% tax = $40 x 1.06 = $42.40.

What is a markup, and how does it differ from a discount?

A markup is the amount added to a cost to set the selling price (an increase); a discount is an amount subtracted from a price (a decrease).

An item costs a store $30 and is marked up 40%. What is the selling price?

$42. Markup is $30 x 0.40 = $12; selling price = $30 + $12 = $42.

State the distance formula relating time, rate, and distance.

Distance = rate x time (d = r x t). Rearranged: rate = distance / time, and time = distance / rate.

A car travels 150 miles in 3 hours. What is its average speed?

50 miles per hour. Rate = distance / time = 150 / 3 = 50 mph.

How long does it take to travel 240 miles at 60 miles per hour?

4 hours. Time = distance / rate = 240 / 60 = 4.

How many inches are in a foot, feet in a yard, and inches in a yard?

12 inches in a foot, 3 feet in a yard, and 36 inches in a yard.

List the common units of liquid measure from smallest to largest: cups, gallons, pints, quarts.

Cups, pints, quarts, gallons. 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon.

How many ounces are in a pound, and how many minutes are in an hour?

16 ounces in a pound; 60 minutes in an hour.

In the metric system, how many centimeters are in a meter and how many grams in a kilogram?

100 centimeters in a meter; 1,000 grams in a kilogram.

When reading a data table, how do you find a specific value?

Locate the correct row and the correct column, then read the value where they intersect (the cell at that row-column crossing).

What is the purpose of a bar graph, and what does the height or length of each bar represent?

A bar graph compares amounts across categories; the height or length of each bar represents the quantity for that category.

What type of data does a line graph best display?

Changes or trends over time (continuous data), shown by points connected with line segments.

What does a pie (circle) graph show, and what do all its slices add up to?

A pie graph shows parts of a whole as proportions; all slices together represent 100% (or the full data set).

On a pie chart, if a category is 25% of the total, how many degrees of the circle does its slice occupy?

90 degrees. 25% of 360 degrees = 0.25 x 360 = 90.

What does 'drawing a conclusion from data' require beyond simply reading a value?

Interpreting the data, such as identifying trends, comparing categories, or making supported inferences, using only what the data actually shows, without assuming information that is not present.

What is estimation, and why use a reasonableness check after solving a problem?

Estimation uses rounded numbers to find an approximate answer quickly. A reasonableness check compares the exact answer to the estimate to catch errors, like a misplaced decimal point or wrong operation.