ACT WorkKeys

The Applied Math assessment measures your ability to apply mathematical reasoning and problem-solving techniques to workplace situations. This is not abstract mathematics but practical math used in real jobs across industries. You will encounter scenarios involving measurements, calculations, conversions, and quantitative reasoning that workers face daily.

The assessment presents problems in context. You might calculate material costs for a construction project, determine medication dosages, figure shipping weights, or compute employee work schedules. Success requires understanding mathematical concepts and knowing when and how to apply them.

Questions range from basic arithmetic through more complex multi-step problems. Lower-level questions test fundamental operations. Higher-level questions require setting up problems, converting units, working with formulas, and synthesizing information from multiple sources.

Levels build on each other: a Level 6 problem also uses the Level 3, 4, and 5 skills. Each practice test in this guide spans all five levels.

Numbers fall into distinct categories based on their properties. Recognizing these categories helps you understand how numbers behave and which operations apply.

Rational Numbers can be expressed as fractions where both numerator and denominator are integers and the denominator is not zero. This includes all integers (since any integer can be written as itself over one), all fractions, and all terminating or repeating decimals. Examples: 3/4, -2/5, 0.75, 0.333...

Real Numbers encompass all rational and irrational numbers. Any number that can be placed on a number line is a real number. This includes every number type mentioned above.

Understanding place value is fundamental to all mathematical operations. In our base-ten system, each position represents a power of ten.

Consider the number 5,847.36. Reading from left to right: 5 is in the thousands place (5 × 1,000 = 5,000), 8 is in the hundreds place (8 × 100 = 800), 4 is in the tens place (4 × 10 = 40), 7 is in the ones place (7 × 1 = 7), 3 is in the tenths place (3 × 0.1 = 0.3), and 6 is in the hundredths place (6 × 0.01 = 0.06).

Place value determines a digit's contribution to the total value. Moving left, each position is worth ten times more. Moving right past the decimal point, each position is worth ten times less.

Positive numbers are greater than zero. Negative numbers are less than zero. Zero itself is neither positive nor negative.

On a number line, positive numbers appear to the right of zero, negative numbers to the left. The further right a number, the greater its value. The further left, the lesser its value. Thus, -2 is greater than -5, even though 2 is less than 5.

Adding positive and negative numbers: When signs are the same, add the absolute values and keep the sign. When signs differ, subtract the smaller absolute value from the larger and use the sign of the number with the larger absolute value.

Subtracting negative numbers: Change the subtraction to addition and change the sign of the second number. Then follow addition rules.

Multiplying and dividing: When signs are the same, the result is positive. When signs differ, the result is negative.

Absolute value represents a number's distance from zero on the number line, regardless of direction. Absolute value is always non-negative. The symbol for absolute value is vertical bars around the number.

|7| = 7 (seven is 7 units from zero) |-7| = 7 (negative seven is also 7 units from zero) |0| = 0 (zero is 0 units from zero)

In workplace contexts, absolute value appears when direction doesn't matter but magnitude does. If a temperature must stay within 5 degrees of a target, you care about the size of the deviation, not whether it's above or below.

Rounding simplifies numbers while maintaining approximate value. The rules are consistent: look at the digit immediately to the right of your rounding position. If that digit is 5 or greater, round up. If it's 4 or less, keep the rounding digit unchanged.

Workplace applications include rounding monetary amounts, measurements, and time. Financial calculations often round to the nearest cent. Measurements might round to practical precision levels based on tools available.

Estimation produces quick approximate answers. This skill helps verify calculator results and catch errors. If your calculated answer differs dramatically from your estimate, something is wrong.

Round numbers to convenient values before calculating. For 487 + 312, estimate 500 + 300 = 800. The actual answer (799) should be close to this estimate.

For multiplication: 48 × 52 approximates 50 × 50 = 2,500. Actual answer: 2,496.

Estimation is particularly valuable when checking multi-step calculations or when an exact answer isn't necessary. A project manager might estimate material needs to confirm they're in the right range before doing precise calculations.