Free NLN NEX Math Exam Flashcards

No. After parentheses and exponents, multiplication and division are done together from left to right, then addition and subtraction together from left to right. In 24 / 6 * 2 the division comes first because it is further left, giving 8, not 2. Treating PEMDAS as six ranked steps is the most common order-of-operations error.

Divide the top by the bottom to get the decimal, then move the decimal point two places right and add a percent sign. So 3/4 becomes 0.75 becomes 75%. Going backward, drop the percent sign and move the decimal two places left.

Write the percent over 100, then simplify. 40% becomes 40/100, which reduces to 2/5. For a percent with a decimal, clear it first: 12.5% becomes 125/1000, which reduces to 1/8.

Only for addition and subtraction. To add 1/3 and 1/4 you rewrite both over 12. Multiplication needs no common denominator at all: multiply straight across, top times top and bottom times bottom. Forcing a common denominator before multiplying wastes time and invites errors.

Keep the first fraction, change the sign to multiplication, and flip the second fraction. So 3/4 divided by 2/3 becomes 3/4 times 3/2, which is 9/8. Flipping the wrong fraction is the usual trap, so always invert the divisor, the number you are dividing by.

To go improper, multiply the whole number by the denominator and add the numerator, keeping the same denominator: 3 and 2/5 becomes (3 * 5 + 2)/5 = 17/5. To go back, divide the numerator by the denominator; the quotient is the whole number and the remainder is the new numerator.

Divide the numerator and the denominator by their greatest common factor, so 24/36 becomes 2/3 after dividing both by 12. The value does not change, only the form. Answer choices are usually written in lowest terms, so an unsimplified result may look like it is missing from the options.

Two like signs give a positive result and two unlike signs give a negative one: -6 * -3 = 18 but -6 * 3 = -18. Count the negative factors: an even number of them makes the product positive, an odd number makes it negative.

Subtracting a negative is the same as adding a positive, so 7 - (-4) = 11. When you add two numbers with opposite signs instead, ignore the signs, take the difference between the two sizes, and give the answer the sign of whichever number sat further from zero: -9 + 4 = -5.

Convert the percent to a decimal and multiply, because the word 'of' signals multiplication. 20% of 85 is 0.20 * 85 = 17. Multiplying by 20 instead of 0.20 is the classic slip and produces an answer 100 times too large.

Divide the part by the percent written as a decimal. If 30 is 20% of a number, the number is 30 / 0.20 = 150. Multiplying instead of dividing is the trap; check by asking whether the whole should be larger than the part.

Percent change equals the amount of change divided by the ORIGINAL value, then converted to a percent. Going from 50 to 60 is 10/50 = 0.20, a 20% increase. Dividing by the new value instead gives 10/60, about 16.7%, which is the most frequent wrong answer.

A part-to-part ratio compares two groups, such as 3 nurses to 2 aides. A part-to-whole ratio compares one group to the total, so the same situation gives 3 nurses out of 5 people. Add the parts to get the whole before writing a fraction of the total.

A rational number can be written as a fraction of two integers, so it ends or repeats as a decimal: 0.75, -3, and 2/9 all qualify. An irrational number never ends or repeats, such as pi or the square root of 2. A square root is only irrational when the number under it is not a perfect square, so the square root of 25 is rational.

Find the digit in that place, then look only at the single digit immediately to its right. If it is 5 or more, round the target digit up; if it is 4 or less, leave it alone. Rounding 6,349 to the nearest hundred gives 6,300 because the 4 after the 3 says leave it alone, and the 9 beyond that is ignored. Rounding 4,850 to the nearest hundred gives 4,900.

Kilo means 1,000 times the base unit, centi means one hundredth, milli means one thousandth, and micro means one millionth. Every step on the metric ladder is a power of 10, so all metric conversions are decimal-point moves rather than long division.

1 kilogram = 1,000 grams, 1 gram = 1,000 milligrams, and 1 milligram = 1,000 micrograms. Each step is a factor of 1,000, so going from grams to micrograms is 1,000 * 1,000, or one million.

1 liter = 1,000 milliliters, and 1 cubic centimeter equals 1 milliliter. For length, 1 meter = 100 centimeters = 1,000 millimeters, and 1 kilometer = 1,000 meters. Centi always means one hundredth, but centiliters and centigrams are rarely used, so volume and mass problems almost always step by 1,000 while length problems often step by 100.

Converting to a SMALLER unit makes the number BIGGER, so you multiply; converting to a LARGER unit makes the number smaller, so you divide. Changing 2.5 g to milligrams gives 2,500 mg. Estimating the direction first catches answers that are off by a factor of 1,000.

Write each conversion as a fraction and arrange it so the unwanted unit sits opposite itself and cancels. To turn 90 minutes into hours, multiply by 1 hour / 60 minutes so that minutes cancel and hours remain. If the leftover unit is wrong, the factor was flipped.

1 kilogram is about 2.2 pounds and 1 inch is exactly 2.54 centimeters, which also makes 1 meter about 39.4 inches. Because a kilogram is heavier than a pound, the number of pounds must be larger than the number of kilograms, which is a fast direction check.

1 teaspoon is about 5 milliliters, 1 tablespoon is about 15 milliliters, and 1 fluid ounce is about 30 milliliters. Since 3 teaspoons make 1 tablespoon and 2 tablespoons make 1 fluid ounce, these three facts chain together.

12 inches = 1 foot, 3 feet = 1 yard, and 5,280 feet = 1 mile. Unlike the metric system there is no single conversion factor, so each step must be memorized and applied separately in a multi-step problem.

16 ounces = 1 pound and 2,000 pounds = 1 ton. Watch the wording: an ounce of weight is not the same as a fluid ounce of volume, and mixing the two is a deliberate distractor.

8 fluid ounces = 1 cup, 2 cups = 1 pint, 2 pints = 1 quart, and 4 quarts = 1 gallon. That makes 1 gallon equal to 16 cups or 128 fluid ounces. Build the chain step by step rather than guessing the final factor.

Fahrenheit = (9/5) * Celsius + 32, and Celsius = (5/9) * (Fahrenheit - 32). Going to Celsius, subtract 32 FIRST and then multiply; doing those two steps out of order is the standard trap. Water freezes at 0 C or 32 F and boils at 100 C or 212 F, which lets you sanity-check any answer.

60 seconds = 1 minute, 60 minutes = 1 hour, and 24 hours = 1 day. Time is base 60, not base 10, so 1.5 hours is 90 minutes, not 1 hour 50 minutes. On a 24-hour clock, add 1200 to afternoon times, so 3:15 p.m. is written 1515.

A unit rate expresses an amount per ONE unit, found by dividing, such as 300 miles in 5 hours giving 60 miles per hour. Distance = rate * time, so rate = distance / time and time = distance / rate. Convert so the time units match before dividing.

Write two equal ratios with matching units in matching positions, then cross-multiply and solve. For 3 mL per 250 mg, finding the volume for 400 mg gives 3/250 = x/400, so 250x = 1,200 and x = 4.8 mL. Putting milligrams on top on one side and milliliters on top on the other is the error that produces a wrong but tempting answer.

Perimeter of a rectangle = 2 * (length + width) and area = length * width. A square with side s has perimeter 4s and area s squared. A triangle has area = (1/2) * base * height, using the perpendicular height rather than a slanted side.

Length answers use plain units such as cm, area answers use square units such as square cm, and volume answers use cubic units such as cubic cm. The volume of a rectangular solid is length * width * height. If the answer choices carry units, the exponent alone often rules out half of them.

Only enough to apply a formula you are given, plus measurement and scale. The NLN Technical Manual states that the NEX dropped the PAX's extended geometry items such as circumference, radius, diameter, and angle problems, and dropped physics content, because neither appears in nursing curricula. Know rectangle, square, and triangle formulas cold, and expect any circle problem to hand you the formula.

Substitute the value in parentheses, then follow the order of operations. If x = -3, then x squared is (-3) * (-3) = 9, while -x squared means take 3 squared and negate it, giving -9. Dropping the parentheses around a negative substitution flips the sign of the answer.

Only like terms, meaning terms with the identical variable raised to the identical power. 4x and 7x combine to 11x, but 4x and 4x squared do not combine at all. Add or subtract the coefficients and keep the variable part unchanged.

Multiply the outside factor by every term inside, carrying its sign to each one. So -2(x - 4) = -2x + 8, not -2x - 8. Failing to distribute the negative to the second term is the single most common algebra mistake on entrance exams.

Reverse the order of operations. Undo addition and subtraction first, then multiplication and division. For 3x + 7 = 22, subtract 7 to get 3x = 15, then divide by 3 to get x = 5. Whatever you do to one side must be done to the other.

Move all variable terms to one side and all constants to the other by adding or subtracting the same quantity from both sides. For 5x - 3 = 2x + 9, subtract 2x to get 3x - 3 = 9, add 3 to get 3x = 12, then divide to get x = 4. Choosing the side that keeps the coefficient positive avoids sign errors.

Multiply every term on both sides by the least common denominator to clear the fractions before solving. For x/3 + 1/2 = 5/6, multiply through by 6 to get 2x + 3 = 5, so x = 1. Multiplying only some terms, rather than every term, is the trap.

Only when you multiply or divide both sides by a negative number. Solving -2x > 8 gives x < -4, with the sign flipped. Adding or subtracting a negative never flips the sign, and neither does multiplying by a positive.

'Is' means equals, 'of' means multiply, 'per' means divide, and 'more than' means add. Watch the reversals: '5 less than a number' is x - 5, not 5 - x, and 'the quotient of 12 and x' is 12/x. Order matters for subtraction and division but not for addition and multiplication.

Multiplying like bases adds the exponents, so x cubed times x squared is x to the fifth. Dividing like bases subtracts them. Raising a power to a power multiplies them, so (x squared) cubed is x to the sixth. Any nonzero number to the zero power equals 1. Adding the exponents when the bases differ is invalid.

Add every value and divide by how many values there are. A value of zero still counts toward the total number of values, so leaving it out of the count inflates the mean. To find a missing value from a known mean, multiply the mean by the count to recover the required sum.

Sort the values from least to greatest first; the median of an unsorted list is meaningless. With an odd count the median is the single middle value. With an even count, average the two middle values, which may produce a number that is not in the data set.

The mode is whichever value occurs with the highest frequency. A set can have two or more modes when several values tie for that highest frequency, and it has no mode at all when every value occurs once. The mode is the only one of these measures that also works for non-numeric categories.

Range = largest value minus smallest value. It measures SPREAD, not center, so two sets can share the same mean while having very different ranges. Because it depends only on the two extremes, a single unusual value changes it dramatically.

An outlier drags the mean toward itself, while the median barely moves because it depends on position rather than size. With one very large salary in a small group, the median describes a typical value better than the mean. Expect a question that asks which measure best represents the data.

Compare a measure of center, such as the mean or median, AND a measure of spread, such as the range. Equal means can hide very different consistency, and the set with the smaller range is the more consistent one. A comparison based on center alone is incomplete.

Read the row heading, the column heading, and the units or scale note, then confirm whether a figure is a raw count, a percent, or a total. Many tables report values in thousands, so a cell reading 42 may mean 42,000. Confirm which row and column intersect at the value you need before you compute.

An axis that does not start at zero, or one with a compressed scale, exaggerates differences between bars. Check the value of one gridline before estimating any amount, and read the axis labels rather than judging by bar height alone. A trend that looks steep may be a small change on a stretched scale.

Every slice is a share of one whole, so the percents sum to 100%. To turn a slice into a count, multiply its percent as a decimal by the total: 25% of 320 patients is 0.25 * 320 = 80. A pie chart shows proportions only, so it cannot tell you the size of the total on its own.