Key Takeaways
- Algebra covers approximately 7 items (~18%) of the NEX math section: solving equations, variables, expressions
- Data & Information also covers approximately 7 items (~18%) — this is NEW content not on the old PAX
- To solve equations, isolate the variable using inverse operations on both sides
- Mean = sum of values / number of values; Median = middle value when ordered; Mode = most frequent value
- Bar graphs compare categories; line graphs show trends over time; pie charts show parts of a whole
- When reading graphs, always check axis labels, units, and scale before answering
- Inequalities use < (less than), > (greater than), <= (less than or equal), >= (greater than or equal)
- Word problems: identify what is being asked, extract relevant numbers, set up the equation, solve, check reasonableness
Algebra & Data Interpretation
Basic Algebra (~7 items)
Algebra on the NEX involves solving equations with one variable. The key principle: whatever you do to one side, you must do to the other side.
Solving One-Step Equations
| Equation Type | Operation | Example |
|---|---|---|
| x + a = b | Subtract a from both sides | x + 7 = 15 → x = 8 |
| x - a = b | Add a to both sides | x - 3 = 12 → x = 15 |
| ax = b | Divide both sides by a | 4x = 28 → x = 7 |
| x/a = b | Multiply both sides by a | x/5 = 6 → x = 30 |
Solving Two-Step Equations
- Undo addition/subtraction first
- Then undo multiplication/division
Example: 3x + 5 = 20
- Subtract 5: 3x = 15
- Divide by 3: x = 5
Example (nursing): A nurse works x hours at $28/hour and earns $476 after a $28 meal deduction. Find x.
- 28x - 28 = 476
- 28x = 504
- x = 18 hours
Evaluating Expressions
Substitute given values into an expression and simplify:
Example: If a = 3 and b = 4, evaluate 2a + 3b - 5
- 2(3) + 3(4) - 5 = 6 + 12 - 5 = 13
Inequalities
| Symbol | Meaning | Example |
|---|---|---|
| < | Less than | x < 5 (x is less than 5) |
| > | Greater than | x > 10 (x is greater than 10) |
| ≤ | Less than or equal to | x ≤ 3 |
| ≥ | Greater than or equal to | x ≥ 7 |
Nursing application: A patient's potassium level must be ≥ 3.5 and ≤ 5.0 mEq/L to be within normal range.
Important rule: When multiplying or dividing both sides of an inequality by a negative number, flip the inequality sign.
Data & Information (~7 items) — NEW on NEX
This subsection is new to the NEX (not on the old PAX) and tests your ability to read and interpret data displays.
Types of Data Displays
| Display Type | Best For | What to Look For |
|---|---|---|
| Bar graph | Comparing categories or groups | Height of bars; relative differences |
| Line graph | Showing trends over time | Slope (rate of change); direction of trend |
| Pie chart | Showing parts of a whole | Relative sizes of slices; percentages |
| Table | Presenting exact numerical data | Row/column labels; specific values |
| Scatter plot | Showing correlation between two variables | Pattern direction; clustering |
Measures of Central Tendency
| Measure | Definition | When to Use |
|---|---|---|
| Mean | Sum of values / number of values | When data is evenly distributed |
| Median | Middle value in ordered data | When data has outliers |
| Mode | Most frequently occurring value | For categorical data or most common value |
| Range | Maximum - Minimum | To show spread/variability |
Example: Patient pain scores: 3, 5, 7, 5, 8, 5, 6
- Mean: (3+5+7+5+8+5+6)/7 = 39/7 = 5.57
- Median: Ordered: 3, 5, 5, 5, 6, 7, 8 → Median = 5
- Mode: 5 (appears 3 times)
- Range: 8 - 3 = 5
Reading Graphs and Tables
Strategy for graph/table questions:
- Read the title — what is being measured?
- Check the axes/labels — what are the units?
- Note the scale — are intervals even? Does the y-axis start at 0?
- Identify the trend — increasing, decreasing, stable, fluctuating?
- Answer the specific question — avoid making assumptions beyond the data
Solve for x: 5x - 12 = 33
A patient's heart rates over 6 readings are: 72, 80, 68, 76, 84, 72. What is the mode?
A line graph shows a patient's weight increasing from 150 lbs in January to 165 lbs in June. What was the average monthly weight gain?
If a = 4 and b = -2, what is the value of 3a - 2b + 5?
The blood glucose readings for a patient over 5 days are: 95, 130, 88, 110, 95. What is the median?
The difference between the maximum and minimum values in a data set is called the _____.
Type your answer below
A nurse earns $32 per hour. She works 36 hours in week 1 and 44 hours in week 2, with overtime pay of 1.5x for hours over 40. What are her total earnings for both weeks?
Which of the following statements about the data set {4, 7, 7, 9, 12, 15} are TRUE? (Select all that apply)
Select all that apply