Data Representation

📊 Reading Data Tables

Part 1 of 7 — Headers, Units, Lookups, Running Totals, and Unit Conversions

How ACT Science Works

On the Enhanced ACT, the Science test is optional: 40 questions in 40 minutes, each with 4 answer choices. It is not part of the composite score (English, Math, and Reading make up the composite); Science gets its own score and is combined with Math into a STEM score. That pace is about one minute per question, including reading time.

Most Science questions are data questions. They give you tables, graphs, and short descriptions of experiments, and the answer comes from the data, not from facts you memorized in biology or chemistry class. This lesson trains the core data skills:

Anatomy of a Data Table

The independent variable is the factor the researchers set (temperature, distance, dose). The dependent variable is what they measured in response (time, mass, growth). Part 6 covers variables and controls in depth; for now, the key habit is noticing which column was set and which was measured.

How to Look Up a Value

1. Match the words. Find the column header that matches the question's wording exactly. "Germinated by Day 7" is not the same column as "Germinated by Day 3."
2. Check the units. Is it mm or cm? Seconds or minutes? mA or A? "Grams per 100 g of water" or grams total?
3. Read across one row. Put a finger (or the cursor) on the row so your eye cannot slip to the line above.
4. Reverse lookups work the same way. If the question gives a result and asks for the condition, find the result in its column, then read back to the left.

Running Totals vs. Per-Interval Values

Headers like "Total volume collected," "Cumulative distance," or "Mass formed so far" describe a running total: each row includes everything from earlier rows.

• The amount produced during an interval = later total − earlier total.
• The largest total is not the interval where the most was produced. A running total always grows (or stays flat), even when production slows down.
• If the header instead says "produced during each interval," each row stands alone, and you would add rows to get a total.

Differences and Ratios Between Columns

When a table has two result columns side by side, some questions ask about the gap or the ratio between them. Compute it row by row, then describe how that new list changes. Two columns can both rise while the gap between them shrinks.

Unit Conversions You Will Need

Sanity check: converting to a larger unit makes the number smaller (36 mA becomes 0.036 A, not 36,000 A). If your conversion went the wrong way, the answer choices usually include that mistake.

Common Table Traps

Worked Examples

A student dropped magnesium ribbon into acid and recorded the total volume of hydrogen gas collected.

Question 1: How much gas was produced from minute 2 to minute 4?

The header says total, so subtract: 54 − 33 = 21 mL. Answering 54 mL would count the gas from minutes 0 to 2 as well.

Question 2: During which 1-minute interval was the least gas produced?

The per-minute amounts are 18, 15, 12, 9, and 6 mL. The least, 6 mL, came from minute 4 to minute 5, even though that row has the largest total.

A student measured the current through a resistor at four voltages.

Question: At what voltage was the current 0.024 A?

1. Units first. The table is in mA, the question is in A. Convert: 0.024 A × 1,000 = 24 mA.
2. Reverse lookup. Find 24 in the Current column and read left: 3.0 V.

A student who skips the conversion looks for "0.024" in the table, finds nothing, and guesses. Converting the question's value to the table's units is almost always faster than converting the whole table.

Practice: Look It Up 🎯

Units and Headers 🔍

ACT-Style Set: Solubility Table 📋

A chemistry class measured the greatest mass of three salts that would dissolve in 100 g of water at five temperatures.

Table 1

ACT-Style Practice

Give yourself about one minute.

A student measured the total distance a snail had crawled every 10 minutes.

Question: During which 10-minute interval did the snail crawl the shortest distance, and how far did it crawl, in meters?

From 20 to 30 min, 0.18 m. The per-interval distances are 42, 36, 18, and 34 cm, so the shortest is 18 cm. Converting, 18 cm ÷ 100 = 0.18 m. A student who reads the last row (130 cm) has confused a running total with one interval, and a student who writes 1,800 m converted in the wrong direction.

Key Takeaways

• Enhanced ACT Science is optional: 40 questions in 40 minutes, 4 choices each, scored separately from the composite.
• Before computing, read the title, headers, and units. Match the question's wording to the exact column.
• The independent variable is the one researchers set (often the left column); the dependent variable is what they measured.
• In a running total, subtract consecutive rows to get what happened in one interval; the largest total is not the busiest interval.
• Watch the basis of a value ("per 100 g of water") and scale it to the question.
• Convert the question's value into the table's units; a larger unit gives a smaller number.

📈 Interpreting Graphs

Part 2 of 7 — Axes, Scales, Reading Points, and Slopes as Rates

ACT Science graphs come in a few familiar forms: line graphs, scatterplots, bar graphs, and graphs with two or more curves. In this lesson, each graph is described by its plotted points (often listed in a small table), which is exactly the information you would pull off a printed graph.

Read the Frame Before the Curve

Reading a Point

To find y for a given x: go up from the x-value to the curve, then across to the y-axis. To find x for a given y, reverse it: across from the y-value to the curve, then down. When a point falls between gridlines, estimate using the scale (halfway between 40 and 50 is 45).

Slope Is a Rate, With Units

The slope of a line between two points is

$\text{slope} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}$

and its units are (y-units) per (x-units). A distance (m) vs. time (s) graph has a slope in m/s, which is speed. A mass (g) vs. time (min) graph has a slope in g/min.

Rise over run, never run over rise. Dividing Δx by Δy flips the units (min/°C instead of °C/min), and the ACT includes that flipped value as a choice.

Average rate between two points uses only those two points, even if the curve wiggles between them.

Comparing Steepness on a Curve

A curved graph has a different slope in different places. To find where it is steepest, compute Δy over equal Δx intervals and compare. If the intervals are unequal, divide each Δy by its own Δx first.

Two Curves on One Graph

• Compare curves at the same x-value.
• Where two curves cross, the two quantities are equal at that x.
• With two vertical axes, read each curve against its own axis. A point that sits halfway up the graph might be 20 on the left axis and 60 on the right.

Cumulative Graphs

If the y-axis is a running total (total gas collected, total distance), the curve can only rise or stay flat. Its slope is the rate of production, and a flat stretch means production stopped. The highest point on the curve is not the fastest moment.

Common Graph Traps

Worked Examples

A beaker of crushed ice was heated steadily. Figure 1 is a line graph of temperature (°C, vertical axis) versus time (min, horizontal axis) through these points:

Question 1: What is the slope from 0 to 4 min?

$\dfrac{0 - (-20)}{4 - 0} = \dfrac{20}{4} = 5$

The slope is 5 °C/min: the temperature rose 5 degrees each minute.

Question 2: What does the graph show from 4 to 8 min?

The graph is flat (slope 0): temperature did not change even though heat was still being added. The description explains why (the ice was melting), but the data alone tell you the temperature stayed at 0°C.

Question 3: Which stretch is steepest?

From 8 to 12 min the slope is 30 ÷ 4 = 7.5 °C/min, steeper than the 5 °C/min at the start. The liquid water warmed faster than the ice did.

Figure 2 shows an algae culture over 10 days. One curve is algae density (left axis, thousands of cells/mL); the other is dissolved nitrate (right axis, mg/L).

Question: On the day the nitrate level was 10 mg/L, what was the algae density?

1. Read the nitrate curve against the right axis: 10 mg/L occurs on Day 6.
2. Go straight up or down to the algae curve and read the left axis: 38 thousand cells/mL.

The trap answer is 10 thousand cells/mL, which reads the nitrate value off the wrong axis. Notice also the relationship: as algae rose, nitrate fell, and both curves flatten after Day 8.

Practice: Points and Slopes 🎯

Slopes on a Cumulative Graph 🧮

A graph of total rainwater collected in a barrel (L, vertical axis) versus time (h, horizontal axis) passes through these points: (0, 0), (2, 6), (5, 15), (9, 15), (10, 19). Enter numbers only.

1. What is the slope from 0 to 2 h, in L/h?

2. What is the slope from 5 to 9 h, in L/h?

3. What is the average rate of collection over the whole 10 hours, in L/h?

ACT-Style Set: Two Curves 📋

Two 50.0 g samples of the same metal, one powdered (Sample P) and one a solid ribbon (Sample R), were placed in separate beakers of acid. Figure 1 is a line graph of the mass remaining (g) versus time (min). The vertical axis runs from 40 g to 52 g in 2 g gridlines. The plotted points are:

ACT-Style Practice

Give yourself about one minute.

A graph shows the speed of a falling parachute (m/s, vertical axis) versus time (s, horizontal axis). The vertical axis has gridlines every 5 m/s. The curve passes through (0, 0), (1, 9), (2, 15), (3, 18), (4, 19), and (6, 19).

Question: Between which two times is the average acceleration (the slope) greatest, and what is it?

From 0 to 1 s, 9 m/s per second. The speed gains in each 1-second step are 9, 6, 3, and 1 m/s, and the curve is flat (0) from 4 to 6 s. The steepest stretch is at the start, even though the speed is highest later. Notice the units: the slope of a speed vs. time graph is m/s per s, an acceleration.

Key Takeaways

• Read the frame first: axis labels, units, gridline scale, where each axis starts, the legend, and which axis belongs to which curve.
• Slope = Δy ÷ Δx, with units of y-units per x-unit. A falling graph has a negative slope; a flat stretch has slope zero.
• To find where a curve is steepest, compare Δy over equal Δx; the highest point is not the steepest point.
• Where two curves cross, the quantities are equal at that x-value.
• On a cumulative graph, slope is the rate of production and a flat stretch means it stopped.
• Convert rate units when the question asks (per minute ÷ 60 = per second).

📉 Identifying Trends

Part 3 of 7 — Direct, Inverse, Linear, Leveling Off, and Peaks

"As X increases, Y ..." is one of the most common ways an ACT Science question begins. To answer it, you need a precise vocabulary for trends and a quick way to check which one the data show.

The Trend Vocabulary

The First-Differences Check

When x goes up in equal steps, subtract each y-value from the next one. The list of differences tells you the shape:

If the x-steps are unequal, divide each difference by its own Δx before comparing. A drop of 8 over 20 units is slower than a drop of 6 over 10 units.

Proportional Relationships

Some questions go beyond "increases" and ask what happens if x doubles.

• Directly proportional: y ÷ x is constant (the graph is a straight line through the origin). Doubling x doubles y.
• Inversely proportional: x × y is constant. Doubling x halves y. The graph is a curve that falls quickly, then flattens; it is not a straight line.
• Doubling each step: if y is multiplied by the same factor for each equal step in x (100, 200, 400, 800), the growth is accelerating, not linear.

Check proportionality by computing the ratio or the product for every row. A relationship can be inverse (one goes up, the other down) without being inversely proportional.

Describing the Whole Trend

• A trend choice must fit every step of the data. If one interval goes the other way, "increases only" is wrong, and you may need "increases, then decreases."
• A peak's location is the x-value with the largest y, not the first big jump.
• Trends describe the data within the tested range. A choice that claims the pattern holds far beyond the data, or "for all values," says more than the table shows.
• With two or more curves or columns, a question may ask about the trend at each level of the second variable ("at every stirring speed") or about the trend in the gap between two columns.

Association Is Not Causation

When researchers only observe two variables changing together (a survey of ponds, neighborhoods, or patients), the data show an association. Other differences between the groups could explain it. A conclusion that one variable causes the other needs an experiment in which the researchers changed only that variable. On the ACT, "is associated with," "tended to," and "was higher when" are safe phrasings; "causes" and "proves" usually overreach.

Common Trend Traps

Worked Examples

Table A — Distance a ball has rolled down a long ramp

Differences: 0.3, 0.9, 1.5, 2.1. They grow each second, so distance increases at an accelerating rate; the ball is speeding up. "Linear increase" is wrong because the steps are not equal.

Table B — Oxygen output of a leaf at different light levels

Differences: 14, 8, 4, 1, 0. They shrink to zero, so oxygen output increases, then levels off. Adding light beyond about 800 lux produced no more oxygen.

A gas was trapped in a syringe and squeezed at constant temperature.

Step 1: Direction. As pressure rises, volume falls, so the relationship is inverse.

Step 2: Check the product. 100 × 60 = 6,000; 150 × 40 = 6,000; 200 × 30 = 6,000; 300 × 20 = 6,000. The product is constant, so volume is inversely proportional to pressure.

Step 3: Use it. At 400 kPa, volume = 6,000 ÷ 400 = 15 mL. Doubling the pressure from 200 to 400 kPa halves the volume from 30 to 15 mL.

Why not linear? The volume drops by 20, then 10, then 10 mL over pressure steps of 50, 50, and 100 kPa. Per kPa, that is 0.4, 0.2, and 0.1 mL; the drop keeps slowing, so the graph curves.

Practice: Name the Trend 🎯

Classify the Pattern 🔍

Each list gives y-values for x = 1, 2, 3, 4, 5.

ACT-Style Set: Dissolving Times 📋

Students timed how long a 2.0 g tablet took to dissolve completely in 200 mL of water at five temperatures and three stirring speeds.

Table 1 — Time to dissolve (s)

ACT-Style Practice

Give yourself about one minute.

A biologist measured how many seeds of a desert shrub germinated at different soil moisture levels.

Question: Which statement best describes the data?

Germination rises to a maximum at 20% moisture, then falls. The differences are +23, +26, +7, −15, and −27: positive, then negative, which is a peak. The biggest single jump is from 10% to 15%, but the peak is where the count is largest, 64 at 20%. "Increases with moisture" ignores the last two intervals.

Key Takeaways

• Direct means both rise; inverse means one rises as the other falls.
• Use first differences: equal → linear; growing → accelerating; shrinking → leveling off; sign change → peak or trough.
• Directly proportional: y ÷ x constant. Inversely proportional: x × y constant, so doubling x halves y. Compute it for every row.
• A trend choice must fit every interval and only the tested range.
• The peak is at the largest y-value, not the biggest jump.
• Observational data show association, not causation; "tended to" beats "causes."

🔗 Comparing Data Sets

Part 4 of 7 — Linking Tables, Comparing Studies, Spread, and Error Bars

Many ACT Science questions cannot be answered from a single figure. They say "Based on Tables 1 and 2" or "According to Figures 1 and 2," or they ask whether two groups really differ. This part covers both skills.

Linking Two Tables Through a Shared Variable

When two tables share a variable, you can chain them: use the first table to get a value, then carry that value into the second table.

The classic trap is stopping halfway and answering with the bridge value itself, such as reporting a pressure when the question asked for a temperature.

Linking Tables by Labels

Sometimes two tables describe the same samples (Sample A, B, C or Trial 1, 2, 3), but the rows are listed in different orders. Match by label, not by row position. Rewriting the pairs side by side (A: pH 4.5, 12 worms; B: pH 5.5, 30 worms) takes ten seconds and prevents most errors.

Comparing Two Studies or Two Curves

• "Both studies show ..." must be true in each study separately. Check every interval for both.
• Agree vs. disagree: find the x-values where the two data sets are close and where they split. A question may ask over which range the gap exceeds some amount.
• Higher vs. faster: a curve that is higher is not necessarily changing faster. Compare values for "greater," slopes for "faster."
• Same conditions? Two studies may cover different ranges or use different units. Compare only where both have data.

Repeated Trials, Means, and Spread

Scientists repeat trials because measurements vary by chance. For a set of repeated trials:

• The mean (average) summarizes the typical value.
• The range (largest − smallest) shows the spread. A small spread means precise, consistent measurements; a large spread means the mean is less certain.
• Two groups whose trial values interleave (some of each group above and below the other) do not clearly differ, even if their means are different.

Error Bars and ± Values

An error bar or a ± value shows a range of uncertainty around a measured value.

To compare two groups:

Wider bars mean less precision. A mean of 50 ± 10 is far less certain than 50 ± 1. The ACT rewards conservative answers here: when bars overlap, avoid choices that say one group "clearly" or "definitely" did better.

Common Comparison Traps

Worked Examples

Table 1 — Light at different depths in a lake

Table 2 — Growth of an alga at different light levels

Question 1: What is the algae's growth rate at a depth of 4 m?

The bridge is light. Table 1: 4 m → 36%. Table 2: 36% → 1.6 doublings/day. Answering "36" reports the light level, not the growth rate.

Question 2: At about what depth would the alga grow at 0.9 doublings per day?

Work backward. Table 2: 0.9 → 22% light. Table 1: 22% → 6 m.

Three groups of tomato plants were grown for 4 weeks. Each mean height is shown with its uncertainty.

Question: Which dose gives clear evidence of taller plants than the control?

• Low dose: 21.5 to 23.5 overlaps the control's 19.5 to 22.5. The 1.5 cm gap in the means is uncertain.
• High dose: 24.8 to 27.2 sits entirely above 22.5. That is clear evidence.

Answer: the high dose only. A choice saying "both doses clearly increased height" trusts the low-dose mean without checking its error bar.

Practice: Link and Compare 🎯

Ranges and Means 🧮

Enter numbers only.

1. A mass is reported as 8.4 ± 0.3 g. What is the lowest value in its range, in grams?

2. What is the highest value in that range, in grams?

3. Five trials gave times of 12, 15, 11, 14, and 13 s. What is the mean time, in seconds?

ACT-Style Set: Paper Helicopters 📋

Experiment 1: Students dropped three paper-helicopter designs from a height of 2.0 m and timed the fall, five trials each.

Table 1 — Fall time (s)

Experiment 2: Using the same paper and no paper clip, the students made helicopters with different wing lengths and recorded the mean of five drops.

Table 2

ACT-Style Practice

Give yourself about one minute.

Table 1 gives the salt content of four water samples, and Table 2 gives the temperature at which each sample froze.

Question: Based on both tables, a sample with 15 g/L of salt would most likely freeze between which two temperatures?

Between −0.6°C and −1.2°C. Matching by label, 10 g/L (P) freezes at −0.6°C and 20 g/L (R) freezes at −1.2°C, and 15 g/L lies between them. A student who matches rows by position would pair 10 g/L with 0.0°C and get the wrong range.

Key Takeaways

• To use two tables together, find the shared (bridge) variable, check its units, and chain: in through one table, out through the other.
• Don't stop at the bridge value; answer in the variable the question asks for.
• Match rows by label, not by position, when two tables list the same samples in different orders.
• "Both studies show" must hold in each study separately.
• A large spread in repeated trials makes the mean less certain.
• x ± u spans x − u to x + u. No overlap is strong evidence of a difference; overlap means the difference is uncertain.

🔮 Making Predictions

Part 5 of 7 — Interpolation, Extrapolation, Working Backward, and Prediction Error

ACT Science regularly asks for a value the researchers never measured: "If a trial were run at 25°C ..." or "If the trend continues ...". Every such question is one of two kinds.

Interpolation: Estimating Between Points

1. Find the true neighbors. Locate the two measured x-values just below and just above the new x. If the x-values are unevenly spaced (0, 10, 30, 50), the neighbors of 20 are 10 and 30, not the next two rows.
2. Find how far along you are. 20 is halfway from 10 to 30, so the fraction is 1/2. 17 between 10 and 20 is 7/10 of the way.
3. Go the same fraction of the way in y. Halfway between 20.0 and 12.0 is 16.0.

The answer must lie between the two neighboring y-values. That alone eliminates many choices.

Curved data: linear interpolation assumes a straight line between points. If the curve is bending, the true value differs a little from the straight-line estimate. For a curve that is falling and flattening (like a cooling cup of coffee), the curve sags below the straight line between two points, so the true value is slightly lower than the linear estimate. On most ACT questions, though, the straight-line estimate (or "between these two values") is what the question wants.

Working Backward

Given a y-value, find the x-value. Locate the two y-values that bracket it, then go the same fraction of the way between their x-values. Example: if 40 g/L gives −2.4°C and 60 g/L gives −3.6°C, then −3.0°C (halfway) corresponds to about 50 g/L.

Extrapolation: Extending the Pattern

1. Identify the pattern. Constant difference (+5 each step) → keep adding 5. Constant ratio (halves each step) → keep halving.
2. Count the steps from the last measured value to the target.
3. Apply the pattern that many times.

To find when a target is reached: time needed = (gap to target) ÷ (rate). If a mass falls 4 g/min and is now at 36 g, reaching 20 g takes 16 ÷ 4 = 4 more minutes. Add that to the current time to get the clock time.

Caution: extrapolation assumes the pattern keeps going, and real patterns often change outside the tested range. Growth levels off, a cooling object stops at room temperature, an enzyme stops working at high heat. The ACT signals when to assume the pattern continues ("if the trend continues"); when a passage gives a physical limit (room temperature, 100% germination, zero mass), a prediction cannot cross it.

Predicted vs. Measured: Prediction Error

When a passage compares a model's predictions with measurements:

"Which prediction was closest" or "largest error" uses absolute error. A prediction that is 5 too high is farther off than one that is 3 too low.

Common Prediction Traps

Worked Examples

A thermometer was placed at different distances from a heat lamp.

Question 1: Estimate the temperature at 30 cm.

The neighbors of 30 cm are 20 cm and 40 cm (not 10 and 20). 30 is halfway between them, so the temperature is halfway between 40 and 32: 36°C.

Question 2: At about what distance would the temperature be 29°C?

29°C lies between 32°C (40 cm) and 26°C (80 cm), exactly halfway. Halfway from 40 cm to 80 cm is 60 cm.

Notice that equal temperature steps take larger and larger distance steps. The spacing of the table is a clue that the relationship is not linear over the whole range, which is why you should always interpolate between the nearest rows.

A water tank was drained through a valve.

Question: If the trend continues, when will the tank be empty?

1. Pattern: the tank loses 15 L every 5 min, a rate of 3 L/min.
2. Gap: 75 L remain at 15 min.
3. Time needed: 75 ÷ 3 = 25 more minutes.
4. Clock time: 15 + 25 = 40 min.

Answering 25 min reports only the extra time. And the pattern cannot continue past 40 min: a tank cannot hold negative water, so any prediction of "−15 L at 45 min" is impossible.

Practice: Estimate It 🎯

Prediction Vocabulary 🔍

ACT-Style Set: A Cooling Cup 📋

A cup of coffee was left to cool in a room kept at 20°C. Its temperature was recorded at the times shown.

Table 1

ACT-Style Practice

Give yourself about one minute.

A detector counted the radiation from a sample every 2 hours.

Question: If the trend continues, what will the count rate be at 10 h?

50 counts per minute. The pattern is a constant ratio: the count halves every 2 hours. From 6 h to 10 h is two more halvings: 200 → 100 (8 h) → 50 (10 h). Subtracting a constant amount instead (the first drop was 800) would give a negative count, which is impossible; the drops themselves shrink by half each step.

Key Takeaways

• Interpolation estimates inside the measured range; extrapolation estimates outside it.
• Interpolate between the true neighbors, going the same fraction of the way in y as in x; the answer lies between the neighboring values.
• Work backward the same way: bracket the given y, then find the matching fraction of x.
• To extrapolate, identify the pattern (constant difference or constant ratio) and count steps; for "when," use gap ÷ rate, then add to the last time.
• Extrapolations cannot cross a physical limit given in the passage.
• "Closest" and "largest error" use absolute error, not signed differences.

🧪 Variables, Controls & Claims

Part 6 of 7 — Independent and Dependent Variables, Controls, Fair Comparisons, and Judging Claims

Data tables come from experiments, and many ACT Science questions ask about the experiment itself: what was changed, what was measured, what was held constant, and whether a conclusion is justified. These questions follow a small set of rules.

The Vocabulary of an Experiment

Quick test for each variable: Did the researchers pick its values (independent), record its values (dependent), or keep it fixed (controlled)?

Fair Comparisons: Change Only One Thing

To see the effect of one variable, compare two trials that differ in that variable only. Everything else must match.

• Finding a pair: for each candidate pair of trials, list what differs. If exactly one variable differs, the pair isolates it.
• Confounded comparison: if two variables changed between trials, a difference in results could come from either one. No conclusion about either variable alone is justified.
• Designing a new trial: to test variable X alone, copy an existing trial and change only X.

Controls and Baselines

A control shows what happens without the treatment. The treatment's own effect is the difference from the control:

$\text{effect of treatment} = \text{treatment result} - \text{control result}$

If a placebo group's blood pressure dropped 4 points and the medicine group's dropped 13, the medicine accounts for about 9 points, not 13. Pick the control that matches what the question isolates: to find the effect of a hormone beyond soaking, compare with seeds soaked in plain water, not unsoaked seeds.

A control does not remove random variation. That is the job of repeated trials, which reveal how much results vary by chance.

Judging Claims and Hypotheses

Every claim gets one of three verdicts:

Absolute words are fragile. "Only," "always," "every," and "never" can be defeated by a single fair comparison. To refute "depends only on temperature," find two trials at the same temperature with different results.

Watch the reasoning, not just the verdict. ACT choices often pair "Yes" or "No" with a reason. The right choice has the right verdict and cites a fair comparison. "Yes, because Trial 5 was fastest" is weak if Trial 5 differs from the others in two ways.

"If the hypothesis is correct, which result would be expected?" Translate the hypothesis into a prediction about the table ("more salt → lower freezing point"), then pick the choice whose numbers follow that direction.

Common Design Traps

Worked Examples

Students grew bean seedlings under lamps for 14 days.

Dependent variable: height, the only value measured. The other three columns were set by the students.

Effect of light color alone: Trials 1 and 2 differ only in color (white vs. red), so red light added 1.3 cm under these conditions.

Effect of hours of light alone: Trials 2 and 3 differ only in hours (12 vs. 16), so 4 extra hours added 2.4 cm.

Effect of water: Trial 4 differs from Trial 3 in both color and water, so it is confounded. Nothing can be concluded about water. To fix it, add a trial with red, 16 h, 30 mL: compared with Trial 3, it changes only the water.

Volunteers touched a lab surface, then either did not wash, washed with plain soap, or washed with antibacterial soap. Their fingertips were pressed onto nutrient plates.

Claim 1: "Antibacterial soap removes 135 more colonies than plain soap." Contradicted. The 135 comes from comparing with no washing (180 − 45). Compared with plain soap, antibacterial soap left only 60 − 45 = 15 fewer colonies.

Claim 2: "Antibacterial soap is the only soap that reduces bacteria." Contradicted. Plain soap cut colonies from 180 to 60.

Claim 3: "Antibacterial soap works better on every type of bacterium." Can't tell. The study counted colonies but never identified types of bacteria.

Practice: Variables and Controls 🎯

Classify the Variables 🔍

A student tests how the number of turns of wire in a coil affects how many paper clips an electromagnet can lift. She uses the same battery, the same iron nail, and the same type of wire in every trial.

ACT-Style Set: Melting Ice 📋

Students placed identical 20 g ice cubes in water and timed how long each took to melt completely.

Table 1

Student A claims that melt time depends only on water temperature. Student B claims that stirring shortens melt time at both 20°C and 40°C.

ACT-Style Practice

Give yourself about one minute.

A student tested how far a paper airplane flew.

Question: The student wants to add one trial that, compared with Trial 2, shows the effect of wing shape alone. What should the new trial use?

Straight wings, 5 g paper, 20° launch angle. Copy Trial 2 and change only the wing shape. Trial 3 already has straight wings, but it also changes the paper mass, so comparing Trials 2 and 3 cannot separate wing shape from mass.

Key Takeaways

• Independent = what researchers change; dependent = what they measure; controlled = what they keep the same.
• A fair comparison uses two trials that differ in only one variable; a pair that differs in two is confounded.
• To design a test of one variable, copy an existing trial and change only that variable.
• A control is a baseline: the treatment's effect is treatment − control, using the control that matches what you want to isolate.
• Claims are supported, contradicted, or can't tell. One counterexample defeats "only," "always," or "every."
• Choose answers whose reason cites a fair comparison, not just the right yes or no.

⏱️ Integrated Timed Practice

Part 7 of 7 — Pacing, a Passage Routine, and Mixed ACT-Style Sets

This part puts Parts 1 through 6 together under time pressure, the way the test does.

The Format, Once More

That works out to about one minute per question, reading included. For a passage with six questions, aim for about six minutes total, and move on if you are well past that.

A Passage Routine

1. Skim the introduction (about 20 seconds). What was studied? What was changed, and what was measured?
2. Glance at each figure. Read titles, axis labels, units, and legends. Don't memorize numbers; just know where things are.
3. Go to the questions. Many name a figure ("According to Table 2 ..."). Go straight there.
4. Answer from the data. Outside knowledge rarely decides a data question, and a choice that sounds scientifically true but isn't shown in the figure is a trap.
5. Read the text only when a question needs it, such as a question about why a step was done or what was held constant.

Recognize the Question Type

Five Checks Before You Choose

Quick Reference: The Arithmetic You'll Use

When You're Stuck

• Eliminate first. Most questions have one or two choices that fail a direction or units check. With two choices left, compute only what separates them.
• Skip and return. A hard question is worth the same as an easy one. Mark it, answer the rest of the passage, and come back if time allows.
• Never leave a blank. With no penalty for wrong answers, a guess can only help.

Worked Example: One Passage, Start to Finish

Passage: Researchers collected rainwater at five distances downwind of a coal-burning power plant and measured its pH. Lower pH means more acidic water.

Routine (about 20 seconds): Distance was chosen (independent); pH was measured (dependent). The distances are unevenly spaced, so be careful with neighbors.

Question 1: As distance increases, the rainwater pH:

Every value is higher than the one before, so pH increases. Per km, the gains are 0.06, 0.08, 0.04, and 0.015, so it rises more slowly at large distances. A choice of "decreases" reverses the trend; "increases, then decreases" has no support. (About 30 seconds.)

Question 2: Assuming linear change between measurements, the pH at 15 km would be closest to:

The neighbors of 15 km are 10 km and 20 km, not 5 and 10. Halfway between 4.9 and 5.3 is 5.1. (About 30 seconds.)

Question 3: Which conclusion is best supported?

The researchers only observed pH at different distances; they did not change the plant's output. The safe conclusion is that rain was more acidic closer to the plant. A choice saying the data prove the plant causes the acidity overreaches, and one saying rain "becomes neutral (pH 7) beyond 40 km" extrapolates past the data. (About 45 seconds.)

Total: under two minutes for three questions, with time banked for harder ones.

Timed Set 1: Coral Growth ⏱️ Aim for 4 minutes.

Marine biologists grew coral fragments in tanks of seawater and measured the rate at which each fragment built its skeleton (calcification rate, in mg/day).

Table 1 — Calcification rate at different seawater pH values (water temperature 26°C)

Table 2 — Calcification rate at different water temperatures (seawater pH 8.2)

Test-Day Decisions 🔍

Timed Set 2: Model Wind Turbines ⏱️ Aim for 5 minutes.

Students built model wind turbines and measured the electrical power produced (in milliwatts, mW) in front of a fan.

Experiment 1: Turbines with different numbers of blades were tested at a wind speed of 5 m/s. Each value is the mean of 6 trials, with its uncertainty.

Table 1

Experiment 2: The 3-blade turbine was tested at different wind speeds.

Table 2

ACT-Style Practice

Give yourself about one minute.

A psychologist measured reaction times with and without background music. Each result is a mean with its uncertainty.

Question: By how many milliseconds did the mean reaction times differ, and is the difference clear?

60 ms, and yes, the difference is clear. The means differ by 0.42 − 0.36 = 0.06 s, and 0.06 × 1,000 = 60 ms. The silence range is 0.34 to 0.38 s and the music range is 0.39 to 0.45 s, so the ranges do not overlap. This one question uses three skills: a table lookup, a unit conversion (Part 1), and an error-bar comparison (Part 4).

Key Takeaways

• Enhanced ACT Science: optional, 40 questions in 40 minutes, 4 choices, no penalty for guessing; budget about one minute per question.
• Routine: skim the introduction, glance at figure labels and units, then go to the questions and to the figure each one names.
• Identify the question type (lookup, rate, trend, linking, prediction, design/claim) and apply that part's method.
• Before choosing, run the five checks: right figure, right variable and units, right direction, inside the data's limits, claim the right size.
• Eliminate, skip hard questions and return, and never leave a blank.