GED Math Practice — Test 1

1. What the nudges are (and are not)

Each question carries a Nudge — a printed hint about which method to use: the formula, the first step, or the operation the question is really asking for (rise over run, part ÷ whole, square before you multiply). A nudge never states the answer or names an option; it names the strategy so a stuck student gets unstuck by reasoning. The show-your-work box under every question is where that reasoning becomes visible — insist it gets used, even when the student is confident. Over time the nudges should become the student's own mental checklist and can be withdrawn.

2. How to run the session

• Try each alone first. Student attempts each question independently and only reads the nudge if they cannot start. Ask them to tick which questions needed a nudge — that tick list is your diagnostic.
• A calculator is allowed, just as on the real GED. Encourage it for the multi-step arithmetic (Q1–Q3, Q6, Q23) so effort goes into method, not hand computation.
• Suggested flow: Stimulus 1 + Q1–4, Stimulus 2 + Q5–8, Stimulus 3 + Q9–12, Stimulus 4 + Q13–16, then Q17–24, then the constructed response (which can be homework).
• This level of math appears on high school equivalency exams with a roughly 115-minute time limit. Build pacing habits during practice, but accuracy and reasoning come first; speed follows.

3. Reviewing the work — WITHOUT handing over a key

The goal of review is not a score — it is to understand how the student is thinking. There is no answer key in this student packet by design; rework each miss together instead of reading off a letter.

• Ask first, tell second. Before confirming anything, ask "How did you get this?" or "Walk me through your steps." Use the show-your-work box as the starting point.
• Correct guesses still need explanation. A lucky guess and sound reasoning look identical on paper. If the student cannot explain why, treat it as a gap, not a pass.
• Rework each miss by the method, not the answer. Send the student back to the relevant formula or table and redo the problem together, checking each step. The fix is the corrected method, not the right letter.
• Look for patterns. If Q2, Q6, and Q19 all break down on multiplication or combined operations, that is one skill gap, not three mistakes — address the concept.
• Change the approach when a pattern appears. If re-explaining the same way hasn't worked, switch it: draw a diagram, use an area model, use real objects, or break the concept into smaller steps.

4. Common errors by question (the specific misconception behind each miss)

Questions 1–4 — Data Table (Coffee Shop)

• Q1 (total coffee): If wrong, ask "Did you add all seven days?" Students often miss a row or accidentally include food sales.
• Q2 (revenue per customer): Students may rank by total revenue (Saturday) rather than revenue-per-customer (Tuesday). Ask: "If you earned $100 from 5 customers vs $200 from 50 customers, which visit was worth more per person?"
• Q3 (food % of total): Common error is dividing food by coffee only, not by total. Reinforce percent = part ÷ whole; ask what the whole is.
• Q4 (range): Students sometimes add instead of subtract. Clarify range = spread = highest minus lowest. A number-line sketch helps.

Questions 5–8 — Line Graph, now a data table (Food Truck Revenue)

• Q5 (largest increase): Students may pick a week whose value is tall rather than one whose jump from the prior week is large. Reinforce: increase = change from previous week, not the height of the point.
• Q6 (mean): Ensure the student adds all five values before dividing. A common shortcut error is averaging only two or three values.
• Q7 (prediction): The projection continues the Week 4→5 rate (+150). If a student picks A or B, they may be eyeballing rather than computing. Require them to write 1,750 + 150 = 1,900.
• Q8 (trend): The one dip (Week 2→3) is the key detail. A student who picks A (steady decrease) has misread the direction entirely.

Questions 9–12 — Geometry (Right Triangle Garden Bed)

• Q9 (hypotenuse): Have the student write a² + b² = c² explicitly: 36 + 64 = 100, √100 = 10. Do not let them skip steps or simply add the legs.
• Q11 (area): If they answer 48, they computed 6 × 8 without halving. Draw a rectangle around the triangle: the triangle is exactly half of it.
• Q12 (doubled legs): Students must apply the Pythagorean theorem to the new legs (12 and 16) to find the new hypotenuse (20), not just double the old perimeter. Require the full calculation.

Questions 13–16 — Probability (Raffle)

• Q13 (grand prize probability): 12 tickets out of 300. If a student picks B (1/300), they are computing as if Jamal has only one ticket.
• Q14 (complement): If the student struggles, try "If there's a 10% chance of rain, what's the chance it stays dry?" Then connect: 1 − P(event) = P(not event).
• Q15 (without replacement): If they write 12/300, they missed that one ticket was already removed. Ask "After one ticket is pulled out and kept, how many are left in the drum?"
• Q16 (inference): Go through each option one at a time — "Is this true or false? How do we know?" This teaches systematic evaluation of claims.

Questions 17–24 — Core Algebra, Geometry, Number Sense

• Q18 (distribution): If they get 5x + 12, they added 3x + 2x but forgot the subtraction. If they get x + 4, they only multiplied 3 × x, not 3 × 4. Use an area model.
• Q22 (inequality): Don't just state the flip rule. Let the student test it: "If −3 < 6 is true, and we divide both sides by −3, does 1 < −2?" Seeing it fail on a concrete case makes it stick.
• Q23 (cylinder volume): If they get 94.2, they used r instead of r². Emphasize: square the radius first, then multiply.
• Q24 (function): If they get 11, they computed 2(4) − 5 using x not x². Require every step: f(4) = 2(4)² − 5 = 2(16) − 5 = 32 − 5 = 27.

5. Constructed Response (25) — scoring & solution guidance

Verified solution. Part A: C = 6x + 850. Part B: R = 22x. Part C: set R = C → 22x = 6x + 850 → 16x = 850 → x = 53.125; since a fractional bag cannot be sold, the business must sell 54 bags to cover all costs and begin making a profit. Part D: revenue at 120 bags = 22 × 120 = $2,640; cost = 6 × 120 + 850 = $1,570; profit = $1,070. The break-even point (54 bags) is where the business exactly covers its costs — fewer means a loss, more means a profit.

Scoring, 0–4

• 4 — Correct cost and revenue equations; sets R = C and solves correctly; interprets the decimal (rounds up to 54 with reasoning); computes the $1,070 profit and explains break-even accurately.
• 3 — Correct setup and solving, but the decimal interpretation or the break-even explanation is thin.
• 2 — Some correct equations or arithmetic, but a key step (e.g. R = C, or rounding) is missing or wrong.
• 1 — Minimal or largely inaccurate work; little correct setup.
• 0 — No response or off-topic.

Coaching notes. Parts A & B: if the student can't start, ask "What stays the same no matter how many bags are made? What changes?" to surface fixed vs. variable costs before giving the equations. Part C: if they set up R = C but stall, walk one step at a time; the decimal (53.125) needs interpretation — "Can you sell a fraction of a bag?" Part D: if they write only "break even means no profit," push further — "What happens if you sell one fewer bag than 54? One more?" Credit the use of specific numbers as evidence over polished prose.