Original mixed revision, not an official enhanced ACT mock or scaled-score predictor. Use the exact form-specific keys and field-test exclusions for official practice.
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act:mixed-revision:1
A paragraph explains a process. A proposed final sentence discusses the author’s favourite holiday. Decide whether to include it and explain.
Answer and reasoning · Réponse et raisonnement
Omit it unless it contributes to the stated process and paragraph purpose; interesting information alone is not relevant.
act:mixed-revision:2
A rectangular floor is 9 m by 12 m. Find its diagonal and the area.
Answer and reasoning · Réponse et raisonnement
15 m by the Pythagorean theorem; area 108 m². Do not confuse the two units.
act:mixed-revision:3
Trials measure 4, 7 and 10 cm of growth at fertiliser levels 0, 1 and 2. Predict at level 1.5 and identify a limitation.
Answer and reasoning · Réponse et raisonnement
Linear interpolation suggests 8.5 cm. The estimate assumes roughly linear behaviour between measured levels; it does not justify unlimited growth beyond the range.
act:mixed-revision:math-1
Evaluate 32^(2/5), multiply (1+2i)(3-i), and explain why √(x²) need not equal x.
Answer and reasoning · Réponse et raisonnement
32^(2/5)=4. Product=5+5i. √(x²)=|x|, so a negative x is not equal to its principal root.
act:mixed-revision:math-2
A displacement is (5,-12). Give its magnitude. A quantity row (4,3) and corresponding prices (2,6) produce what cost?
Answer and reasoning · Réponse et raisonnement
Magnitude 13; cost 4·2+3·6=26. Counts and prices must use the same item order.
act:mixed-revision:math-3
Factor x³-16x and give all roots. Solve (x-2)(x-6)>0.
Answer and reasoning · Réponse et raisonnement
x(x-4)(x+4), roots -4,0,4. Strict inequality holds x<2 or x>6; endpoints excluded.
act:mixed-revision:math-4
Solve √(x+12)=x and check every candidate. Is (1,3) in the region y>2x and x+y≤4?
Answer and reasoning · Réponse et raisonnement
Squaring gives x²-x-12=0, candidates 4,-3; only 4 works. (1,3) satisfies 3>2 and sum 4≤4, so it is included.
act:mixed-revision:math-5
For f(x)=2x-1 and g(x)=x+3, evaluate f(g(4)) and g(f(4)). Find f⁻¹(9).
Answer and reasoning · Réponse et raisonnement
f(g(4))=13; g(f(4))=10. f⁻¹(x)=(x+1)/2, so f⁻¹(9)=5.
act:mixed-revision:math-6
Find the fourth term and four-term sum of 5,10,20,… . Solve log₃(x-2)=2.
Answer and reasoning · Réponse et raisonnement
Fourth term 40; sum 75. x-2=9 gives x=11, valid for x>2.
act:mixed-revision:math-7
Give amplitude, period and maximum of y=5 sin(4x)-2 for radian x. Find sin150°.
Answer and reasoning · Réponse et raisonnement
Amplitude 5, period π/2, maximum 3. sin150°=1/2.
act:mixed-revision:math-8
Rotate (-2,4) 90° counterclockwise about the origin. Find the midpoint and distance between (0,-1) and (6,7).
Answer and reasoning · Réponse et raisonnement
Rotation (-4,-2). Midpoint (3,3); distance √(36+64)=10.
act:mixed-revision:math-9
For (x-3)²/16+(y+1)²/9=1, give centre and semiaxes. A cone radius 4, height 6 has what volume?
Answer and reasoning · Réponse et raisonnement
Centre (3,-1), semiaxes 4 horizontal and 3 vertical. Cone volume=π·16·6/3=32π.
act:mixed-revision:math-10
A normal model has mean 80 and SD 6. Give the approximate 68% interval. Observed value 31 with predicted 34 has what residual?
Answer and reasoning · Réponse et raisonnement
Approximately 74–86. Residual 31-34=-3; a prediction error alone does not explain causation.
act:mixed-revision:math-11
Choose an ordered leader/deputy pair and an unordered two-person team from seven people. How many possibilities of each? A prize 12 has probability 1/4; otherwise the prize is zero. Find expected prize.
Answer and reasoning · Réponse et raisonnement
Ordered 7·6=42; unordered 21. Expected prize=12·1/4=3.
act:mixed-revision:math-12
A hire model C=9+2t predicts 15 for three hours. Every observed bill is four units higher at several durations. Propose a revision. Convert a 2.5 m length to centimetres and to its length on a 1:50 plan.
Answer and reasoning · Réponse et raisonnement
C=13+2t adjusts the constant offset while retaining slope. 2.5 m=250 cm; at 1:50 the drawing length is 5 cm.
act:mixed-revision:task-19
An argument proposes wider aisles to improve wheelchair access. Choose a useful addition: measured aisle widths or a history of the shop’s logo. Explain one limit on what the widths establish.
Answer and reasoning · Réponse et raisonnement
Widths directly address access; logo history does not. Widths alone do not establish usability at every turn or during crowded periods.
act:mixed-revision:task-20
Order A “These entries were then checked against receipts.” B “The clerk listed each payment.” C “Discrepancies were marked for review.” Choose a transition from the check to the discrepancies and explain.
Answer and reasoning · Réponse et raisonnement
B–A–C. These entries requires the list. A sequence or result expression can fit depending on sentence wording; a contrast is unsupported.
act:mixed-revision:task-21
Edit “During the first week, workers returned back approximately around noon. This epic result proves the schedule always works.” Keep all defensible information.
Answer and reasoning · Réponse et raisonnement
During the first week, workers returned approximately at noon. Remove back and one approximating expression; delete the unsupported universal claim and exaggerated judgement.
act:mixed-revision:task-22
Repair “Although the readings were stable. The set of measurements were incomplete, reviewing them, a missing value worried Al.” Explain the real subject.
Answer and reasoning · Réponse et raisonnement
For example: Although the readings were stable, the set of measurements was incomplete. Reviewing them, Al noticed a missing value. Set is singular; Al reviews the readings.
act:mixed-revision:task-23
A narrator says “The first trial was slow. After we labelled the drawers, two visitors found their tools without asking. We have not tried the system on a busy day.” State a supported inference and a limit.
Answer and reasoning · Réponse et raisonnement
Labels may have helped those two visitors retrieve tools; busy-day performance remains untested. Do not infer universal efficiency or causation proved by this small observation.
act:mixed-revision:task-24
“The repair breathed new life into the hall. Yet one corner stayed unused.” Explain the figurative phrase and the function of Yet.
Answer and reasoning · Réponse et raisonnement
Breathed new life means restored activity or usefulness, not literal breathing. Yet introduces a limitation on the apparent success.
act:mixed-revision:task-25
Author A wants longer hours; B agrees that access matters but asks for staffing evidence first. Visits/waiting counts are daytime 40/8 and evening 15/6. Compare views and waiting proportions.
Answer and reasoning · Réponse et raisonnement
Shared goal: access. Disagreement: immediate expansion versus evidence before staffing changes. Rates 20% and 40%; fewer evening visitors does not mean a smaller proportion waited.
act:mixed-revision:task-26
Two sensors differ in housing material and ventilation. Temperature differs. Design a test of ventilation alone; choose a design meeting cost ≤8 and error ≤2 from A (7,2), B (5,3), C (9,1).
Answer and reasoning · Réponse et raisonnement
Keep housing material and other conditions fixed while varying ventilation, with repeats. A satisfies both; B fails error and C fails cost.
act:mixed-revision:task-27
Models P and Q both predict a fall in output with time; only Q predicts a further fall with increasing humidity at fixed time. What test separates them? What does a shared prediction prove?
Answer and reasoning · Réponse et raisonnement
Use matched devices at different humidities with runtime and measurement conditions fixed. A fall with time alone cannot discriminate between the models.
act:mixed-revision:task-28
At times 0, 2, 4 min, output is 10, 18, 22 units. Interpolate at 3 min. Compare interval rates and assess extending the first rate to minute 4.
Answer and reasoning · Réponse et raisonnement
Interpolated output 20. Rates 4 and 2 units/min. First rate predicts 26 at minute 4, contradicting measured 22; constant rate across the full interval is unsupported.
act:mixed-revision:task-6
For the learning-centre booking issue, draft a relationship statement and one developed reason for your own position. Then annotate which of the four writing domains each revision would improve.
Answer and reasoning · Réponse et raisonnement
Accept a clear relationship to a supplied perspective and a developed example with an explained implication. Label changes by analysis, development/support, organisation or language; no stance-based grading or official score prediction.