1. What This Capstone Asks
A real placement test doesn't test any single topic in isolation — it mixes all of them, under a hard time limit, and rewards knowing which questions to attempt first as much as knowing how to solve any individual one. This capstone reproduces that exact condition rather than one more topic-by-topic drill.
The deliverable is simple to state and genuinely demanding to do properly: sit Section 2's 30-question test under a real 35-minute clock, score it honestly, and turn every miss into a permanent entry in the error log Section 4 builds — the actual skill this capstone is testing is whether you can turn a test result into targeted improvement, not just whether you can solve the 30 questions with unlimited time.
2. The Full Mock Test — 30 Questions
One or two questions from every module, roughly ordered the way a real test paper mixes topics — not grouped by chapter. Set a timer for 35 minutes before starting, and don't check the answer key until the timer ends or you've genuinely finished.
1. Is 4,824 divisible by 8?
2. Find the LCM of 18 and 24.
3. Find 45% of 260.
4. An item bought for 400 is sold for 460. Find the profit %.
5. Find the SI on 5,000 at 6% for 3 years.
6. Divide 720 in the ratio 4:5.
7. Find the average of 12, 18, 24 and 30.
8. A does a job in 15 days, B in 10 days. Working together,
how many days will they take?
9. A car travels 180km in 3 hours. Find its speed.
10. Solve for x: 2x + 5 = 17.
11. Find the 10th term of the AP: 4, 7, 10, ...
12. In how many ways can 4 distinct books be arranged on a
shelf?
13. A die is rolled once. Find the probability of getting an
even number.
14. Simplify sqrt(48).
15. Find the area of a triangle with base 10cm and height 6cm.16. Find the angle between the hour and minute hands at
exactly 9:00.
17. A pie chart slice measures 90 degrees. What percentage
of the total does it represent?
18. Find the remainder when 3^10 is divided by 4.
19. Two numbers have HCF 6 and LCM 72. If one number is 18,
find the other.
20. A number, increased by 20%, gives 240. Find the original
number.
21. Find the CI on 8,000 at 5% per annum for 2 years.
22. If A:B = 3:4 and B:C = 2:3, find A:C.
23. A boat's downstream speed is 20 km/h and upstream speed
is 12 km/h. Find the boat's speed in still water.
24. Find the sum of the roots of x^2 - 6x + 8 = 0.
25. From a group of 6 people, in how many ways can a
committee of 3 be chosen?
26. Two coins are tossed. Find the probability of getting at
least one head.
27. Find the volume of a cube with side 5cm.
28. A is twice as old as B. In 5 years, the sum of their ages
will be 40. Find their current ages.
29. In a school of 300 students, 60% play a sport. How many
students do NOT play a sport?
30. Find the remainder when 7^100 is divided by 5.
✓
Reveal the full answer key (only after your 35 minutes are up)
Reveal the full answer key (only after your 35 minutes are up)
1) Yes (824÷8=103). 2) 72. 3) 117. 4) 15%. 5) 900. 6) 320 and 400. 7) 21. 8) 6 days. 9) 60 km/h. 10) x=6. 11) 31. 12) 24. 13) 1/2. 14) 4√3. 15) 30 cm². 16) 90° (the smaller angle). 17) 25%. 18) 1. 19) 24. 20) 200. 21) 820. 22) 1:2. 23) 16 km/h. 24) 6. 25) 20. 26) 3/4. 27) 125 cm³. 28) A=20, B=10. 29) 120. 30) 1.
3. Time Allocation & Question-Selection Strategy
35 minutes for 30 questions is 70 seconds per question on average — but treating every question as equally worth 70 seconds is a losing strategy. The actual skill is triage.
PASS 1 (first ~15 minutes): solve every question you
recognize INSTANTLY -- a formula you have cold, a shortcut
that applies immediately. Skip anything that makes you
pause and think "how do I even start this."
PASS 2 (next ~15 minutes): return to skipped questions.
Most will now be easier, because Pass 1 warmed up the exact
mental muscles this test is exercising.
PASS 3 (final ~5 minutes): anything still unsolved, take
your single best educated guess (never leave a question
blank if there's no penalty for wrong answers) and move on.This mirrors Week 17's approximate-first discipline, applied at the level of a whole test instead of a single question: spend your limited time where it returns the most correct answers per minute, not in the order the questions happen to be printed.
Real placement tests are graded on total correct answers, not on finishing every question — sinking four minutes into one stubborn problem while three easier questions go unattempted is a strictly worse outcome than skipping it and returning in Pass 2 with a fresher perspective.
4. Building an Error Log
The single highest-leverage habit this course can leave you with isn't a formula — it's a simple log that turns every practice test into targeted, compounding improvement instead of just a score.
Date | Topic | Question | My Answer | Correct Answer |
Root Cause | Fix
Example row:
2026-08-11 | Percentages | Q20 (reverse %) | 288 | 200 |
Multiplied by 1.2 instead of dividing by it -- confused
"increased BY 20%" with "increased TO 120% of X, solve
backward" | Redo the base-value section of Week 3 before
next practice testThe Root Cause column is the one that actually matters — "I made a silly mistake" is almost never the true root cause; there's nearly always a specific, nameable confusion underneath (a formula misapplied, a sign flipped, the wrong base value used) that, once named, becomes something you can deliberately watch for next time. Reviewing this log before every subsequent practice test — not just after — is what makes the same mistake stop recurring.
5. The Capstone Project
Sit the mock test, score it, and build your first error log
Take Section 2's 30-question test fully through the process this capstone describes — timed, triaged, scored and reviewed.
Requirements:
- Sit the full 30-question mock test under a genuine 35-minute timer, using Section 3's three-pass strategy rather than solving strictly in question order.
- Score yourself against the answer key, and compute your accuracy percentage (correct ÷ attempted) separately from your completion percentage (attempted ÷ 30) — these measure different things and both matter.
- Build a complete error log (Section 4's format) for every question you got wrong, including an honest root cause for each — not just "careless mistake."
- Identify which ONE topic module produced the most errors, and go back and redo that week's practice problems before attempting another mock test.
- Take a second, fresh 30-question mock test (write 30 new questions yourself, one or two per module, following Section 2's format) at least 3 days later, and compare your accuracy and completion percentage against the first attempt.
Writing a question that correctly tests a concept requires understanding that concept more precisely than solving someone else's question does — you have to know exactly what makes a problem "about" percentages versus ratios, and what numbers would make it too easy or ambiguous. This step is deliberately part of the capstone, not an optional extra.
6. Final Checklist
Before calling the capstone — and the course — done, confirm each of these honestly:
✓
Was the mock test taken under a genuine, enforced 35-minute timer, not an approximate or self-extended one?
Was the mock test taken under a genuine, enforced 35-minute timer, not an approximate or self-extended one?
A test taken without real time pressure measures something different from what an actual placement test will demand — untimed practice builds problem-solving ability, but only timed practice builds the triage and speed judgment Section 3 describes, which is the harder, less obvious half of test performance.
✓
Does the error log name a specific, nameable root cause for every wrong answer, rather than "careless mistake" as a catch-all?
Does the error log name a specific, nameable root cause for every wrong answer, rather than "careless mistake" as a catch-all?
"Careless mistake" describes the symptom, not the cause — pushed further, it's almost always a specific, recurring confusion (a formula direction, a sign, a base value) that will keep happening until it's named and deliberately watched for. An error log that stops at "careless" hasn't actually diagnosed anything yet.
✓
Was the weakest topic module actually revisited and re-practiced, not just identified?
Was the weakest topic module actually revisited and re-practiced, not just identified?
Identifying a weak topic without going back and redoing that week's practice problems leaves the actual gap unaddressed — the diagnostic step (the error log) only creates value once it's followed by the corrective step (targeted re-practice), which is where the real improvement happens.
✓
Did the second mock test show measurable improvement in accuracy or completion percentage over the first?
Did the second mock test show measurable improvement in accuracy or completion percentage over the first?
If the numbers didn't improve, that's real information, not a failure of the process — it means the error log's root causes weren't the true bottleneck, or the targeted re-practice wasn't sufficient, and it's worth another honest pass through Sections 4 and 5 rather than assuming the process itself doesn't work. This error-log-then-retest cycle is meant to repeat well beyond this course's last week.