Week 1 · Day 2 Lesson 1.1–1.2 About 9 minutes Free

How the CSCA math paper works + your plan by track

By the end: Know how a full mock is built and scored, how to spend your 60 minutes, which tracks the course offers, and what a study day contains, so every later lesson fits into a plan.

This lesson has no formulas to memorise. It is the map: the numbers here (48 questions, 60 minutes, 100 points) are the ones every mock in this course uses.

Understand it

The paper. A full ACE CSCA mock follows the pattern of a real sitting: 48 multiple-choice questions in 60 minutes, scored out of 100. It is split into three bands:

Q1–30: 2 points each, 60 points in all.
Q31–40: 2 points each, 20 points in all.
Q41–48: the hard questions, 2.5 points each, 20 points in all.

So $80$ of the $100$ points are in Q1–40. A wrong answer scores $0$ , exactly like a blank, so never leave a question empty.

The 60-minute plan. The average is $60\div48=1.25$ minutes, or 75 seconds, per question. That is only an average: the early questions take much less, which buys time for the hard ones. Train with this pacing guide:

Q1–30 in about 25 minutes (50 seconds each).
Q31–40 in about 15 minutes (90 seconds each).
Q41–48 in about 15 minutes (just under 2 minutes each).
The last 5 minutes for the questions you flagged and for any blank.

Three habits go with it. First, go in order and answer what you can. Second, flag and move: when a question has taken twice its time, choose your best option, flag it, and move on. Third, do not stay with one hard question: a 2-point question you skipped is worth the same as one you solved in 20 seconds.

The three tracks. The course adapts to the score you need:

60–75: 45 minutes a day, with one core practice set on the Q1–40 question types. The hardest questions are optional.
75–85: 60 minutes a day, with Set A (exam level) and Set B (one notch harder), plus a weekly 41–48 drill.
85+: 60 minutes a day, the 75–85 course with more hard questions.

Your track is shown on your Profile, and your plan changes with it while your progress stays.

What a study day looks like. Every day takes about an hour or less:

A lesson like this one: read it, work the examples, and pass the knowledge check.
Daily questions: Set A and Set B, 8 questions each, with a soft 10-minute timer. The target is $6$ out of $8$ .
Fix to 100%: redo every miss until you understand it. A set only counts as finished when every miss is fixed.
Drills and flashcards: the speed drill, easy tricks, and your Mistakes list.

Day 1 is the diagnostic, Days 2–5 are lessons, Day 6 is a drill day, and Day 7 is the weekly mock. The pattern repeats, and Mocks 1–4 come at the end.

The top traps of Week 1. Three mistakes cost the most points early, and each has its own lesson this week: using $\in$ where $\subseteq$ belongs (Lesson 1.3), putting a quadratic inequality inside the roots when it belongs outside, or closing a bracket at a denominator root (1.5–1.6), and trusting one number to prove an inequality (1.7).

Essential formulas

\text{score}=2\times(\text{correct in Q1–40})+2.5\times(\text{correct in Q41–48})

Out of

2\times40+2.5\times8=100

. A wrong answer and a blank both score

0

\text{average time per question}=\frac{60\text{ min}}{48}=1.25\text{ min}=75\text{ s}

Use the band pacing (50 s, 90 s, about 110 s) rather than the flat average, so the easy questions fund the hard ones.

\text{Set target}:\ 6\text{ of }8\ \ (75\%)

Your first score on a daily set is the one that counts, and you then fix every miss until the set shows 100%.

See it

Q1–30: 25 min. Q31–40: 15 min. Q41–48: 15 min. Check flagged questions: 5 min. Total 60 min.

Worked examples

Worked example 1

A student answers 34 of Q1–40 correctly and 3 of Q41–48 correctly. What is the mock score?

Questions 1–40 are worth 2 points each: $34\times2=68$ .
Questions 41–48 are worth 2.5 points each: $3\times2.5=7.5$ .
Add them: $68+7.5=75.5$ out of $100$ .

Answer: $75.5$ points.

Worked example 2

After 30 minutes a student is on question 28. By the pacing guide, how far behind are they, and what should they do?

The guide gives Q1–30 about 50 seconds each. Question 28 should be reached after $28\times50=1400$ seconds, which is about $23$ minutes $20$ seconds.
The student used $30$ minutes, so they are about $30-23\tfrac13\approx6\tfrac23$ minutes, roughly 7 minutes, behind.
The fix is not to rush everything. Flag and move any question that has taken more than about 90 seconds, choose a best guess so no answer is blank, and collect the easy points first.

Answer: About 7 minutes behind: flag slow questions, guess, and keep moving.

Try it yourself

Work it on paper first. Open a hint only when you are stuck, then compare with the solution.

A mock gives a student 36 correct answers in Q1–40 and 5 in Q41–48. What is the score, and how many more Q1–40 questions would lift it to at least 85?

Hint 1 of 2

Score Q1–40 at 2 points each and Q41–48 at 2.5 points each.

Hint 2 of 2

Find how many points are missing from 85, then divide by 2.

Show the step-by-step solution

$36\times2=72$ and $5\times2.5=12.5$ , so the score is $72+12.5=84.5$ .
The student needs $85-84.5=0.5$ more points. One more standard question gives $2$ points, which is enough.
With one more correct answer the score would be $86.5\ge85$ .

Answer: $84.5$ points; one more correct question in Q1–40 would give $86.5$ .

Common mistakes

Spending four minutes on one hard question and leaving easy ones unread. Every question in a band is worth the same, so a skipped question you could have solved costs more than a hard one you missed.
Leaving questions blank. A wrong answer scores $0$ , the same as a blank, so guess and flag.
Using the flat 75 seconds per question. Early questions should take about 50 seconds; the spare time belongs to Q31–48.
Finishing a set and moving on without fixing the misses. The fix step is where the points come from.
Skipping the weekly mock because the lessons felt fine. The mock is the only place you practise the timing.

Exam tips

Check the clock at question 10, 30 and 40. If you are at 8 minutes, 25 minutes and 40 minutes, you are on pace.
Make your guess before you flag, so the flagged question already has an answer.
Read each question’s last line first. It tells you what to find before you start.
Do the lesson first and the sets second. The sets show you which part of the lesson to reread.

In short

48 questions, 60 minutes, 100 points; Q41–48 are worth $2.5$ each, the rest $2$ .
Pace: Q1–30 in 25 min, Q31–40 in 15 min, Q41–48 in 15 min, 5 min to check.
Never leave a blank; flag and move when a question runs over time.
A day is a lesson, daily sets, Fix to 100%, drills and flashcards; Day 7 is the weekly mock.

Knowledge check

4 questions on this lesson, marked as you go. Take them in ACE CSCA with a free account: passing them completes the lesson, and your progress is saved on every device.

All of Week 1 is free: the eight lessons, the daily questions and the Week 1 test.

Start Week 1 free