1.3 Preparation & Problem-Solving Strategies

Knowing the format (Section 1.1) and the scoring (Section 1.2) tells you what ICAS is. This section tells you how to prepare — the habits and routines that separate students who plateau from students who climb award levels.

Why ICAS Rewards Thinking, Not Memorising

A school test often asks you to repeat a procedure you practised in class: solve this equation, find this area, convert these units. ICAS does something different. It wraps those same skills in unfamiliar problems — a puzzle about patterns in a table, a geometry question hiding inside a floor plan, a data question about a graph drawn in a way you have never seen. The official papers are built to measure higher-order thinking: analysing, combining ideas and choosing an approach when none is handed to you.

The practical consequence: grinding hundreds of identical drill questions has diminishing returns. What works is practising varied problems and, after each one, asking 'what was the trick here — what did I have to notice?' That reflection is what transfers to an unseen ICAS question.

A Routine for Multi-Step Word Problems

Most marks are lost in word problems not because the maths is too hard, but because students answer the wrong question or skip a step. Use this five-step routine every time:

1. Read the whole question once without touching anything. Get the story.
2. Underline (or note on paper) exactly what is asked. 'How many are left?', 'what is the total cost?', 'which statement is true?' — these demand different finishing moves.
3. Choose the operation(s) before computing. Write the plan: 'multiply, then subtract'.
4. Estimate the answer. A rough number in your head is an error detector.
5. Calculate, then check against your estimate and against what was actually asked.

Worked example

A school buys 8 boxes of pencils. Each box holds 24 pencils. The pencils are shared equally among 6 classes. How many pencils does each class get?

• Step 2: asked for pencils per class — a single number.
• Step 3: plan = total pencils ÷ number of classes.
• Step 4: estimate — 8 × 24 is a bit under 8 × 25 = 200; 200 ÷ 6 is about 33. Expect an answer near 32-33.
• Step 5: 8 × 24 = 192; 192 ÷ 6 = 32. Matches the estimate. If 32 is an option, select it with confidence; if the options were 32, 42, 128, 1152, the estimate alone eliminates the last three.

Elimination and Estimation in Multiple Choice

Most ICAS questions are multiple-choice, and those hand you the answer hidden among the wrong ones. On any question that shows you options, exploit that:

• Eliminate the absurd. If a jacket costs $80 and is discounted by 25%, any option above $80 is impossible; any option below half price is implausible. Often two options die immediately.
• Estimate before you compute exactly. For 19% of 312, think 'about a fifth of 300, so about 60'. Options near 60 survive; the rest go.
• Test the options backwards. For 'which number satisfies...' questions, substitute the middle-sized option into the condition and adjust. This is often faster than solving from scratch.
• When guessing, guess from the survivors. Eliminating even one option lifts a blind guess from 25% to 33%; eliminating two lifts it to 50%.

Time Management on a Paper That Gets Harder

Because difficulty rises through the paper, your time budget should not be flat. For a 40-question, 60-minute paper:

• First 10 questions: move briskly — these are the foundation questions, and every minute saved here is a minute earned for the end. Aim for well under a minute each.
• Middle 20: steady pace, roughly 90 seconds each, using your word-problem routine.
• Final 10: these are designed to be hard. Give them the time you banked. If one defeats you after a genuine attempt, eliminate what you can, pick the best survivor, flag it, and move on.

Two rules protect your score. First, never leave a question blank — there is no penalty for an incorrect answer, so on a multiple-choice item a reasoned guess always beats a guaranteed zero, and even on a written free-response item a sensible estimate can earn the mark. Second, do not let one hard question eat five minutes; the next question might be easier for you even if it is later in the paper.

No-Calculator Arithmetic Fluency

Since personal calculators are banned and the on-screen calculator appears only for selected questions, arithmetic fluency is directly worth marks. The highest-value skills to drill:

• Times tables to 12 × 12 — instant, not counted on fingers.
• Mental percentage shortcuts: 10% is divide by 10; 5% is half of that; 25% is a quarter; 15% is 10% + 5%.
• Fraction-decimal equivalents: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/8 = 0.125, 1/3 ≈ 0.333.
• Written multiplication and division with two- and three-digit numbers, laid out neatly so you can catch slips.
• Estimation by rounding: 49 × 11 ≈ 50 × 11 = 550, so the true answer (539) should sit just below.

Ten minutes of daily mental arithmetic beats an occasional hour. Speed here buys thinking time there.

Using the 120-Question Practice Bank

This site provides a practice bank of 120 original multiple-choice questions spanning the five strands at Years 3-10 difficulty. Use it deliberately:

1. Diagnose first. Attempt a spread of questions across all five strands before any targeted revision, and record which strand costs you the most marks.
2. Practise under time. Occasionally do sets of 10 questions against the clock to rehearse pacing, not just accuracy.
3. Review every wrong answer properly. For each miss, classify the error — knowledge gap, misread question, or arithmetic slip — then re-attempt the question a few days later without looking at the solution. If you can explain why the correct option is correct and why your choice was wrong, the lesson has stuck.
4. Revisit strand weaknesses using the later chapters of this guide, then return to the bank to confirm the gap has closed.

Wrong answers in practice are not failures; they are the exact questions ICAS would have caught you on. Treat each one as a free preview of a mistake you no longer have to make on the real paper.