--- title: "NSW Selective Test Mathematical Reasoning Practice" description: "NSW selective test Mathematical Reasoning: 35 questions in 40 minutes, no calculator, what the department says about coaching, and original tape diagram practice." canonical: https://learn.modernagecoders.com/nsw-selective-test-mathematical-reasoning-practice source: src/pages/nsw-selective-test-mathematical-reasoning-practice.html --- > NSW selective test Mathematical Reasoning: 35 questions in 40 minutes, no calculator, what the department says about coaching, and original tape diagram practice. In short Mathematical Reasoning is one of four sections in the NSW Selective High School Placement Test for Year 7 entry. Students answer 35 multiple-choice questions, each with five possible answers, in 40 minutes on a department computer. No calculator is allowed in any section. The department says questions draw on the NSW curriculum up to Year 6 and that coaching is not necessary. Maths worth learning anyway ## Three courses that build reasoning, not tricks Useful for any capable upper-primary student, test or no test. [![Problem Solving and Computational Thinking for Kids course thumbnail](/images/problem-solving-kids.webp) NMR / 01 Problem solving Multi-step thinking, drawn and explained before calculated. Open the syllabus →](/courses/problem-solving-and-computational-thinking-for-kids)[![Elementary Maths for Grades 1-5 course thumbnail](/images/elementary-maths.webp) NMR / 02 Primary maths in depth Fractions, ratio and measurement from the upper-primary curriculum. Open the syllabus →](/courses/elementary-mathematics-complete-masterclass)[![Maths Olympiad & Competition Course course thumbnail](/images/olympiad-competition-maths.webp) NMR / 03 Competition maths For students who enjoy harder problems for their own sake. Open the syllabus →](/courses/olympiad-competition-mathematics-mastery) The section, as published ## 35 questions, 40 minutes, five options each Every detail comes from the NSW Department of Education, read on 7 October 2026. | Section | Questions | Time | Type | | --- | --- | --- | --- | | Reading | 17 (3 questions have multiple parts) | 45 minutes | Multiple choice | | Mathematical Reasoning | 35 | 40 minutes | Multiple choice, five possible answers | | Thinking Skills | 40 | 40 minutes | Multiple choice, four possible answers | | Writing | 1 | 30 minutes | Open response | The test is computer-based and sat on computers the department provides, at test centres that are mostly local public high schools. Students can do working out on paper; the department's video for students says they "can use paper for working out" in Mathematical Reasoning. Calculators are on the list of items not allowed, and the practice page states: "Students cannot use a calculator during this, or any other, test." For Year 7 entry in 2027, the department lists the test on Friday 1 to Saturday 2 May 2026, with a make-up test on Friday 22 May 2026. Each student sits on one day only. From 2026 the placement tests are held only in New South Wales. The department describes the section as testing "mathematical reasoning skills" in which a child "will use different concepts from maths to solve problems", and notes that the concepts are based on what the child already learns at school. Sources: [NSW Department of Education, Placement test](https://education.nsw.gov.au/schooling/parents-and-carers/choosing-a-school-setting/selective-high-schools/placement-test); [Selective high school practice tests](https://education.nsw.gov.au/schooling/parents-and-carers/choosing-a-school-setting/selective-high-schools/placement-test/selective-high-school-practice-tests). Checked on 7 October 2026. We are independent of the department. What the department says ## Coaching is not necessary, in the department's own words We think families deserve to read this before paying anyone, including us. From the NSW Department of Education "It is important to know that coaching or tutoring for the placement test is not necessary. The test will not need your child to know any new or special knowledge. So, extra paid coaching outside of school will not give your child an advantage." The department goes further: it "does not recommend or endorse coaching for the placement test", and it warns that too much coaching can harm a child's wellbeing. It provides free resources, including online computer-based practice tests and PDF practice tests, in its Student Resource Hub. Our advice is the same. Start with the department's free practice tests. They show the real screens, the timer and the question styles, and they cost nothing. So what is this page for? Some children genuinely love problem solving and want more of it, whether or not they sit the test. Others find upper-primary fractions and ratio shaky, which will matter in Year 7 regardless of school. Our classes teach mathematics: fractions, ratio and multi-step reasoning from the curriculum the test already draws on. We do not run test-coaching courses, and we will tell you honestly if we think your child does not need us. Source: [Selective high school practice tests, "Helping your child prepare for the placement test"](https://education.nsw.gov.au/schooling/parents-and-carers/choosing-a-school-setting/selective-high-schools/placement-test/selective-high-school-practice-tests). Checked on 7 October 2026. Problems we wrote ## Tape diagrams for multi-step problems A tape diagram turns a word problem into equal units drawn as strips. Once the picture is right, the arithmetic is small. All problems below use only upper-primary content and need no calculator. ### Draw equal units If one amount is four times another, draw one strip of 1 unit and one strip of 4 units. Equal-sized boxes are the whole idea. ### Label what you know Write the total, or the difference, against the strips it belongs to. The question usually tells you one of these. ### Find one unit Divide to find the value of a single unit, then build every answer from it. Check by putting the numbers back into the story. | Problem | The diagram | One unit | Answer | | --- | --- | --- | --- | | Three fifths of a class are girls. There are 12 more girls than boys. How many students are in the class? | Girls 3 units, boys 2 units; the difference is 1 unit | 12 | 60 students | | Sam has 4 times as many cards as Lee. Together they have 85. How many does Sam have? | Lee 1 unit, Sam 4 units: 5 units altogether | 17 | 68 cards | | Red and blue beads are in the ratio 2 to 3. There are 10 more blue beads than red. How many beads in total? | Red 2 units, blue 3 units; the difference is 1 unit | 10 | 50 beads | | A tank is two fifths full. Adding 18 litres makes it seven tenths full. What does the tank hold? | Tenths: 4 shaded, then 7 shaded; 3 tenths added | 6 litres per tenth | 60 litres | | Ana uses a quarter of her stickers, then a third of what is left. She has 30 left. How many did she start with? | Quarters: 1 used, 3 left; a third of those 3 used, 2 quarters left | 15 per quarter | 60 stickers | | Three consecutive whole numbers add to 72. What is the largest? | Three equal strips plus 0, 1 and 2 extra | 23 | 25 | Notice how the ratio and fraction problems collapse into the same move: find the gap or total in units, divide once, then rebuild. The sticker problem looks like two separate fraction steps, but on a diagram the second step simply halves what is left, and the whole question becomes "2 quarters are 30". Walk through the first problem slowly. The class is split into fifths, so draw five equal boxes: three for girls, two for boys. The girls have one box more than the boys, and the story says that difference is 12 students, so one box is 12. Five boxes make 60. To check, three fifths of 60 is 36 girls and two fifths is 24 boys, and 36 is indeed 12 more than 24. Every problem in the table can be read back into its story the same way. With five options per question, a tape diagram also helps eliminate answers. If the class must be a multiple of 5 units, any option that is not a multiple of 5 can be crossed out before any calculation. Pacing ## About 68 seconds per question Our arithmetic: 40 minutes divided by 35 questions is roughly 68.6 seconds each. ### Habits that help Read the last sentence of a question first, so you know what is being asked before reading the story. Draw small and fast. A tape diagram on scrap paper takes five seconds and saves a muddled calculation. Use the five options as a check, not a shortcut. If your answer is not among them, the diagram needs another look. ### Habits to avoid Spending three minutes on one problem. A question left for later is better than five questions never reached. Guessing from the look of the numbers. Options are often built from common mistakes. Practising under time pressure every day. Calm, accurate reasoning first; speed follows. Building multi-step reasoning ## Four stages across Years 4 to 6 Most capable students move through these over two or three years of ordinary good teaching. | Stage | What the student does | Secure when | | --- | --- | --- | | 1. Part and whole | Draws a total split into parts | Solves "together they have 85" problems | | 2. Comparison | Draws two strips and marks the difference | Solves "12 more girls than boys" problems | | 3. Fractions of a whole | Divides a strip into fifths or tenths | Solves the tank problem without converting | | 4. Two-step changes | Redraws the strip after each change | Solves the sticker problem in one diagram | ### Keeping it healthy The department warns that too much coaching can harm wellbeing, and we agree. An hour a week of enjoyable maths is plenty for most children. If your child is stressed, stop practising tests and go back to puzzles they choose themselves. ### The other sections Thinking Skills is a separate 40-minute section; our [Thinking Skills page](/nsw-selective-test-thinking-skills-practice) covers it in the same honest way. For the Year 4 Opportunity Class test, see [OC test maths practice](/oc-test-maths-practice-nsw). Courses for upper primary ## Maths courses for Years 4 to 6 Grouped by focus. Each card links to a full syllabus. I ### Reasoning Problem solving and logic NMR / R / 01 #### Problem solving and computational thinking Breaking problems into clear steps. [Open the syllabus](/courses/problem-solving-and-computational-thinking-for-kids) NMR / R / 02 #### Competition maths Harder problems for keen students. [Open the syllabus](/courses/olympiad-competition-mathematics-mastery) NMR / R / 03 #### Maths through coding Patterns and logic explored in code. [Open the syllabus](/courses/maths-through-coding)II ### Core maths Fractions, ratio and measurement NMR / C / 01 #### Primary maths The upper-primary curriculum, taught deeply. [Open the syllabus](/courses/elementary-mathematics-complete-masterclass) NMR / C / 02 #### Mental maths Fast, careful calculation without a device. [Open the syllabus](/courses/mental-maths-mastery-kids) NMR / C / 03 #### Statistics and probability Data and chance for upper primary. [Open the syllabus](/courses/statistics-probability-maths-course)III ### Looking ahead For students ready for secondary maths NMR / A / 01 #### Middle years maths Years 7 to 9, started early. [Open the syllabus](/courses/comprehensive-middle-school-mathematics-mastery) NMR / A / 02 #### Algebra foundations Units in tape diagrams become letters. [Open the syllabus](/courses/algebra-foundations-masterclass) NMR / A / 03 #### Abacus mental maths Visual calculation for younger learners. [Open the syllabus](/courses/abacus-mental-maths-course-for-kids) Our lessons ## Mathematics first, for children who enjoy it Teachers work from India, which is behind Sydney. During daylight saving a 4.30 pm Sydney class starts at 11 am India time, so after-school slots are simple to keep. After school The usual slot for Years 4 to 6. Saturday For families with weekday commitments. Holidays Short blocks on fractions or ratio. ### Diagrams before numbers Students draw the problem before they calculate anything. ### Explain every answer A correct answer without a reason counts as half done. ### Groups of fifteen to twenty Children at a similar level learn together. ### One-to-one available For a child who wants a particular topic strengthened. ### No test coaching We teach maths from the curriculum, as the department advises. ### No placement promises Selection is the department's decision; we make no claims about it. Student work ## Student projects Made by learners who wanted to build something. More in the [student labs](/student-labs). ![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp) AI and ML #### NutriLife An AI nutrition coach that reads what you eat and works you toward a target. by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app) ![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp) AI and ML #### Misti A chatbot that answers mathematics and programming questions, built and deployed by a student. by Harshit · [Open it](https://misti.modernagecoders.com) ![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp) AI and ML #### GuardianX An assistant that helps a young person recognise unsafe situations online. by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app) ![SkyCast weather forecast application screenshot](/images/projects/skycast.webp) Web app #### SkyCast A weather forecasting site with live conditions for any location. by Krish Fees ## Fees Families in New South Wales pay monthly in US dollars, the rate we charge in every country other than India. There is no up-front payment and no minimum term. Free first class USD 0 no card required - A real lesson with a teacher - Our honest view, including if no help is needed - No card details Book it Group batch USD 100 a month, billed in US dollars - Fifteen to twenty children at one level - The same teacher each week - Work explained and checked - A certificate at the end Start here One to one USD 150 a month, billed in US dollars - One teacher for one child - Focus on chosen topics - Times to suit your family Enquire What families say ## Rated 4.9 across 547 Google reviews Parent reviews from Google, copied exactly. ★★★★★ "The one step solution for my son. Modern Age Coders make learning coding so simple that kids love it. The teachers explain complex concepts clearly with practical exercises and interactive content." Ria Mukherjee Parent ★★★★★ "Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I can now confidently write complex programs with ease." Samriddha Mondal Student ★★★★★ "One of the most wonderful education centres out there. Education is not limited to school syllabus but focuses on skill development." Vansh Agarwal Student ★★★★★ "My child Dhairya is really enjoying the Modern Age Coders classes. This is his first online class and he eagerly looks forward to it. I can already see his improvement, and the teachers are very cooperative." Sonam Oswal Parent of Dhairya ★★★★★ "Modern Age Coders have wonderful teachers who teach in a clear, easy and practical way. The teacher boosts students' confidence and inspires them to learn without hesitation." Sonu Goyal Parent ★★★★★ "I highly recommend this computer coding class! The teachers are incredibly knowledgeable and passionate about coding." Ritu Kedia Parent Questions about Mathematical Reasoning ## What NSW families ask us ### How many questions are in the selective test Mathematical Reasoning section? 35 multiple-choice questions, each with five possible answers, in 40 minutes, according to the NSW Department of Education. ### Can students use a calculator? No. The department says students cannot use a calculator during Mathematical Reasoning or any other section, though they can work out on paper. ### Is the selective test on a computer? Yes. It is computer-based and sat on computers provided by the department at test centres, mostly local public high schools. ### What maths does it cover? The department says questions draw on concepts from the NSW curriculum up to Year 6, and that children do not need to study extra concepts. ### Does my child need coaching? The department says coaching or tutoring for the placement test is not necessary and that it does not recommend or endorse coaching. Its free practice tests are the place to start. ### What is a tape diagram? A drawing of a word problem as equal-sized strips or boxes, so that totals, differences and fractions can be seen as units before any calculation. ### When is the test? For Year 7 entry in 2027 the department listed Friday 1 to Saturday 2 May 2026, with a make-up test on Friday 22 May 2026. Check the department's site for later years. ### Can you advise on which school to choose? No. We do not give school-choice, placement or appeals advice. Those questions belong with the department and the schools. ### Will lessons improve my child's chances? We make no promise about scores or placement. We teach mathematics that is worth knowing regardless of the test. ### When would lessons run? We agree one weekly time after the free trial, usually after school. During daylight saving Sydney is five and a half hours ahead of India time. Related pages ## More for NSW families Other test sections, NAPLAN and coding. ### [Selective test Thinking Skills](/nsw-selective-test-thinking-skills-practice) The 40-question reasoning section. ### [OC test maths](/oc-test-maths-practice-nsw) The Year 4 Opportunity Class test. ### [Coding and AI in NSW](/coding-and-ai-classes-in-new-south-wales) Our state page for New South Wales. ### [NAPLAN Year 5 numeracy](/naplan-year-5-numeracy-practice) Upper-primary maths in NAPLAN. ### [Maths tutoring in Australia](/online-maths-tutoring-australia) Live classes for every year. ### [Competitions calendar](/australian-coding-maths-and-ai-competitions-calendar) Contests for students who love problems. Start here ## Book a free maths class Tell us your child's year and what they enjoy or find hard. The trial is a real maths lesson, and we will say honestly whether ongoing classes make sense. Prefer to read first? Every course is on the [course atlas](/course-atlas), and [how we teach](/how-we-teach) describes a lesson in full. [WhatsApp us](https://wa.me/919123366161?text=Hello%20Modern%20Age%20Coders%2C%20I%20would%20like%20a%20free%20maths%20class%20for%20my%20Year%205%20or%206%20child%2C%20on%20multi-step%20problem%20solving.) · [+91 91233 66161](tel:+919123366161) · [connect@modernagecoders.com](mailto:connect@modernagecoders.com) WhatsApp is the quickest way to reach us. Our number is Indian (+91) because the school is based in India; we have no office in Australia. ### Want a class sooner? Book a priority demo A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off. [Book a priority demo](/book-demo) ## Keep exploring Modern Age Coders ### Related courses and guides - [The New Computing GCSE Explained](/new-computing-gcse-explained) - [NumPy, Pandas & Matplotlib Masterclass: Python Data Analysis in Depth](/numpy-pandas-matplotlib-masterclass) - [Natural Language Processing Course (NLP)](/natural-language-processing-course) - [OCR A-level Computer Science H446 Help](/ocr-a-level-computer-science-h446-help) - [National Cipher Challenge Preparation](/national-cipher-challenge-preparation) - [OCR GCSE Computer Science J277 Help](/ocr-gcse-computer-science-j277-help) - [Best Coding Classes in Wollongong](/best-coding-classes-in-wollongong) - [T Level Digital Software Development Help](/t-level-digital-coding-help) - [Best Coding Classes in Armidale](/best-coding-classes-in-armidale) ### Learn more - [SA Ignite Assessment Maths Practice](/sa-ignite-entry-maths-practice) - [Queensland Academies Entrance Test Maths Practice](/queensland-academies-entry-maths-practice) - [Victorian Selective Entry Exam Maths Practice](/victorian-selective-entry-exam-maths-practice) - [WA GATE ASET Maths Practice](/wa-gate-aset-maths-practice) ### Free resources - [Java Tutorial for Beginners to Advanced](/resources/java) - [CREATE, ALTER, DROP Tables](/resources/sql/creating-and-modifying-tables) - [File Handling in Java](/resources/java/file-handling-in-java) - [JOINS - INNER, LEFT, RIGHT, FULL OUTER, CROSS | SQL Tutorial](/resources/sql/joins-inner-and-outer) ### From the blog - [PCEP vs PCAP: Which Python Certification Is Worth It?](/blog/pcep-vs-pcap-which-python-certification) - [Who Are Modern Age Coders? 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