NSW Selective School: Mathematical Reasoning
Master multi-step non-routine word problems, rate calculations, ratio algebra, and geometric deduction for the NSW Selective High School Placement Test.
Curriculum Overview & Practical Context
Core Concepts Tested in Year 6
Setting up simple algebraic equations from word problem statements
Solving combined rate-of-work and distance-speed-time problems
Calculating proportional ratios and sharing quantities in given ratios
Deconstructing composite geometric areas and perimeter boundaries
Interactive Practice Questions with Worked Solutions
Select an answer to reveal immediate teacher-style step-by-step explanations.
In a school library, the ratio of fiction books to non-fiction books is 5 to 3. If there are 240 fiction books, how many total books (fiction and non-fiction combined) are in the library?
A train travels at an average speed of 90 km/h for 40 minutes, and then travels at 60 km/h for another 30 minutes. What is the total distance travelled by the train?
A fruit seller has twice as many apples as oranges. After selling 15 apples and buying 5 oranges, she has the same number of apples and oranges. How many apples did she start with?
Parent Home Practice Checklist
- Have your child write out the first step on paper rather than doing multi-stage arithmetic in their head.
- Practise unit conversions (minutes to hours, millilitres to litres, grams to kilograms) until automatic.
- Work backwards from the answer options if an algebraic formulation seems too complex during practice.
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