HSC Maths Ext 1 case studies
HSC Maths Ext 1 · Put your knowledge to work in context.
Mathematics Extension 1 is a one-unit Board Developed Stage 6 course in New South Wales, offered as course 11250 in Year 11 and 15250 in Year 12. It is designed for students who want a deeper, more rigorous treatment of mathematics than the Advanced course alone: the syllabus emphasises constructing mathematical arguments and proofs, using mathematical models extensively, and appreciating the interconnected nature of mathematics and its applications in science, engineering, finance and economics. The HSC Maths Ext 1 case studies are 4 cases and about 3,158 words.
1The Suspension Bridge Cable
An engineer models the main cable of a suspension bridge. The two towers are 80 m apart and 30 m tall, and the cable is attached at the top of each tower.
454 words, about 2 min2Solving a Trigonometric Equation on a Restricted Domain
A student is solving 2sin²x + 3cos x − 3 = 0 for 0 ≤ x ≤ 2π. They convert sin²x to 1 − cos²x and reach 2 − 2cos²x + 3cos x − 3 = 0, which simplifies to 2cos²x − 3cos x + 1 = 0.
393 words, about 2 min3Optimising a Folded Box from a Sheet
A manufacturer cuts squares of side x cm from each corner of a rectangular sheet measuring 24 cm by 18 cm and folds up the sides to make an open box. The volume is V(x) = x(24 − 2x)(18 − 2x).
512 words, about 3 min4Counting Seating Arrangements with Restrictions
A committee of 5 women and 4 men is to be seated in a row of 9 chairs for a photograph. The photographer imposes two rules: no two men may sit adjacent to each other, and a particular pair, Ava and Ben, must not sit next to each other.
1,799 words, about 9 min