Three similar steel bars of lengths 200cm, 300cm, and 360cm are cut into equal pieces: Mathematics Assignment, SUTD, Singapore

Questions

1. Three similar steel bars of lengths 200cm, 300cm, and 360cm are cut into equal pieces.  Find the largest possible area of a square that can be made from any of the three pieces.
2. Expand ( 2 + x)⁵ in ascending powers of x up to the term in x³.  Hence approximate the value of (2.03)5 to four significant figures.
3. Water flows from a pipe at a speed of 200 liters per minute.  If the pipe is used to drain a tank full of water measuring 3.2m by 2.5m by 2m, how many minutes would it take to drain the tank completely?
4. Given that A (5, 1 ) and B ( 2, 5 ) find:
   i) AB as a column vector.
   ii) AB
5. a) Construct a parallelogram PQRS such that PQ = 8cm, PS =4.5cm and angle QPS = 60
   b) Locate the locus of a point X such that X is equidistant from P and R
6. Calculate the shortest distance in nautical miles between M (450N, 380E ) and N (450N, 1420W).
7. The sides of a triangle are in the ratio 3: 5: 6 and the perimeter is 56cm. Find the area of the triangle.
8. The longer parallel sides of a trapezium are twice as long as the shorter parallel side. The height between the parallel sides is 10cm. If the area of the trapezium is 225cm², find the length of the longer parallel side.
9. In the figure below, ABC is a tangent at B and CDE is a straight line Ð BED = 50⁰, Ð DEF = 35^0, and ÐECB = 25⁰.
   
10. Solve for x

( Log x)²  –  ½ log  x = ³/₂