Chittagong Board · SSC Mathematics · 2021
Chapter Coverage
| Q | Chapter | Topic | Marks |
|---|---|---|---|
| 1 | Ch 2 · Sets | Set operations with coastal data | 10 |
| 2 | Ch 3 · Algebra | Algebraic fraction simplification | 10 |
| 3 | Ch 5 · Linear Equations | Ship charter cost problem | 10 |
| 4 | Ch 9 · Series | Compound interest — maritime insurance | 10 |
| 5 | Ch 11 · Triangles | Angle bisector theorem | 10 |
| 6 | Ch 12 · Area | Area theorem — field partition | 10 |
| 7 | Ch 14 · Trigonometry | Ship bearing and distance | 10|
| 8 | Ch 15 · Statistics | Port traffic data — ogive and quartiles | 10 |
A survey of 100 fishermen finds: 60 use nylon nets (N), 50 use trawl nets (T), and 25 use both types.
(a) Find |N ∪ T| (fishermen using at least one type). [2 marks]
(b) Find the number who use only nylon nets. [4 marks]
(c) How many use neither type? Draw a Venn diagram. [4 marks]
(a) [2 marks]
(b) [4 marks]
(c) [4 marks]
Simplify the following algebraic expressions.
(a) Simplify: (a²−b²)/(a+b). [2 marks]
(b) Simplify: (x²+5x+6)/(x²+3x+2) ÷ (x²+4x+3)/(x²+2x). [4 marks]
(c) If a/(b+c) = b/(c+a) = c/(a+b) = k, prove that k = 1/2 (when a+b+c ≠ 0). [4 marks]
(a) [2 marks]
(b) [4 marks]
(c) [4 marks]
Chartering a cargo ship costs a fixed amount plus a rate per tonne of cargo. Chartering with 200 tonnes costs 80,000 taka. Chartering with 350 tonnes costs 117,500 taka.
(a) Write two linear equations for fixed cost F and rate per tonne r. [2 marks]
(b) Find F and r. [4 marks]
(c) What is the maximum cargo (in tonnes) that can be chartered with a budget of 150,000 taka? [4 marks]
(a) [2 marks]
(b) [4 marks]
(c) [4 marks]
A shipping company takes a maritime insurance policy for 500,000 taka. The insured value grows by 8% per year (compounded annually).
(a) Write the formula for the insured value after n years. [2 marks]
(b) Find the insured value after 3 years. (1.08³ = 1.2597) [4 marks]
(c) In how many years will the value first exceed 1,000,000 taka? (log 1.08 = 0.0334, log 2 = 0.3010) [4 marks]
(a) [2 marks]
(b) [4 marks]
(c) [4 marks]
In triangle PQR, the angle bisector from P meets QR at point D.
(a) State the angle bisector theorem. [2 marks]
(b) If PQ = 8 cm, PR = 6 cm, and QR = 14 cm, find QD and DR. [4 marks]
(c) Find the ratio of areas of triangles PQD and PRD. [4 marks]
(a) [2 marks]
(b) [4 marks]
(c) [4 marks]
Parallelogram ABCD has base AB = 15 cm and height 8 cm. E is the midpoint of BC.
(a) Find the area of parallelogram ABCD. [2 marks]
(b) Find the area of triangle ABE. [4 marks]
(c) A diagonal AC divides ABCD into two triangles. Prove they are equal in area. [4 marks]
(a) [2 marks]
(b) [4 marks]
(c) [4 marks]
A ship departs Chittagong Port and sails 40 km due East, then turns and sails 30 km due North.
(a) Find the straight-line distance from the port to the final position. [2 marks]
(b) Find the bearing (angle from North) of the final position from the port. (tan θ = 4/3) [4 marks]
(c) Another ship starts at the final position and returns to port sailing in a straight line. What is its bearing? [4 marks]
(a) [2 marks]
(b) [4 marks]
(c) [4 marks]
Monthly container traffic (in thousands) at Chittagong Port for 8 months: 42, 47, 53, 38, 61, 55, 49, 59.
(a) Find the mean monthly traffic. [2 marks]
(b) Find the range and the variance of the data. [4 marks]
(c) Find the standard deviation and comment on the spread. [4 marks]