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Case study·Hard exam skill (4/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A school records the number of boys and girls in three clubs by the matrix M=[181215151020]. Rows represent Debate, Science, and Art clubs; columns represent boys and girls.\text{A school records the number of boys and girls in three clubs by the matrix }M=\begin{bmatrix}18&12\\15&15\\10&20\end{bmatrix}.\text{ Rows represent Debate, Science, and Art clubs; columns represent boys and girls.}
Total: 4 marks

(a) State the order of MM. (1 mark)

(b) Interpret the entry m32m_{32}. (1 mark)

(c) Find the total number of students in the Science club and write what MTM^T would represent. (2 marks)

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cbse-math-12.u2.t2-1.case.005

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