Title Target Exam 04_English.pdf ✅

AL / 2025 / 10 / E - I (NEW) – TARGET EXAM 04 - 2 - Combined Mathematics Ruwan Darshana 1. Let a1 = 1 2 and an+1 = 1 (n+1)(n+2) +an for all n ∈ Z +. Using the theorem of mathematical induction, show that an = n n+1 for all n ∈ Z +. 2. Draw the graphs of the functions y = x 2 and y = 1 2 |x + 1| on the same diagram. Hence or otherwise, find all real values of x that satisfy the inequality x 2 < 1 2 |x + 1| . Derive all real values of x that satisfy the inequality x 2 < 1 2 (|x| + 1). 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[See page three.
AL / 2025 / 10 / E - I (NEW) – TARGET EXAM 04 - 3 - Combined Mathematics Ruwan Darshana 3. Both conditions |Z − 4| ≤ 5, Re(Z) + Im(Z) ≥ −1 are satisfied for the complex number Z . Find the area of the region S in the argand diagram which include Z that satisfies these conditions. 4. If there is no term containing x 3 in the expression (1 − 2x + ax 2 ) 4 , find the value of a. .............................................................................................................................................................................................. .............................................................................................................................................................................................. .............................................................................................................................................................................................. .............................................................................................................................................................................................. 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[See page four.