Tkgs 2026 Sec 4 T2 WA Paper Solutions with feedback

Mark scheme for Sec 4 Math WA2 2026 1 (a) Show that   3 4 8 3 6433 x y x y   . [1] Solutions/Alternative Methods Remarks Skills/Concept/Success Criteria     3 484 48 36 3 4 3 3 3 xy xy xy      For “show” questions, working must show use of Laws of Indices explicitly. Apply Law & Definition of Indices: •     mm n mn na a a  • () n n nab a b  (b) Hence, simplify   1 63 2484 8 813 xxy y             and leave your answer in positive index form. [2]   1 63 2484 8 3 36 4 10 813 93 27 xxy y xxy y y                          Apply Law & Definition of Indices: • n n n aa bb          • 1 ,0 n naa a   • m n m na a a   • m n m naaa   • 0 1, 0 aa  Overall Item Demand Content Complexity Context Response A01 Low Medium Low Low 2 Mandy deposited $150 000 in a 5 -year investment plan. For the first two years, it offers a simple interest rate of 4% per annum. After two years, the accumulated sum will enjoy a compound interest of 5% per annum, compounded quarterly for 3 years. Show that the amount of interest she will receive at the end of 5 years is about $38 000 (rounded to the nearest thousand). [4] Solutions/Alternative Methods Remarks Skills/Concept/Success Criteria Simple interest earned after 2 years $150000 4 2 100 $12000 I = = Accumulated sum after 2 years = $162 000 Total amount at the end of 5 years Apply simple interest formula 100 PRTI  with correct P, R and T to find simple interest. Adjust r and n according to frequency of calculating compound interest.

2 34 54$162000 1 100 $188042.2319  =+  = Total interest earned at the end of 5 years $188042.2319 $150 000 $38042.23 $38000 (nearest thousand)    Alternatively, Total interest earned at the end of 5 years ($188042.2319 $162000) $12000 $38042.23 $38000 (nearest thousand)    For “show” question, students should show value $38042 before rounding off to required accuracy. Apply compound interest formula 1 100 n rAP          to find total amount with compound interest. Find total interest by taking the difference of total amount and initial principal. Overall Item Demand Content Complexity Context Response A02 Medium Medium Medium Somewhat unfamiliar 3 The diagram shows the positions of the points X, P and Q where 4 2PQ =  is represented in the grid below. (a) Y is the point such that PQXY is a parallelogram. (i) Mark and label the point Y on the grid above. [1] (ii) Express PY  as a column vector. [1] Solutions/Alternative M