TKGS 2024 S4 Math Prelim P1_Solution

2024 TKGS PRELIM MATH P1 SOLUTION Qn Solution Content/Success Criteria 1 (a) 8700 I can perform calculations with a calculator. I can round off values to the nearest hundred. (b) 1050 Content L Complexity L Context L Response Strategy L Assessment Objective AO1 Qn Solution Content/Success Criteria 2 (a) 5 2(6 1)x−− I can expand and simplify algebraic expressions. I can apply simplify expression using laws of indices. 5 12 2x= − + 7 12 x=− Content L Complexity L Context L (b) 11 96 33 69 27 27 ba ab −     =       Response Strategy L 2 33 a b= Assessment Objective AO1

Tanjong Katong Girls’ School [Turn over 4052/S4Prelim/01/2024 Qn Solution Content/Success Criteria 3 Let amount of savings Albert and Chris have initially be 5x and 3x respectively. 5 30 2 3 30 1 5 30 2(3 30) 5 30 6 60 30 3 90 x x xx xx x x − =− − = − − = − = = The amount of savings Chris has at the start = $90 Content L Complexity L Context L Response Strategy M Assessment Objective AO2 Qn Solution Content/Success Criteria 4 (a) 321400 2 5 7=   I can express a number in its prime factors. (b) 321400 2 5 7=   22 3 7 84q=   = 2HCF 2 7= 84q= I can use the prime factors from HCF to find the original number. Content L Complexity H Context L Response Strategy M Assessment Objective AO1/ AO2

Qn Solution Content/Success Criteria 5 3333 1 1 22222a− = + + + 1 1 322a− = 1522 a− = Comparing indices, 15 a−= 4a =− I can solve equation using laws of indices. m n m na a a += 1n na a − = Content L Complexity H Context L Response Strategy H Assessment Objective AO2 OR 3333 1 1 22222a− = + + + 3 1 1 2 (1 1 1 1)2a− = + + + 32 1 5 1 ( 1) 5 1 2 (2 )2 1 22 22 15 4 a a a a a − − −− = = = −+= =− Qn Solution Content/Success Criteria 6 (a) 2 22 2(5 3 ) 2(25 30 9 ) mn m mn n + = + + I can use identity 2 2 2( ) 2a b a ab b+ = + + to expand algebraic expressions. 2250 60 18m mn n= + + (b) 23 2 2 3 2 24( ) 21 24 21 3 (8 7 ) mn mn m n mn mn m n − =− =− I can factorise algebraic expressions by taking out common factor. Content L Complexity M Context L Response Strategy M Assessment Objective AO1

Tanjong Katong Girls’ School [Turn over 4052/S4Prelim/01/2024 Qn Solution Content/Success Criteria 7 1 (4.5)(7.1)sin 12.62 15.975sin 12.6 12.6sin 15.975 56sin 71 XYZ XYZ XYZ XYZ = = = = I can use 1 sin2 ab C for area of triangle to find sine of acute and obtuse angles in radians. 11 12.6 12.6sin or sin15.975 15.975 0.909 radian 2.23 radian XYZ XYZ XYZ XYZ −−    =  = −        =  = Content L Complexity M Context L Response Strategy L Assessment Objective AO2 7.1 4