Peirce Prelim 2021 S4E Add Math P2 MS

FOR TEACHERS ONLY PEIRCE SECONDARY SCHOOL 2021 Preliminary Examination for Secondary 4E/4AO/5A ADDITIONAL MATHEMATICS Paper 2 Mark Scheme Question Answer Mar ks Partial Marks Guidance 1(i) 2 = = M1 For attempt to apply . Allow for numerical errors and algebraic slips = = A1 Ignore extra brackets. OR 2 M1 Correct dividend: Correct divisor: For attempt to apply long division A1 Ignore extra brackets.

1(ii) 0 marks for attempt to solve M1 For attempt to apply factorisation by taking out common factor . Allow for algebraic slips and numerical errors but the other factor must be quadratic factor. M1 For attempt to apply factorisation. Step must be shown explicitly but allow for errors in factors ∴ , x = 5 or x = 1 A1 For all 3 correct solutions. 2(i) 5 M1 Attempt for partial fractions. M1 For attempt to remove denominator. Allow for numeric slips and algebraic slips At , M1 Correct choice of value for substitution At x = 0, M1 Correct choice of value for substitution At , ∴ A1 Accept or o.e.

Ignore redundant brackets by students. i i = M1 Replace with their partial fractions. Correct application of addition/subtraction rule. = = M1 M1 Attempt to apply power rule for 1st term Attempt to apply reciprocal rule for 2nd and 3rd term. No penalty if c is missing. Allow for numerical and sign errors = = = 1.2232 − (−2) = 3.22 A1 Ignore ‘units2’ if given. OR [4] = M1 Replace with their partial fractions. Correct application of addition/subtraction rule. = M1 M1 Attempt to apply power rule for 1st term Attempt to apply reciprocal rule for 2nd and 3rd term. Allow for numerical and sign errors No penalty if c is present and later omitted. = = 3.22 A1 o.e. single expression such as

3(i) , OR , OR , OR , 1 B1 Accept ‘and’ in place of comma. Reject ‘or’ in place of comma. 3(ii) 5 M1 B1 Attempt to apply change of base Allow for numerical errors and algebraic slips Correct evaluation to get −4 Let , M1 Simplify to any quadratic equation This steip might be implied. or M1 Their u values Allow for numerical errors But , and ∴ or 9 A1 Not awarded if any value is rejected.

3(iii) 4 M1 Correct conversion from radical form to index form M1 Attempt to apply change of base Allow for numerical errors and algebraic slips M1 Single logarithm on each side of equation OR A1 Accept and . Reject and . 4(a) 4 M1 Attempt to apply addition rule for cosine and for sine Allow for errors in sign M1 Attempt to evaluate trigo function of special angles Allow for numerical errors M1 Attempt to obtain tan A eventually. Allow for numerical errors A1 Need not rationalize surd in denominator

4(b)(i) 3 = = M1 Attempt to apply addition rule for cosine Allow for errors in sign = M1 Attempt to evaluate trigo function of special angles Allow for numerical errors = A1 4(b)(ii) = 3 = M1 Substitute result from (b)(i) = M1 Multiplying numerator and denominator by = = = A1 Accept o.e.

5(i) 2 cos2 x + 5 sin x cos x 3 = 2 cos2 x − 1 + 1 + = M1 M1 Uses Uses = A1 Must be in required order ⎯ sin, cos and 1 ∴ , 5(ii) cos x (2 cos x + 5 sin x) = 1 5 M1 Simplify to get LHS = part(i) M1 Simple trigo equation Allow for numerical errors and algebraic slips basic ∠, α = 21.801° M1 Acute angle based on their trigo equation , = 79.1°, 169.1°, 259.1°, 349.1° A1 A1√ A1√ for angles in second revolution

6(i) cm3/s 4 At , = M1 Replace h with 3r Allow for errors in formula for volume V = M1 Correct differentiation based on their V. M1 Correct substitution for Chain Rule After 4 seconds, At , OR 7.2684 At ,

= 0.60570 = 0.606 A1 Ignore wrong or no units 6(ii) 2 M1 To show rate, , is increasing Use of power rule on their Allow for numerical errors or algebraic slips As , ⇒ the rate is a decreasing function ⇒ the rate will decrease as t increases. B1√ Argues correctly based on sign of their . 7(a) 5 For max. pt., M1 1st inequality to use later For real distinct roots, B1

M1 Simplify to quadratic inequality A1√ Allow for solving to arrive at equality, 2nd inequality to use later ∴ A1√ Combine correctly based on their inequalities 7(b)(i) 3 = M1 For correct substitution, ignore inequality that follows if any = Since , Since , M1 Need to show preceding steps beginning from or explanation (−ve) x (+ve) = (−ve) (−ve) − (+ve) = (−ve) Accept Accept is always negative Will not award begin with without leading from . Will not accept trial and error. ∴ the curve has no real roots. A1 Reject ‘no roots’, ‘no solution’. Must be preceded by above step. 7(b)(ii) 3 y = 5 M1 Substitute one eqn. into another