YCKSS EM P1 PRELIM MS 2025

1 Yio Chu Kang Secondary School 4E/5N Prelim Mathematics P1 2025 Marking Scheme Qn Solutions Marks Marker’s Comments 1 ( )5 4 3 2 6 5 4 3 2 6 4 13 p p p p p p p − − + + − = − − − + − =− M1 A1 Well done 2a 03x or x A1 Poorly done 2b 3 B1 3 ( ) ( ) ( ) ( ) 713 2 5 3 12 8 6 2 3 2 3 5 3 4 7 1 24 6 4 15 9 28 28 24 37 23 24 xxx x x x x x x x +−− −− − − − −  += − − + − −= −−= M1 M1 A1 Many did not use LCM of denominators, hence some final answers were not in lowest term 4a 35 B1 4b Incorrect. Median mark means 50% of students scored both more than or less than the mark. B1 Poor 5a ( ) 2224 15 9 3 8 5 3 pq pq p q pq q p +− = + − B1 5b ( ) ( ) ( )( ) ( )( ) 2 2 5 2 5 2 5 5 2 2 5 1 2 1 1 5 2 accept 1 2 5 a bc ac ab ac a bc ab ac ab ac ac ab ac ab + − − = − + − = − − − = − − − − M1 A1 6a 1.25 : 1 11 : 1.25 1010 : 8 1.25 km cm km cm km cm = M1 A1 Poor conversion of units 6b 2 2 2 2 2 2 2 2 1 :1.25 1.5625 6.56 : 6.56 1.25 10.25 cm km km cm km km = = M1 A1 Some did not take square of the map scale 7 ( ) ( ) ( ) ( )23 3 23 2 23 23 23 80 5 115 80 7 2, 9, 16, 30 d d d d d d w x y z − + − + − + + + = − + = = = = = = B2 Deduct 1 mark for each error Poorly done despite being a common past yr’s O lvl qn

2 8a ( )2 44 28 28 44 72 76 72 72 76 32 72 108 72 1.5angle AOB       − + + = − = − − −= =− M1 A1 Poorly done as many used the formula for degree 8b ( ) ( ) ( ) 22 2 11 44 1.5 28 1.522 946 3 area cm sf =  − −  − = M1 A1 (ecf) Poorly done as many used the formula for degree 9a 11 55cos or cos12 12 55cos cos 65.37512 12 114.624 180 65.375 114.6 ACD ACB ACD ACB ACD −−  =−  =  = −  = =  =   = −  = M1 A1 Some did not leave answer in 1dp 9b ( )360 114.624 90 335.4− −  =  B1 Some did not leave answer in 1dp 10ai 60 – 30 = 30 M1A1 10aii 36 marks B1 10b 390 180 21 400 40 − = (accept 0.525 & 52.5%) M1A1 11a 168.0 (4sf) B1 Generally ok 11b 2 2 22 2 2 2 2 2 2 2 2 xyPw w xy wPw x y w Pw w Pwx y w Pwx y =− =− =− −= −= M1 M1 A1 Some wrote: 2 2 2 2 xyPw w Pw x y =− =− Quite a number still weak in algebraic manipulation . Many did not include the  12 22 2 2 2 2 2 26 676 24 10 676 AB AC BC AB == + = + = = By the converse of Pythagoras’ Theorem, ∆ABC is a right-angled triangle. Hence, by the converse of right-angle in semi-circle, AB is the diameter of the circle. M1 M1 A1 Poorly done as students are weak in explanation. Did not use the word ”converse” when explaining using Pythagoras’ Thm

3 13 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 8 3 25 1 12 5 9 2 1 5, 40 15 125 3 2 3, 36 15 27 4 3 4 , 76 152 2 3 xy xy xy xy x x y − = −−−−− + = −−−−−  − = −−−−−  + = −−−−− += = =− M1 A1 A1 Generally well done. 14 S1 – correct shape MP1 – correct max pt I1 – correct x-ints and y-int Generally ok except for the location of the maximum point. Some indicate the point at (0,16) 15 3 12 3.61250000 1 100 55693.38 55693.38 50000 $5693.38 A Int   =+  = =− = M1 M1 A1 Badly Done. Did not divide by 12 for 3.6 and change 3 years to 36 months although the question stated to compound monthly. 16a B1 Generally ok

4 16b 'AB B1 Generally ok 17a 37.28 10 − B1 Generally well done 17bi 50081.7 10 B1 Those who got it wrong did not understand what the question is asking. 17bii ( ) ( ) ( ) 500 501 500 500 501 6.3 10 8.17 10 6.3 81.7 10 88 10 8.8 10  +  = +  = =  M1 A1 Most of the students who did not get b(i) correctly will not be able to solve b(ii) as well. 18i 32504 2 3 7=   B1 Generally well done 18ii ( ) ( ) st d 2 2n 1 number : 2 168 2 number : 3 252 2 3 7 2 3 7 =   =   B2 Generally ok. Those who did not answer correctly were mainly because they did not understand HCF and LCM fully. 19 25.277 180 25.277 25.3 154.7 x or x or =  −  =   B2 Many did not correct to 1 dp for degrees 20a 1944 66 24 1944 1584 $360 D D = +  =− = M1 A1 Generally ok 20b ( )( )( ) : 1800 360 21944 1800 100 144 100 51440 2 Int R R −−= ==  M1 A1 Poorly done. Did not know that they need to use simple interest formula to calculate the interest rate per annum. For those who knew, they substitute either the wrong interest or principal value. 21a ( )( ) ( ) ( ) 2 2 2 7  6   28   25 13 8 1 0 167 8 6 7 2 3 4 9 0 1.5 2 2 .25 t j tt tt t shown or re t = + − = + + + + + − + = =− + M1 M1 A1 Generally ok.

5 21b 1. Kalea studied longer, on average, as her mean is higher. 2. Kalea’s studying hour is more widespread as her SD is higher. B1 B1 Generally ok. Some students are not explain when SD is higher, it means more widespread. 22 ( )( ) 2 3 2 2 32 2 5 3 5 4 10 8 25 20 15 12 10 33 35 12 x x x x x x x x x x x − + − = − − + + − = − + − M1 A1 Generally ok except for some students are not able to expand with careless mistakes such as -20x instead of +20x.

6 23a ( )( ) ( ) 2 22 8 3 2 3 4 16 18 9 16 18 9 y x x x x x x x = − + − = + − − =− Since 18x is an even number & 9 is an odd number, therefore 18x – 9 will be an odd number. M1 M1 A1 Poorly done. Some students assumed that 18x-9 is the final answer and did not explain why 18x-9 will be an odd number. 23b x = 1 and y = 9 B1 Poorly done as they did not substitute an appropriate value for x to the equation 18x-9. They did not see the connection to part (a) 24 ( ) ( )( ) ( ) ( )( )( ) ( )( ) 2 4 22 2 2 5 15 81 53 99 53 3 3 9 5 39 xx x xx xx xx x x x x xx − − −= −+ −= − + + = ++ M2 A1 Most is able to factorize the numerator by picking up common factor of 5x. However, most did not factorize 4 81x − . Those who manage to factorize 4 81x − = ( )( ) 22 99xx−+ but did not factorize ( ) 2 9x − 25 ( ) ( ) ( ) ( ) 2 2 2 2 16 18 0 8 8 18 8 18 64 8 46 1.22 2 14.78 2 xx x x x x dp or dp + + = + − =− + =− + + = =− − M1 A2 Generally ok for those who use the completing the square method. Some students use quadratic formula to solve. There are quite a number who roundoff to 3 S.F instead of 2 d.p.

7 26i ( ) ( ) 21 6 14 1683V == B1 Generally ok. Some students did not leave answers in terms of  26ii ( ) ( ) 2 Using Similar s, 7 6 14 3 1 3 7 213 r r V  = = == M1 A1 Some students who did not use similar triangles to get radius is 3cm. 26iii ( ) 3 3 Using Similar figures, 168 21 14 168 147 14 168 13.4 3 h h h sf   − = = = M1 A1 Poorly done. Students did not see that they can use similar figures to get the volume. Some tried to get the values for radius or height but applied the wrong concept of using height of 7cm and 14cm as the ratio of similar heights. 27a ( ) ( ) 4 1 3   13 4 33 43 3 5 3 3 AE AO OE AO OC shown OC OB BC =+ =+ =− + + =− + + + ++ = == − a a a b a a b b ab M1 A1 Generally ok.

8 27b ( ) 33 5 333 5 93 5 95 53 AF AO OF OB =+ =− + =− + =− + = − + a ab ab ab M1 A1 Generally ok. 27c Since 9 5AF AE= & A is a common point, points A, E and F lie on a straight line. M1 A1 Poorly done. Students did not know how to get the scalar and state that A is a common point. 27d 21 30 152 cm= B1 Generally ok.