2025 GDLSS Emath P1 MS

Marking Scheme 4Exp/5NA Prelim P1 2025 Question Feedback 1 Difference = 7 1.9513 = 1.05 m Most students were able to solve this question. 2(a) 1 (25.6)(17.2)sin 124.72 sin 0.56640625 34.5 180 34.5 145.5 ABC ABC ABC or ABC = =  =   = − =  Most students were able to solve this problem. Some common errors include • Not able to give the obtuse solution • Use cosine rule instead of area formula 2(b) 127 180 2.2165 2.22 radians   = = Most students were able to solve this question. Some students left their answer as 127 180 . A number of students used the wrong conversion of 360  instead of 180  3(a) ( ) 25 2 1039xy x y= 3(b) 50 55 5 5 6 4 3 4 243 3 4 3 1 3 3 3 (4 1) 3 3 (3) 3 33 6 m m m m m m  −  =  −  = −= = = = Many students did not use the Indices Laws as stated in the question. Students who evaluated the LHS to 729 and then expressed it as 63 were not given the mark. 4(a) 3 66 2 3 11 rM p q =  Smallest r = 4 This is relatively poorly attempted. 4(b) 522 3 5X =   Y p q= HCF = 235m LCM = 522 3 5 7   23 5 7 1 Y m =   = This was very poorly attempted. 5 Finance company: 24 0.375$8000 1 100 $8751.92 A =+  = Common mistakes include • Calculating as simple instead of compound interest

Question Feedback Bank: 2 4.5$8000 1 100 $8736.20 A =+  = Alvin is wrong as the interest is higher if he borrows from the finance co. • Wrong substitution like 2 0.375128000 1 100+ or 2 0.375 128000 1 100+ 6(a) ( ) 2 26 12 36x q x x q− − = − + − By comparing, 12 12 p p − = − = 36 5 41 41 q q q − = − − = − = Common error of giving -12 and/or -41 as their answer 6(b) ( ) 22 12 5 6 41x x x− − = − − Line of symmetry, 6x = About half of the students do no know how to get this answer, or gave their answer as y=6 or just 6. 7(a) 50 2506 60 50 25 75 v v v − = −= = A number of students did not change the time to hours. Some students changed the acceleration wrongly to 225 km/min6 which was not accpetable 7(b) Dist. travelled by A = Dist. travelled by B 1 6 4 1 10 1(75 50) (50) (50 5) (80)2 60 60 2 60 2 60 120 throughout : 750 400 55 550 80 tt tt −       + + + + =                + + − = 600 55 80 600 25 24 tt t t += = = Very poorly attempted Majority of the students calculated the total distance travelled by A wrongly by leaving out the area from 0-5km/h or assuming that the area after 10 minutes was a triangle. 8(a) 1120 120 120 206 100 −  = − = n = 24.5 minutes A number of students gave their answer wrongly as 15 ( 1 1206 ) 8(b) 16, 24 Most students got this correct. Those who got the answer wrong did not check to ensure the total was 120. 8(c)(i) Mean = 20.25 ECF from (b) given. Most students were able to calculate this correctly. Some students did not use the mid-value of x in their calculation.

Question Feedback 8(c)(ii) SD = 4.87 ECF from (b) given. Most students were able to calculate this correctly. 8(d) Median = 21.5 minutes Most students were able to find the answer. 8(e) The curve will pass through the same median but it will be wider / more spread out around the median. Very badly explained. Many of the students said that the curve will be steeper instead of less steep. Majority of the students did not make any remark regarding the same median. 9 $800$800 A$1$0.8323 A$961.19 = = A$961.19 5$1 800 A$1.21 (2 d.p.) += = Most students were able to solve this question 10 37 ( )( 7)7 4 3 47 7 3 28 y mx c c c yx yx =+ = − − + = =− + += Most students were able to solve this question. Unacceptable working include substituting the x/y values into the given equation instead of showing how the equation is obtained. 11 ( ) ( ) ( )( ) ( )( ) ( )( ) 2 2 3 5 2 3 1 3 1 3 5 2 5 2 3 1 3 15 6 5 2 3 1 3 14 6 5 2 3 1 x xx x x x xx x x x xx xx xx −−+ + − −= −+ + − += −+ −+= −+ This question was well-attempted by most students 12(a)(i) ( ) 3 2 2pq p q pq q p+ = + This question was well-attempted by most students 12(a)(ii) ( ) ( ) ( )( ) 220 8 15 6 4 5 2 3 5 2 4 3 5 2 ac a bc ab a c a b c a a b c a + − − = + − + = − + This question was well-attempted by most students

Question Feedback 12(b) ( )( ) 22 22 5 3 2 7 10 35 6 21 35 11 6 m r r m mr m r mr m mr r +− = − + − = − − + This question was well-attempted by most students 13 ( ) ( ) 16 4 15 16 7 16 4 31 7 7 16 4 31 112 7 124 4 3 12 4 n n n n nn nn n n + =++ + =+ + = + + = + = = This question was well-attempted by most students. Alternative working using ratio (of girls to total) was acceptable. 14 Given that ABC is right angled and AD DC= , D is the centre of the circle ABC  ABC is angle in semicircle. Since A, B and C lie on the circle, BD, AD and CD are the radii of the circle and therefore D is equidistant to A, B and C. Very poorly explained. Most students were unable to • quote the circle property correctly, • identify the diameter and the centre • make connection to the radii 15 ( ) ( )( ) ( )( ) ( )( ) 2 22 22 22 2 2 3 3 3 1 4 12 9 3 3 3 4 12 9 3 4 3 4 12 9 3 12 9 n n n n n n n n n n n n n n n n n + − + + = + + − + + + = + + − + + = + + − − − = Since 2 0 and 0nn , it will always be positive. About half the students expanded and simplified the expression (but some had algebraic errors). However, a number of them simply said that 2 0n  without justifying that 0n . 16 The chart is misleading as the volume (size) of the smaller to bigger cube is 1 : 8, hence people may misinterpret the increase in the sales to be more than double. Poorly explained. Many were not able to explain that the misinterpretation was caused by the volume ratio or area ratio (also accepted). 17(a) Well attempted. Shading could be better done. Students used precious time to actually ‘shade’. Pencil line drawing is sufficient 17(b) 'AB Well attempted. A B

Question Feedback 18(a) 3 54 3 3: 5250 5== A few cube rooted num and den separately and obtained non- integer answer. TIP: learn to use the calculator correctly. 18(b) Surface area in contact with the water 2 112(4 7) 2(4 11) 2( 11 30.2) 2( 7 30.5)22 144 332.2 213.5 689.7 cm =  +  +   +   = + + = Surprisingly a number could not 144. 19 AMa students clear advantage here. Common mistakes include: i) wrong shape. ii) wrong max coordinates iii) wrong y-intercept iv) incomplete or no labelling 20 22 22 22 12 27 2 7 15 3(4 9 ) (2 3 )( 5 ) 3(2 3 )(2 3 ) (2 3 )( 5 ) 3(2 3 ) 5 xy x xy y xy x y x y x y x y x y x y xy xy − −− −= +− +−= +− −= − A good number struggled. Forgotten factorisation skills: i) difference of 2 squares ii) x-method. The y variable confused them? A couple forgot to include the y. Penalised. Poor bracketing skills seen. 21(a) 2084 3 2 1 128 4 4 4 84 64 2 128 80 4 4 xy x xy     =         +   =    ++    R = MN Very well attempted. Those who did poorly need to reflect. y x 0 (3, 2) (0, -7)

Question Feedback 84 64 2 20 2 10 128 80 4 4 128 80 40 4 84 2 x x x xy y y y =+ = = = + + =++ = = 21(b)(i) ( ) ( ) 8420 50 128 8080 =  = SR Very well attempted. A few missed the brackets. Penalised. 21(b)(ii) The total cost needed to manufacture all the tables. 22(a) Area of rectangle R = Area of triangle T ( ) ( )( ) ( ) 2 22 2 2 12 2 2 3 2 2 2 3 2 2 3 35 5 3 5 3 x y x x x y xy x x x y xy x x xy xy x xy x yx − = − − = − − = − = = = A number did poorly despite getting starting line correct. Poor algebraic manipulation skills. Poor bracketing skills seen. 22(b) Perimeter of rectangle R + 2 = Perimeter of triangle T ( )2 2 2 2( ) 2 2 2 4 4 2 2 2 2 2 2 2 2 2 4 2 52 4 23 10 423 2 23 3 y x x y x y x x y x y x x yx xx xx x x − + + = + − + + = + − + = =−  =− =− − =− = Poorly at