E.g. M1 or for (=16.18…) or = 5×tan72 (=15.38…) = 5 ÷ tan18 (=15.38…) or or AX AX = 5×tanADC or = 5 ÷ tanDAX or AX AX = 102 + 102 2×10×10cos108 (=261.8) or 16 or 16.2 for throughout AD2 AD − = (=16.18) or AD = (=16.18) NB: Allow the value on the diagram for angle AD ADC or if used in an otherwise correct trig statement DAX E.g. Area = × 10 × oe or M1 dep on previous M1 “15.38…” 0.5 × 10 × × sin72 0.5 × or or “16.18” “16.18”×”16.18”×sin36 0.5 × 10 × × sinADC or 0.5 × NB: Allow the value on the diagram for angle ADC “16.18” “16.18”×”16.18”×sinDAX or if used in an otherwise correct area statement DAX 76.9 6 A1 for answer in the range 76.5 77 – SC: B4 for an answer in the range 53 53.5 – Total 6 marks 13 Scheme 2 (only interior needed) Let be midpoint of X DC (Angle =) = 108 M1 or for 108 seen as an interior angle DEA =102 + 102 2×10×10cos108 (=261.8) or M1 Allow 16 or 16.2 for throughout AD2 AD − = (=16.18) AD = 52 (= 236.8) or M1 AX2 “261.8” − = 52 (= 236.8) AX2 “16.18”2 − (=15.38..) M1 0.5 × 10 × M1 “15.38” 76.9 6 A1 for answer in the range 76.5 77 – SC: B4 for an answer in the range 53 53.5 – 6 marks 14a 3×2×x2 3×2x 12 M1 for one of 3×2×x2 (=6x2) or (=6x) or − − −3×2x −12 2 A1
E.g. AX = 5×tan72 (=15.38…) or AX = 5 ÷ tan18 (=15.38…) or AX = 5×tanADC or AX = 5 ÷ tanDAX or AD2 = 102 + 102 − 2×10×10cos108 (=261.8) or AD = (=16.18) or AD = (=16.18) M1 or for (=16.18…) or 16 or 16.2 for AD throughout NB: Allow the value on the diagram for angle ADC or DAX if used in an otherwise correct trig statement E.g. Area = × 10 × “15.38…” oe or 0.5 × 10 × “16.18” × sin72 or 0.5 × “16.18”×”16.18”×sin36 or 0.5 × 10 × “16.18” × sinADC or 0.5 × “16.18”×”16.18”×sinDAX M1 dep on previous M1 NB: Allow the value on the diagram for angle ADC or DAX if used in an otherwise correct area statement 76.9 6 A1 for answer in the range 76.5 – 77 SC: B4 for an answer in the range 53 – 53.5 Total 6 marks 13 Scheme 2 (only interior needed) Let X be midpoint of DC (Angle DEA =) = 108 M1 or for 108 seen as an interior angle AD2 =102 + 102 − 2×10×10cos108 (=261.8) or AD = (=16.18) M1 Allow 16 or 16.2 for AD throughout AX2 = “261.8” − 52 (= 236.8) or AX2 = “16.18”2 − 52 (= 236.8) M1 (=15.38..) M1 0.5 × 10 × “15.38” M1 76.9 6 A1 for answer in the range 76.5 – 77 SC: B4 for an answer in the range 53 – 53.5 6 marks 14a 3×2×x2 − 3×2x − 12 M1 for one of 3×2×x2 (=6x2) or −3×2x (=6x) or −12 2 A1
igcse-9-1-maths-practice-paper-3-mark-scheme.docx