Junior Cert Maths Samples

_________________________________________ juniorcertsolutions.com ________________________________________ 2016 Question 12 – Higher Paper 2 Solution (a) Net (b) We are asked to use trigonometry to find the length of side x Since the given triangle is isosceles, if we construct a perpendicular from a to bc , it will bisect the [ bc ] (i) 3.5 is the adjacent, x is the hypotenuse ( ) 3.5 3.5 cos70 3.5 cos70 10.23 cos70 x x x = ⇒ = ⇒ = = D (ii) The area of face A = 12 × 7 = 84 cm 2 The area of face B = 12 × 10.23 = 122.76 cm 2 Face C is a triangle. You could use the formula 1 sin 2 ab C from the tables to get ( ) ( ) 2 2 1 10.23 10.23 sin 40 33.63 cm 34 cm 2 = = D Or First find the perpendicular height of C + ( ) 2 2 2 3.5 10.23 h + = ( ) ( ) 2 2 2 10.23 3.5 92.40 h = − = 92.80 9.61 h = = Area = ( ) ( ) 1 7 9.61 33.64 34 2 = = cm 2 Comment: Nice question. Mixture of geometry and trigonometry. 4 4 6 4 4 6 8 8 a b c 40° 70° 70° x 7 a b d 70° x 3.5 10.23 3.5 h