Angle = 39° Angle = 45° Angle = 55° CBD ADB DBA = 18 cm. BC Calculate the size of the angle between the line and the plane AD ABC. Give your answer correct to 1 decimal place. The angle AD makes with the plane ABC is angle DAC First find CD using tan: tan 39 = P1 = tan 39 × 18 = 14.576 CD Then find BD using cos: cos 39 = BD = 18 ÷ cos 39 = 23.162 M1 Use sine rule to find AD; Angle BAD (angle A) = 180 (55 + 45) = 80 – = = M1 AD = = 19.26589… Now use sine to find angle DAC: sin DAC = = M1 Angle DAC = = 49.1589 49.2° A1 (Total 5 marks) Question 21. For all values of x f(x) = 2x 5 and g(x) = 25 + x2 − (a) Find g(−6) 25 (−6)2 – 36 25 = 11 – 11 B1 (1) (b) Show that gf(x) = 4x2 + 20x (2x + 5)2 25 B1 – (2x + 5)(2x + 5) 25 – 4x2 + 10x 25 25 +10x + – 4x2 + 20x C1
Angle CBD = 39° Angle ADB = 45° Angle DBA = 55° BC = 18 cm. Calculate the size of the angle between the line AD and the plane ABC. Give your answer correct to 1 decimal place. The angle AD makes with the plane ABC is angle DAC First find CD using tan: tan 39 = P1 CD = tan 39 × 18 = 14.576 Then find BD using cos: cos 39 = BD = 18 ÷ cos 39 = 23.162 M1 Use sine rule to find AD; Angle BAD (angle A) = 180 – (55 + 45) = 80 = = M1 AD = = 19.26589… Now use sine to find angle DAC: sin DAC = = M1 Angle DAC = = 49.1589 49.2° A1 (Total 5 marks) Question 21. For all values of x f(x) = 2x + 5 and g(x) = x2 − 25 (a) Find g(−6) (−6)2 – 25 36 – 25 = 11 11 B1 (1) (b) Show that gf(x) = 4x2 + 20x (2x + 5)2 – 25 B1 (2x + 5)(2x + 5) – 25 4x2 + 10x +10x + 25 – 25 4x2 + 20x C1
pixl_ppe_march_edexcel_3h_ws.docx