Week 6 If sin θ= 5 13 and θ is acute, find the value of cos θ Solve for n log 4 𝑛+6 + log 4 𝑛 =2 Simplify 3+ 2 2 +1 − 1 1− 2 Find the coordinates of the local minimum point of y = x3 + 3x2 + 72 If 𝑑𝑦 𝑑𝑥 =3+ 12 𝑥 4 and the curve y = f(x) passes through the point (1,1), find f(x)

1 If sin θ= 5 13 and θ is acute, find the value of cos θ 13 2 − 5 2 =12 𝑐𝑜𝑠𝜃= 12 13 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

2 Solve for n log 4 𝑛+6 + log 4 𝑛 =2 log 4 𝑛(𝑛+6 ) = log 4 16 n2 + 6n = 16 n2 + 6n – 16 = 0 (n + 8)(n – 2) = 0 n = -8 (no solution) n = 2 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

3 Simplify 3+ 2 2 +1 − 1 1− 2 (3+ 2 )( 2 −1) ( 2 +1)( 2 −1) − 1+ 2 1− 2 1+ 2 -1 +2 2 − −1− 2 =3 2 CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

4 Find the coordinates of the local minimum point of y = x3 + 3x2 + 72 𝑑𝑦 𝑑𝑥 =3 𝑥 2 +6𝑥 𝑑 2 𝑦 𝑑 𝑥 2 =6𝑥+6 3 𝑥 2 +6𝑥=0 3𝑥 𝑥+2 =0 x = 0 or x = -2 x = 0 𝑑 2 𝑦 𝑑 𝑥 2 > 0 minimum (0, 72) CLICK FOR SOLUTION NEXT QUESTION www.mathsbox.org.uk

5 If 𝑑𝑦 𝑑𝑥 =3+ 12 𝑥 4 and the curve y = f(x) passes through the point (1,1), find f(x) 𝑦= 3+ 12 𝑥 4 𝑑𝑥 = 3𝑥 − 4 𝑥 3 +𝑐 x = 1 , y = 1 3− 4 1 +𝑐 = 1 c = 2 𝑓 𝑥 =3𝑥 − 4 𝑥 3 +2 CLICK FOR SOLUTION CLICK FOR SOLUTION www.mathsbox.org.uk

Week 6 If sin θ= 5 13 and θ is acute, find the value of cos θ 12 13 Solve for n log 4 𝑛+6 + log 4 𝑛 =2 n = 2 Simplify 3+ 2 2 +1 − 1 1− 2 3 2 Find the coordinates of the local minimum point of y = x3 + 3x2 + 72 (0, 72) If 𝑑𝑦 𝑑𝑥 =3+ 12 𝑥 4 and the curve y = f(x) passes through the point (1,1), find f(x) 𝑓 𝑥 =3𝑥 − 4 𝑥 3 +2