Unit 10

What is the value of the gradient at a stationary point of a curve?

Write down the formula for the area of a triangle when two sides are of length and and the included angle is .

Calculate the value of .

In triangle XYZ, sides XY = 9 cm, XZ = 7 cm, and YZ = 12 cm. Angle YXZ is opposite side YZ. Can you use the sine rule to find angle YXZ? Explain your answer.

The triangle below has sides PQ = 5.0 cm and QR = 6.0 cm, and angle PQR = 60°.

The table below gives values for the function . Complete the missing values for and .

State whether the sine rule or cosine rule would be used to find the third side of a triangle when you know two sides and the included angle.

Calculate the area of a triangle with sides 9.0 cm and 4.5 cm and included angle 45°. Give your answer to 2 decimal places.

A coin is tossed twice. Calculate the probability that both tosses show heads. Give your answer as a decimal.

A bag contains 1 red, 2 blue and 3 green counters. You take one at random, replace it, and then take a second counter at random. Explain why a tree diagram can be used to represent all possible outcomes for this problem.