Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 10
108 practice questions
Topics covered
Practice questions
31–40 of 41 · Easy
Question 31
3 marks · Easy
Answer and see the solution →(a)[1 mark]A bag contains 2 white balls and 4 black balls. One ball is picked at random (without replacement), then a second ball is picked. Write down the probability that the first ball picked is white.
(b)[2 marks]Calculate the probability that both balls picked are black.
Question 32
3 marks · Easy
Answer and see the solution →A card is drawn at random from a pack of 52 playing cards. The card is then replaced and another card is drawn. Calculate the probability that both cards are aces.
Question 33
1 mark · Easy
Answer and see the solution →A tree diagram has 2 branches at the first stage and each of these has 3 branches at the second stage. How many possible outcomes are shown at the end of the diagram?
Question 34
2 marks · Easy
Answer and see the solution →The probability that a train arrives late on any day is 0.1. Find the probability that the train is late on two days in a row. Give your answer as a decimal.
Question 35
1 mark · Easy
Answer and check →The probability that it rains on a day is 0.3. Given that it rained yesterday, the probability that it will rain today is 0.4. What is the probability that it rains today, given that it rained yesterday?
Question 36
8 marks · Easy
Answer and see the solution →The curve passes through points P and Q. Triangle RST has sides with lengths 5 cm, 7 cm and angle RST = 38°.
(a)[2 marks]Find the derivative of .
(b)[2 marks]Find the stationary point by solving and state its x-coordinate.
(c)[3 marks]In triangle RST, sides RS = 5 cm, ST = 7 cm and angle RST = 38°. Find the length of side RT, giving your answer to 3 significant figures.
(d)[1 mark]State which rule you have used for part (c) and why.
Question 37
8 marks · Easy
Answer and see the solution →A particle moves along a straight line so that its displacement from the starting point after t seconds is given by metres.
Triangle PQR has sides PQ = 6.4 cm, QR = 7.2 cm and angle PQR = 42°.
(a)[2 marks]i. Find the velocity of the particle in terms of t.
(b)[2 marks]ii. Calculate the velocity when t = 4.
(c)[3 marks]i. Calculate the area of triangle PQR using the sides and included angle.
(d)[1 mark]ii. Explain why the sine rule or cosine rule is not required for this area calculation.
Question 38
8 marks · Easy
Answer and see the solution →The cubic function has stationary points. Triangle GHI has sides GH = 10 cm, HI = 7 cm and IG = 12 cm.
(a)[1 mark]Find for this function.
(b)[2 marks]Solve to find the x-coordinates of the stationary points.
(c)[3 marks]Triangle GHI: Find the size of angle HGI, giving your answer to 1 decimal place.
(d)[2 marks]Explain your steps for part (c).
Question 39
8 marks · Easy
Answer and see the solution →A curve has equation .
(a)[2 marks]Differentiate the equation to find .
(b)[3 marks]Find the coordinates of the stationary point of the curve.
(c)[3 marks]A triangle has sides 12 cm, 8 cm and 7 cm, opposite angles respectively. Use the cosine rule to find the size of angle .
Question 40
8 marks · Easy
Answer and see the solution →The distance, metres, travelled by a moving object after seconds is given by .
(a)[2 marks]Find an expression for the velocity of the object at time .
(b)[1 mark]Calculate the velocity when seconds.
(c)[5 marks]A triangle has sides of lengths 10 cm and 15 cm, and the angle between them is . Work out the area of the triangle, giving your answer to 3 significant figures.