Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
11–19 of 19 · Hard
Question 11
4 marks · Hard
Answer and see the solution →Given the vectors , , and , express the vector as a column vector. Then, calculate its magnitude, giving your answer correct to 1 decimal place.
Question 12
4 marks · Hard
Answer and see the solution →A vector has a magnitude of 13 and makes an angle of with the positive -axis. Prove that the vector could be , giving your reasoning using the definitions of vector magnitude and direction.
Question 13
2 marks · Hard
Answer and see the solution →A bag contains 5 blue counters and 3 red counters. Two counters are picked from the bag one after the other, without replacement. What is the probability that both counters picked are red?
Question 14
2 marks · Hard
Answer and see the solution →The table shows the probability that each branch is followed on a probability tree diagram. | First Event | Probability | |:-----------:|:----------:| | Heads | 0.4 | | Tails | 0.6 |
What does the sum of the probabilities on the branches from any single event add up to in a tree diagram? Explain briefly.
Question 15
4 marks · Hard
Answer and see the solution →A box contains 3 orange balls and 2 purple balls. A ball is picked at random, not replaced, then a second ball is picked at random.
Calculate the probability that: (a) Both balls are orange (b) The two balls picked are different colours
(a)[2 marks]Calculate the probability that both balls are orange.
(b)[2 marks]Calculate the probability that the two balls are different colours.
Question 16
4 marks · Hard
Answer and see the solution →Maria chooses a marble from bag X and a marble from bag Y. In bag X there are 4 red and 6 blue marbles. In bag Y there are 3 red and 5 blue marbles.
She claims: 'Picking a blue marble from bag X and a red marble from bag Y is independent from picking a red marble from bag X and a blue marble from bag Y.' Is Maria correct? Give reasons for your answer.
Question 17
11 marks · Hard
Answer and see the solution →This question is about solving problems involving unit conversions and vectors.
(a)[3 marks]The rectangular floor of a hall measures 48 m in length and 32 m in width. Convert the area of the floor into square centimetres. Give your answer in standard form.
(b)[2 marks]A cleaner moves from point A (at one corner of the hall) to B (at the diagonally opposite corner). Express the displacement vector from A to B as a column vector in metres.
(c)[2 marks]Calculate the magnitude of her displacement from part (b). Give your answer to 3 significant figures. State the unit.
(d)[2 marks]Suppose another cleaner moves from A to C, where C is halfway along the width from A (i.e., 16 m from A along the width), and then to D, which is halfway along the length from C (i.e., 24 m farther in the length direction). Express the total displacement vector from A to D as a column vector in metres.
(e)[2 marks]Calculate the magnitude of the displacement from A to D. Give your answer as a surd or to 2 decimal places.
Question 18
10 marks · Hard
Answer and see the solution →This question asks you to convert units of area and calculate the magnitude of a vector.
(a)[3 marks]A farmer's rectangular field measures 150 m by 80 m. Express the area in square kilometres. Give your answer in standard form.
(b)[2 marks]A cow walks from one corner of the field at (0,0) to the corner at (150,80). Write the displacement vector as a column vector (in metres).
(c)[2 marks]Calculate the magnitude of this displacement, giving your answer to 2 decimal places. State the unit.
(d)[3 marks]The same cow walks to the midpoint of the opposite side, at position (75, 80). Find the magnitude of the displacement from the start to this midpoint. Give your answer as an exact surd.
Question 19
10 marks · Hard
Answer and see the solution →This question is about compound measures and vector geometry.
(a)[2 marks]A metal block of mass 540 g has a volume of 180 cm³. Calculate the density of the block in g/cm³.
(b)[2 marks]The block is then subjected to a force of 72 N, uniformly distributed across one face of area 30 cm × 6 cm. Calculate the pressure exerted on this face in N/cm².
(c)[2 marks]The force is now applied at two points, A and B. From the centre of the face, the force at A is represented by the vector N, and at B by N. (i) Write the total force vector (A+B), as a column vector.
(d)[2 marks](ii) Calculate the magnitude of the total force vector. Give your answer to 2 decimal places, including units.
(e)[2 marks](iii) Find the unit vector in the direction of the total force vector. Give each component to 3 significant figures.