Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
101–106 of 106
Question 101
9 marks · Normal
Answer and see the solution →Let the function be defined as , for all real values of . In a probability experiment, the results are summarised in the table:
(a)[2 marks]State the domain and range of .
(b)[3 marks]Possible scores and their frequencies Score (x) Frequency (f) 1 6 2 4 3 5 4 2 5 3 A score is chosen at random. Work out the probability that the score is in the domain of and that .
(c)[2 marks]A score is selected at random. Another score is selected at random without replacement. Find the probability that both scores are greater than 3. Give your answer as a fraction in its lowest terms.
(d)[2 marks]The function is now restricted to the domain . For this domain, is one-to-one or many-to-one? Explain your answer.
Question 102
8 marks · Normal
Answer and see the solution →This question involves composite functions and probability tree diagrams.
(a)Let the function be defined by and the function by .
(i)[2 marks]Write down an expression for the composite function and simplify your answer.
(ii)[1 mark]Calculate the value of .
(b)A bag contains 5 red and 3 blue balls. A ball is chosen at random, noted, and replaced. A second ball is chosen. Tree diagrams are to be used for this part.
(i)[2 marks]Draw a tree diagram showing all possibile outcomes and label the probabilities on each branch.
(ii)[1 mark]Work out the probability that both balls chosen are red.
(iii)[2 marks]Work out the probability that one ball is red and one is blue (in any order).
Question 103
9 marks · Normal
Answer and see the solution →This question is about functions and probability. Answer each part, using reasoning and showing your methods.
(a)A function is defined by .
(i)[2 marks]Explain why is a function.
(ii)[2 marks]What is the domain and range of if can be any real number?
(b)A bag contains 2 red, 1 blue, and 1 green ball. A ball is selected at random, noted, replaced, and then a second ball is selected at random.
(i)[2 marks]Draw a probability tree diagram to show the outcomes for both selections.
(ii)[1 mark]Calculate the probability that both balls selected are red.
(iii)[2 marks]Calculate the probability that at least one of the balls selected is green.
Question 104
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 105
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 106
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.