Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 10
108 practice questions
Topics covered
Practice questions
1–10 of 18 · Hard
Question 1
2 marks · Hard
Answer and see the solution →The length of one side of a square is cm. Express the area of the square in the form cm², where and are integers and is as small as possible.
Question 2
4 marks · Hard
Answer and see the solution →State for each of the following numbers whether it is rational or irrational. If rational, write it as a fraction in the form , where and are integers. Show full reasoning.
(a)[1 mark](the decimal repeats with 25)
(b)[1 mark](c)[1 mark](d)[1 mark]Question 3
2 marks · Hard
Answer and see the solution →Simplify the following algebraic fraction as far as possible:
Question 4
4 marks · Hard
Answer and see the solution →Express the following as a single simplified fraction:
Question 5
4 marks · Hard
Answer and see the solution →Solve the following equation for x. Give your answer in its simplest form.
Question 6
2 marks · Hard
Answer and see the solution →Differentiate the function with respect to , and state the value of the gradient when .
Question 7
4 marks · Hard
Answer and see the solution →(a)[2 marks]Find the coordinates of the stationary points of the curve .
(b)[2 marks]Determine the nature (maximum or minimum) of each stationary point.
Question 8
4 marks · Hard
Answer and see the solution →A particle moves along a straight line such that its displacement after t seconds is given by , where s is in metres.
(a)[2 marks]Find the times when the particle is at rest.
(b)[2 marks]Explain how you would determine whether the particle is speeding up or slowing down at seconds.
Question 9
2 marks · Hard
Answer and see the solution →Calculate the value of .
Question 10
4 marks · Hard
Answer and see the solution →In triangle DEF, side DE = 11.3 cm, side EF = 8.7 cm, and angle DEF = 38°. Calculate the length of side DF. Give your answer correct to 3 significant figures.