Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 4
104 practice questions
Topics covered
Practice questions
1–10 of 19 · Hard
Question 1
4 marks · Hard
Answer and see the solution →A painting is sold for €25,310 after its price first increases by 6% at the end of 1 year and then further increases by 4% at the end of the next year.
(a)[3 marks]Work out the original price of the painting before any increases.
(b)[1 mark]By how much did the price increase in total over the two years? Give your answer to the nearest euro.
Question 2
3 marks · Hard
Answer and see the solution →An antique statue is sold for $7,480 after having lost 30% of its original value. Describe and calculate the steps needed to find the original price of the statue. Give your answer to the nearest dollar.
Question 3
3 marks · Hard
Answer and see the solution →A large TV loses 15% of its value in the first year after purchase, and then loses another 10% of its remaining value in the second year. The TV originally cost $2,400.
(a)[1 mark]Calculate the value of the TV after the first year.
(b)[1 mark]Calculate the value of the TV after the second year.
(c)[1 mark]Calculate the total percentage loss in value over the two years. Give your answer to 1 decimal place.
Question 4
4 marks · Hard
Answer and see the solution →Solve the equation . Show all your working.
Question 5
4 marks · Hard
Answer and see the solution →Change the subject of the formula to , giving your answer in terms of and .
Question 6
4 marks · Hard
Answer and see the solution →Solve the equation . Show all your working clearly.
Question 7
3 marks · Hard
Answer and see the solution →A student writes the statement . State whether this is an expression, an equation, or an identity, and explain your reasoning.
Question 8
4 marks · Hard
Answer and see the solution →A projectile is launched so that its height, metres, above the ground after seconds is given by .
(a)[3 marks]Find the maximum height reached by the projectile and the time at which it occurs.
(b)[1 mark]Determine the time when the projectile returns to the ground.
Question 9
3 marks · Hard
Answer and see the solution →A quadratic graph has the general form .
(a)[3 marks]Explain how the values of , , and affect the shape and position of the graph in the coordinate plane.
Question 10
4 marks · Hard
Answer and see the solution →A rectangular field is to be enclosed on three sides with fencing. The fourth side is a hedge and requires no fence. The length of the field is metres and the width is metres. If 160 m of fencing is available, express the total area of the field in terms of , and find the value of that gives the maximum area.
(a)[1 mark]Show that .
(b)[3 marks]Calculate the value of that produces the largest field area, and find this maximum area.