Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
1–10 of 17 · Hard
Question 1
4 marks · Hard
Answer and see the solution →A scientist measures the mass of a metal rod to be 756.7 g to the nearest gram and its length to be 120.5 cm to the nearest 0.1 cm.
(a)[2 marks]Write down the lower and upper bounds for the mass and length measurements.
(b)[2 marks]Calculate the minimum and maximum possible density of the rod in g/cm³. Density = Give both answers correct to 3 significant figures.
Question 2
4 marks · Hard
Answer and see the solution →The diameter of a pipe is measured as 8.60 cm to the nearest 0.05 cm. The length of the pipe is given as 2.00 m to the nearest 1 cm.
The volume of the pipe is calculated using the formula: \[ V = \pi r^2 h \] where is the radius (in cm) and is the length (in cm). Calculate the lower and upper bounds for the volume of the pipe, giving your answers to 3 significant figures.
Question 3
4 marks · Hard
Answer and see the solution →A stopwatch measures time in a sprint race as 12.4 seconds, correct to the nearest 0.1 second.
The distance of the race is measured as 100 metres, correct to the nearest metre.
Calculate the upper bound for the runner's average speed in m/s. Give your answer correct to 3 significant figures. (Speed = distance/time)
Question 4
4 marks · Hard
Answer and see the solution →Solve the equation by factorising, and write down all possible values of as exact values.
Question 5
5 marks · Hard
Answer and see the solution →A garden is to be designed with a rectangular lawn of width m and length m. A path of uniform width m is built all around the lawn. The total area (lawn plus path) is m.
(a)[1 mark]Show that .
(b)[4 marks]Given that the width of the path, , is 2 m, form and solve a quadratic equation to find the dimensions of the lawn.
Question 6
4 marks · Hard
Answer and see the solution →Rearrange the formula to make the subject, expressing your answer in terms of . Show the necessary algebraic steps.
Question 7
4 marks · Hard
Answer and see the solution →The equation of a quadratic curve is . The graph of is transformed to the graph of .
Write down the equation of the transformed graph in terms of .
Calculate the coordinates of the new vertex (minimum point) after these transformations.
Question 8
4 marks · Hard
Answer and see the solution →Consider the function . The graph of passes through the point (2, 10) and has a stationary point at .
Find the values of and . Show all reasoning.
Question 9
4 marks · Hard
Answer and see the solution →A triangle has vertices at (1, 1), (3, 1), and (1, 4). The triangle is first reflected in the line y = x, and then the image is translated by the vector .
(a)Write down the coordinates of the triangle after the reflection.
(b)[2 marks]Write down the coordinates of the triangle after the translation.
(b)[2 marks]Write down the coordinates of the triangle after the translation.
(c)[0 marks]Question 10
3 marks · Hard
Answer and see the solution →Explain how you would distinguish between congruent and similar triangles on a coordinate grid. Give examples of a transformation that produces congruent triangles and one that produces similar triangles.