Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
51–60 of 107
Question 51
3 marks · Normal
Answer and see the solution →The graph of is drawn for .
Explain how you can estimate, from the graph, the value of when , and describe the process for doing this accurately.
Question 52
2 marks · Hard
Answer and see the solution →A company models the cost, $C, in dollars, of producing x batches of items by the equation below. \[ C = \frac{1800}{x} + 70x \] For what value of x is the cost C minimized (to the nearest whole number)?
Question 53
4 marks · Hard
Answer and see the solution →The function is to be plotted for .
Complete the table below by calculating the value of y for each value of x.
x y -2 -1 0 1 2 Question 54
4 marks · Hard
Answer and see the solution →Consider the algebraic form of a reciprocal equation.
(a)[1 mark]Write down the general algebraic form of a reciprocal equation.
(b)[2 marks]Explain how you can identify a reciprocal equation just by looking at its algebraic form.
(c)[1 mark]Give an example of a reciprocal equation and state its asymptotes.
Question 55
1 mark · Easy
Answer and see the solution →State one property that two similar triangles always have.
Question 56
2 marks · Easy
Answer and see the solution →A circle has a radius of 5 cm. The angle at the centre of a sector is 90°.
Calculate the length of the arc. Give your answer to 2 decimal places.
Question 57
2 marks · Easy
Answer and see the solution →Explain, using reasoning, why the volume of a cylinder increases if the height is doubled but the radius stays the same.
Question 58
3 marks · Easy
Answer and see the solution →The two pentagons below are similar. The side of the smaller pentagon is 4 cm. The side of the larger pentagon is 10 cm.
(a)[1 mark]Write down the scale factor for the sides from the smaller pentagon to the larger pentagon.
(b)[2 marks]If the area of the smaller pentagon is 13 cm², calculate the area of the larger pentagon.
Question 59
3 marks · Easy
Answer and see the solution →The table shows data for three sectors of a circle. The radius of all the sectors is 6 cm.
Sectors in a circle Sector Angle at Centre Arc Length (cm) A 60° B 120° C 180° Calculate and complete the missing arc lengths for sectors A, B, and C. Enter your answers to 2 decimal places.
Question 60
1 mark · Easy
Answer and see the solution →Write down the formula for the surface area of a sphere of radius .