Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
91–100 of 107
Question 91
4 marks · Hard
Answer and see the solution →In a club, every member either plays table tennis (T), badminton (B), or both. There are 60 members in total. 42 members play table tennis, 28 play badminton, and members play both.
Given that a member is chosen at random and is known to play table tennis, the probability that they also play badminton is .
(a)[2 marks]Express the number of members who play both sports in terms of the information above.
(b)[2 marks]Find the value of .
Question 92
5 marks · Easy
Answer and see the solution →A sector of a circle has a radius of 5 cm and angle 72°. A water tank is connected to a pipe with outflow rate modelled by a reciprocal graph.
(a)[2 marks]Calculate the length of the arc of the sector. Give your answer correct to 2 decimal places.
(b)[2 marks]The volume of water in the tank at time t hours after midnight is given by the equation \[ v = \frac{600}{t} \] where v is in litres and t ≥ 1. Using t = 5, find the volume v of water left in the tank at 5 a.m.
(c)[1 mark]Explain one feature of the graph of (such as its intercept or asymptote).
Question 93
5 marks · Easy
Answer and see the solution →A solid plastic cone has height 10 cm and base radius 4 cm. The equation y = x^3 – 2x^2 models the height (in cm) y above a point, for various x values along its base.
(a)[1 mark]Write the algebraic form of the equation for the graph y = x^3 – 2x^2. What type of function is this?
(b)[2 marks]Calculate the volume of the cone. Give your answer correct to 2 decimal places. (Use π = 3.14)
(c)[1 mark]For x = 2, find the value of y using the equation y = x^3 – 2x^2.
(d)[1 mark]Find the surface area of the curved part of the cone correct to 2 decimal places.
Question 94
5 marks · Easy
Answer and see the solution →Two solids, A and B, are similar cones. The radius of cone A is cm and the radius of cone B is cm.
The equation of a reciprocal function is given by , where .
(a)[2 marks]Explain how you would use the scale factor between cones A and B to find the ratio of their volumes.
(b)[1 mark]Find the ratio of the volume of cone B to the volume of cone A.
(c)[1 mark]The height of cone B (in cm) is substituted into the reciprocal function above. If the height of cone B is 15 cm, calculate the value of .
(d)[1 mark]Explain what happens to the value of as (the height of cone B) increases. Give a reason using the equation.
Question 95
5 marks · Easy
Answer and see the solution →The function models the height (in metres) of a walkway at position metres, for .
(a)[2 marks]Using the graph of , state the values of for which the walkway is below ground level (i.e. where ).
(b)[3 marks]Solve the inequality . Write your answer as a set of values of .
Question 96
5 marks · Easy
Answer and see the solution →A rectangular field is 20 metres longer than it is wide. The area of the field is 1200 m².
(a)[3 marks]Let the width of the field be metres. Form a quadratic equation in \( x \ ) for the area of the field and solve it to find the width and length of the field.
(b)[2 marks]The width you obtained in part (a) is used as the input in the function . Work out the value of , giving your answer to 2 decimal places.
Question 97
5 marks · Easy
Answer and see the solution →The temperature, °C, in a greenhouse at time hours is modelled by the cubic function .
(a)[1 mark]Find the temperature at hours.
(b)[1 mark]State the value of (hours) when the graph of cuts the vertical (temperature) axis.
(c)[1 mark]The temperature reaches a minimum at some value of . Write down a quadratic equation that must be solved to find the value of where the minimum occurs.
(d)[2 marks]Solve the equation using the quadratic formula. Give both values for , correct to 2 decimal places.
Question 98
5 marks · Normal
Answer and see the solution →a) Convert the recurring decimal into a fraction, giving your answer in its simplest form.
b) The value you obtain in (a) is used as a coefficient in the quadratic equation . Solve this equation for , giving your answers in terms of .
(a)[2 marks]Convert into a fraction in its simplest form.
(b)[3 marks]Let be your answer to (a). Solve in terms of . Give your answer for in terms of .
Question 99
5 marks · Normal
Answer and see the solution →This question tests understanding of recurring decimals and solving quadratic equations.
(a)[2 marks]Write the recurring decimal as a fraction in its simplest form.
(b)[3 marks]Let be the fraction you found in part (a). Solve the quadratic equation for .
Question 100
5 marks · Normal
Answer and see the solution →Part of a probability experiment involves the recurring decimal 0.1\dot{4}.
(a)[2 marks]Express the decimal 0.1\dot{4} as a fraction in its lowest terms.
(b)[1 mark]In a class of 30 students, the probability that a randomly chosen student has a score less than is equal to this fraction. Work out the number of students expected to have a score less than .
(c)[2 marks]In a different group, a Venn diagram shows:
Category Number of students Only English 8 Only Maths 12 Both English and Maths 5 Neither x It is known that the probability a randomly chosen student from this group studies either English or Maths is the same as the fraction found in part (a). Work out the value of .