Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 10
108 practice questions
Topics covered
Practice questions
91–100 of 108
Question 91
4 marks · Hard
Answer and see the solution →A rare disease affects 2 out of every 1000 people. A test for the disease gives a positive result in 99% of cases when the person actually has the disease, but also gives a false positive result in 2% of cases when the person does not have the disease. If a person is selected at random and tests positive, how likely is it that they actually have the disease? Explain your reasoning.
Question 92
8 marks · Easy
Answer and see the solution →The curve passes through points P and Q. Triangle RST has sides with lengths 5 cm, 7 cm and angle RST = 38°.
(a)[2 marks]Find the derivative of .
(b)[2 marks]Find the stationary point by solving and state its x-coordinate.
(c)[3 marks]In triangle RST, sides RS = 5 cm, ST = 7 cm and angle RST = 38°. Find the length of side RT, giving your answer to 3 significant figures.
(d)[1 mark]State which rule you have used for part (c) and why.
Question 93
8 marks · Easy
Answer and see the solution →A particle moves along a straight line so that its displacement from the starting point after t seconds is given by metres.
Triangle PQR has sides PQ = 6.4 cm, QR = 7.2 cm and angle PQR = 42°.
(a)[2 marks]i. Find the velocity of the particle in terms of t.
(b)[2 marks]ii. Calculate the velocity when t = 4.
(c)[3 marks]i. Calculate the area of triangle PQR using the sides and included angle.
(d)[1 mark]ii. Explain why the sine rule or cosine rule is not required for this area calculation.
Question 94
8 marks · Easy
Answer and see the solution →The cubic function has stationary points. Triangle GHI has sides GH = 10 cm, HI = 7 cm and IG = 12 cm.
(a)[1 mark]Find for this function.
(b)[2 marks]Solve to find the x-coordinates of the stationary points.
(c)[3 marks]Triangle GHI: Find the size of angle HGI, giving your answer to 1 decimal place.
(d)[2 marks]Explain your steps for part (c).
Question 95
8 marks · Easy
Answer and see the solution →A curve has equation .
(a)[2 marks]Differentiate the equation to find .
(b)[3 marks]Find the coordinates of the stationary point of the curve.
(c)[3 marks]A triangle has sides 12 cm, 8 cm and 7 cm, opposite angles respectively. Use the cosine rule to find the size of angle .
Question 96
8 marks · Easy
Answer and see the solution →The distance, metres, travelled by a moving object after seconds is given by .
(a)[2 marks]Find an expression for the velocity of the object at time .
(b)[1 mark]Calculate the velocity when seconds.
(c)[5 marks]A triangle has sides of lengths 10 cm and 15 cm, and the angle between them is . Work out the area of the triangle, giving your answer to 3 significant figures.
Question 97
8 marks · Easy
Answer and see the solution →The function is shown below.
(a)[2 marks]Differentiate with respect to .
(b)[3 marks]Sketch the graph of for . On your graph, clearly label the maximum and minimum points and the value of at which .
(c)[1 mark]For the function in part (a), find the value of the derivative when .
(d)[2 marks]State the gradient of the graph when .
Question 98
9 marks · Normal
Answer and see the solution →This question is about rational and irrational numbers and simplifying algebraic fractions.
(a)[4 marks]State, with a reason, whether each of the following is rational or irrational:
(i) (ii) (iii)
(b)[3 marks]Simplify the following algebraic fraction as much as possible:
(c)[2 marks]Given that , write the answer to part (b) in its simplest form.
Question 99
9 marks · Normal
Answer and see the solution →This question is about simplifying surds and combining algebraic fractions.
(a)[3 marks]Simplify the following expression, giving your answer as a surd in its simplest form:
(b)[3 marks]Express as a single algebraic fraction and simplify as far as possible:
(c)[3 marks]Let . Substitute this value into your answer for part (b) and write your answer as a surd in its simplest form.
Question 100
9 marks · Normal
Answer and see the solution →This question connects knowledge of number types and algebraic fractions.
(a)[2 marks]Write the number in its simplest surd form and state whether it is rational or irrational.
(b)[4 marks]Simplify the following algebraic fraction as much as possible:
(c)[3 marks]If , write your answer to part (b) in its simplest form.