Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
101–104 of 104
Question 101
7 marks · Normal
Answer and see the solution →The graph below shows the curve .
Quadratic curve y = x² - 4 (a)[1 mark]State the points where the curve cuts the x-axis.
(b)[2 marks]Use the graph or otherwise to write down the equation solved at the y-intercept. Find the y-intercept.
(c)[2 marks]Describe the transformation that maps the graph of to the graph of .
(d)[2 marks]Solve the inequality . Give the solution set for .
Question 102
7 marks · Hard
Answer and see the solution →An environmental scientist measures the length of a rectangular tank as 6.9 m to the nearest 0.1 m and the width as 4.0 m to the nearest 0.1 m. The height is exactly 3 m. Water is pumped into the tank at a constant rate, and the depth of water in the tank follows the quadratic equation where is in hours and is in metres.
(a)[2 marks]Calculate the lower and upper bounds for the length and width of the tank.
(b)[2 marks]Hence, calculate the lower and upper bounds for the cross-sectional area of the base of the tank.
(c)[3 marks]After 2 hours, the measured depth of water is 1.8 m. The scientist models the depth by the quadratic equation . Does the model fit the data at ? Show your working.
Question 103
6 marks · Hard
Answer and see the solution →A cumulative frequency diagram shows the results of a survey measuring the heights, in cm, of 80 students. The median height is 162 cm and the upper quartile is 170 cm. The heights have been recorded to the nearest centimetre.
(a)[1 mark]Write down the lower and upper bounds of the median height.
(b)[2 marks]If a box plot is drawn for the data, what is the minimum range of heights that could possibly be represented by the interquartile range? Give your answer to 1 decimal place.
(c)[3 marks]Calculate the lower and upper bounds for the proportion of students with a height strictly greater than 170 cm.
Question 104
7 marks · Hard
Answer and see the solution →The point P(2, 3) is transformed onto Q by a translation of and then by a reflection in the x-axis. The coordinates of Q are used as root values of the quadratic equation , where s and p are the sum and product of the coordinates of Q, respectively.
(a)[2 marks]Find the coordinates of Q after both transformations.
(b)[2 marks]Write down the values of s and p.
(c)[3 marks]Solve the quadratic equation for x.