Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Graphs 8
18 practice questions
Practice questions
11–18 of 18
Question 11
4 marks · Normal
Answer and see the solution →The curve is drawn for .
Curve \( y = x^2 + 2 \) with point at \( x=1 \). (a)[3 marks]Draw a tangent to the curve at , and estimate its gradient.
(b)[1 mark]Write down the equation of the tangent to the curve at , using the gradient found in part (a).
Question 12
4 marks · Normal
Answer and see the solution →The graph below shows the temperature (in °C) of a liquid as it cools over time.
Temperature-time graph for a cooling liquid. (a)[2 marks]Estimate the rate of temperature change at min.
(b)[2 marks]Describe how the rate of temperature change varies as time increases.
Question 13
2 marks · Normal
Answer and see the solution →Write down the algebraic equation for the graph that results from stretching by a scale factor of 4 in the y-direction.
Question 14
3 marks · Normal
Answer and see the solution →Find the gradient and y-intercept of the straight line with equation .
Question 15
3 marks · Normal
Answer and see the solution →Below are graphs of , , and .
Explain how each of the following transformations affects the graph of :
(i) Replacing x with x-1
(ii) Replacing x with x+3
Question 16
2 marks · Hard
Answer and see the solution →The curve y = x^2 + 2x + 1 is shown below.
Graph of y = x^2 + 2x + 1 Estimate the gradient of the curve at the point where x = -1.
Question 17
4 marks · Hard
Answer and see the solution →The graph of y = f(x) is shown below.
(a)[2 marks]The graph is reflected in the x-axis and then translated by the vector . Write down the equation of the resulting graph in terms of f(x).
(b)[2 marks]If the original graph is y = , write down the equation of the final transformed graph.
Question 18
4 marks · Hard
Answer and see the solution →Below are functions f(x) and g(x):
Describe fully the sequence of transformations that map the graph of y = f(x) onto y = g(x), giving the algebraic form, and provide the order they are applied in.