Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
11–20 of 47 · Normal
Question 11
3 marks · Normal
Answer and see the solution →A student claims that all prime numbers are odd. Explain, giving a counter-example, whether this claim is true or false.
Question 12
4 marks · Normal
Answer and see the solution →Solve the following system of equations.
(a)[3 marks]Given y = x^2 + 1 and x + y = 7, find the two possible values of x.
(b)[1 mark]For one of the solutions in part (a), find the corresponding value of y.
Question 13
4 marks · Normal
Answer and see the solution →The table shows several points that lie on the graph of y = x^2 – 3x + 2.
Some values of y = x^2 – 3x + 2 x y 0 2 1 0 2 0 3 2 (a)[2 marks]Plot the points from the table on the axes below and draw a smooth curve through them.
Axes for y = x^2 – 3x + 2 (b)[2 marks]Use your graph to estimate the solutions to y = 0.
Question 14
2 marks · Normal
Answer and see the solution →Give a counter-example to show that the statement below is false:
The difference between two numbers is always less than their sum.
Question 15
3 marks · Normal
Answer and see the solution →Solve the following simultaneous equations for x and y:
Question 16
3 marks · Normal
Answer and see the solution →Explain, using algebraic methods, why the system below can have zero, one or two solutions:
where c is a number.
Question 17
2 marks · Normal
Answer and see the solution →Find the gradient of the straight line joining the points and .
Question 18
3 marks · Normal
Answer and see the solution →The graph of is shown below.
Graph of \( y = f(x) \) and its translation. Describe fully the transformation that maps the graph of to the graph of .
Question 19
3 marks · Normal
Answer and see the solution →The graph of is reflected in the y-axis and then stretched in the y-direction by a scale factor of 2. Write down the equation of the resulting graph, and describe each transformation algebraically.
Question 20
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).