Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Algebra 9
17 practice questions
Practice questions
11–17 of 17
Question 11
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 12
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 13
3 marks · Normal
Answer and see the solution →Solve the following simultaneous equations for x and y:
Question 14
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 15
2 marks · Hard
Answer and see the solution →Prove that for any integer , the sum is always an odd number.
Question 16
4 marks · Hard
Answer and see the solution →Solve the simultaneous equations:
(a)[1 mark]Write down the equation to solve for \( x \ ).
(b)[2 marks]Solve the equation to find all possible values of \( x \ ). Give your answers to 2 decimal places.
(c)[1 mark]For each value of \( x \ ), find the corresponding value of \( y \ ). Give answers to 2 decimal places.
Question 17
4 marks · Hard
Answer and see the solution →A student claims: "A pair of equations, one linear and one quadratic, must always have two solutions for ." Is the student correct? Explain using an example for each possibility, referring to the graphs of the equations.