Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
31–40 of 105
Question 31
3 marks · Normal
Answer and see the solution →Solve the following simultaneous equations for x and y:
Question 32
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 33
2 marks · Hard
Answer and see the solution →Prove that for any integer , the sum is always an odd number.
Question 34
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 35
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.
Question 36
1 mark · Easy
Answer and see the solution →Write down the vector that translates the graph of onto the graph of .
Question 37
2 marks · Easy
Answer and see the solution →The graph of is shown below.
Estimate the gradient of the curve at the point where by drawing a tangent.
Question 38
2 marks · Easy
Answer and see the solution →The graph of is translated to become the graph of .
Describe the transformation fully.
Question 39
3 marks · Easy
Answer and see the solution →The graph of is transformed to .
(a)[1 mark]Describe the transformation.
(b)[1 mark]Write down the equation of the transformed graph if .
(c)[1 mark]Give the new coordinates of the point (2, 8) on the transformed graph.
Question 40
3 marks · Easy
Answer and see the solution →The table shows part of the data for the function .
Values for y = h(x) x y 0 0 1 2 2 6 3 12 Estimate the gradient of the curve at using the values given.