Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
1–10 of 19 · Hard
Question 1
2 marks · Hard
Answer and see the solution →A supermarket sells a 950 ml bottle of cooking oil for $4.71. Another supermarket sells a 2.5 litre bottle for $12.15. Work out which bottle is better value for money and give the cost per litre for the better value bottle.
Question 2
4 marks · Hard
Answer and see the solution →Maria earns $92,000 per year in Kalculus, where income tax is paid at 20% on the first $50,000 and 40% on any amount above $50,000.
Calculate:
(a)[3 marks]How much income tax does Maria pay in a year?
(b)[1 mark]How much does she receive per month after tax is deducted? Give your answer to the nearest dollar.
Question 3
4 marks · Hard
Answer and see the solution →In the table below are some exchange rates:
Currency Exchange Rates Currency Exchange rate to $1 (USD) UK Pound (£) 0.70 Japanese Yen (¥) 154.50 South African Rand (R) 16.78 (a)[3 marks]A student has ¥30,900 (Japanese yen). She wants to convert her money first to US dollars, and then use all of her dollars to buy UK pounds. Work out how many UK pounds (£) she will get. Give your answer to the nearest pound.
(b)[1 mark]Explain why she will not get exactly the same number of pounds if she first converts her yen to South African rand, and then all her rand to US dollars, and finally all her dollars to UK pounds.
Question 4
2 marks · Hard
Answer and see the solution →Prove that for any integer , the sum is always an odd number.
Question 5
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 6
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 7
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 8
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 9
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.
Question 10
2 marks · Hard
Answer and see the solution →In the prism shown, the base is a rectangle measuring 6 cm by 8 cm, and the height (the perpendicular distance between the two rectangular faces) is 5 cm. Work out, to 3 significant figures, the angle that the longest diagonal of the prism makes with the base.
Rectangular prism: Rectangle base ABCD with AB = 8 cm, BC = 6 cm. Height (vertical distance from base to top face) = 5 cm. Diagonal AE from A on base to E on the top face, above D.