Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 8
106 practice questions
Topics covered
Practice questions
31–40 of 40 · Easy
Question 31
2 marks · Easy
Answer and see the solution →Mia flips two different coins. She draws a tree diagram to show the possible outcomes. Explain why a tree diagram is helpful for finding the probabilities of different results.
Question 32
3 marks · Easy
Answer and see the solution →A number card is chosen at random from a box containing 6 cards numbered 1 to 6. The card is replaced and another card is chosen.
(a)[1 mark]Find the probability that both cards show an even number.
(b)[2 marks]What is the probability that one card shows an odd number and one card shows an even number?
Question 33
1 mark · Easy
Answer and see the solution →What do the branches in a probability tree diagram represent?
Question 34
2 marks · Easy
Answer and see the solution →The probability that Amira will be chosen for the school play is 0.3. What is the probability that she is not chosen for the play?
Question 35
3 marks · Easy
Answer and see the solution →The table shows the probability that a spinner will land on each colour.
Colour Probability Red 0.3 Green 0.5 Blue p a) Write down the value of .
Question 36
7 marks · Easy
Answer and see the solution →This question is about using a graph to solve a quadratic equation and expressing a vector as a column vector.
(a)The sketch below shows the graph of for .
Graph of \( y = x^2 - 4x + 3 \) (sketch) (i)[1 mark]Write down the values of where the graph crosses the -axis.
(ii)[2 marks]By drawing a suitable horizontal line on the graph, explain how you would use it to solve .
(b)[1 mark]A triangle has vertices at and .
Write down the vector as a column vector.
(c)[1 mark]The vector is given by .
What are the components of ?
(d)[2 marks]The vector .
Write down the magnitude of .
Question 37
9 marks · Easy
Answer and see the solution →This question is about graphs and vectors. Answer each part, showing your methods.
(a)[2 marks]Draw the graph of the curve for .
(b)[2 marks]Use your graph to solve the equation . Write down the values of correct to 1 decimal place.
(c)[2 marks]Let vector and vector .
Calculate the column vector .
(d)[1 mark]The point has coordinates . The vector represents the movement from to point .
Write down the coordinates of point .
(e)[2 marks]Find the magnitude of the vector from part (c). Give your answer to 2 decimal places.
Question 38
8 marks · Easy
Answer and see the solution →Answer the questions about quadratic equations and vector geometry below.
(a)[2 marks]The graph below shows for .
Graph of \( y = x^2 - 5x + 4 \) for \( 0 \le x \le 5 \) (b)[2 marks]Use the graph to estimate the solutions to . Give your answers correct to 1 decimal place.
(c)[2 marks]In the diagram below, vector and vector .
Write as a column vector.
(d)[2 marks]Find the magnitude of . Give your answer to 2 decimal places.
Question 39
8 marks · Easy
Answer and see the solution →A point P moves so that its coordinates (x, y) satisfy the quadratic equation .
(a)[2 marks]Draw the graph of for .
(b)[1 mark]Write down the coordinates of the points where the graph crosses the x-axis.
(c)[1 mark]Let A be the point where on your graph. Write the vector , from the origin O(0,0) to A, as a column vector.
(d)[2 marks]On the same grid, draw the vector , starting from the origin O(0,0).
You may estimate the y-value using the graph if needed.
(e)[1 mark]Write down as a column vector.
(f)[1 mark]What is the magnitude of ? Give your answer to 2 decimal places.
Question 40
8 marks · Easy
Answer and see the solution →The graph of the equation is shown below.
y = x^2 - 2x - 3 Point A is at and point B is at on this graph.
(a)[2 marks]Write down the solution(s) to the equation using the graph.
(b)[2 marks]Express the vector as a column vector.
(c)[2 marks]Find the magnitude of the vector , giving your answer to 1 decimal place.
(d)[2 marks]Point C has coordinates . Write vector as a column vector and calculate its magnitude to 1 decimal place.