Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 2
105 practice questions
Topics covered
Practice questions
21–30 of 48 · Normal
Question 21
3 marks · Normal
Answer and see the solution →A taxi company charges a $4.50 fixed fee plus $1.20 for every kilometre travelled.
Complete the table below to show the total charge $C$ in dollars ($) for $k$ kilometres.
Taxi Fare Table k (km) C ($) 0 5 10 Question 22
4 marks · Normal
Answer and see the solution →The equations $y = 3x + 1$ and $y = -x + 17$ are plotted on the same set of axes.
(a)[3 marks]Find the coordinates of the point of intersection of the two lines.
(b)[1 mark]What is the gradient of the second line?
Question 23
3 marks · Normal
Answer and see the solution →Line $L$ passes through the points $P(-6, 8)$ and $Q(0, -4)$. Without finding its full equation, show that $L$ crosses the x-axis at $x = 2$.
Question 24
4 marks · Normal
Answer and see the solution →A fitness tracker records the number of steps and the calories burned for four days, as shown in the table below.
Steps and Calories Data Steps (thousands) Calories burned 5 190 7 266 9 342 11 418 (a)[1 mark]Plot a graph of calories burned against steps (thousands) for the four days.
(b)[1 mark]By drawing a straight line through the points, estimate the number of calories burned if 8,000 steps are recorded.
(c)[2 marks]Write down the equation of the line in the form $C = ms + c$, where $C$ is calories burned and $s$ is steps in thousands.
Question 25
2 marks · Normal
Answer and see the solution →A right-angled triangle has shorter sides of lengths 7 cm and 24 cm. Calculate the length of the hypotenuse.
(a)[2 marks]Question 26
2 marks · Normal
Answer and see the solution →Find the length of the side marked x in this right-angled triangle.
(a)[2 marks]Question 27
1 mark · Normal
Answer and see the solution →Write down the name given to a straight line that touches a circle at only one point.
(a)[1 mark]Question 28
3 marks · Normal
Answer and see the solution →A, B, C, and D lie on a circle with centre O. Angle ABC is 115°.
Diagram not accurately drawn. (a)[2 marks]Work out the size of angle CDA.
(b)[1 mark]Explain why your answer is correct.
Question 29
4 marks · Normal
Answer and see the solution →The diagram shows a circle with centre O. The radius of the circle is 5 cm. Chord AB is 8 cm long.
(a)[3 marks]Find the perpendicular distance from O to AB.
(b)[1 mark]Explain why this line bisects AB.
Question 30
4 marks · Normal
Answer and see the solution →In the circle below, centre O, angle BAC = 70° and chord BC is a diameter.
(a)[2 marks]Calculate angle ABC.
(b)[2 marks]Give a reason for your answer.