Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 4
104 practice questions
Topics covered
Practice questions
101–104 of 104
Question 101
5 marks · Normal
Answer and see the solution →In a right-angled triangle, the horizontal side measures 8 cm and the hypotenuse is 13 cm. The triangle's area is substituted into a formula for the cost (C) of materials needed to make a sign: C = 6A + 12, where A is the area in cm².
(a)[2 marks]Calculate the perpendicular height of the triangle.
(b)[1 mark]Find the area of the triangle.
(c)[2 marks]Using A as your answer to part b), calculate the cost of materials for the sign.
Question 102
5 marks · Normal
Answer and see the solution →A saving scheme gives interest at 4% per year, compounded annually. The sequence of balances over five years is plotted on a graph. Simultaneously, an algebraic expression relates to the yearly deposit amount.
(a)[2 marks]Amira deposits $3000. Calculate the total value of her savings after 5 years.
(b)[1 mark]The graph of Amira's savings, plotted against number of years n, is shown below.
Savings growth vs years (years 0–5, values not shown, curve rises) Describe how the graph shows that the total increases by a larger amount each year.
(c)[2 marks]Write an algebraic expression for the value S after n years using the starting amount $3000 and the yearly multiplying factor.
Question 103
7 marks · Hard
Answer and see the solution →A circle has equation . The point P(3, 4) lies on the circle.
(a)[4 marks]Find the equation of the tangent to the circle at point P in the form .
(b)[3 marks]If this tangent is written as , write down the value of m and interpret its meaning in the context of the circle.
Question 104
9 marks · Hard
Answer and see the solution →A data analyst investigates the scores of students in a mathematics test. He finds the following results:
Scores of 12 students Student Score A 43 B 47 C 55 D 58 E 62 F 64 G 65 H 67 I 73 J 78 K 81 L 82 (a)[3 marks]Calculate the interquartile range (IQR) of the scores.
(b)[4 marks]The analyst models the relationship between score, S, and student position, n (when students are ordered by their score from lowest to highest), with the equation where c is a constant. Using the data for students C and J, form two simultaneous equations to find the value of c.
(c)[2 marks]Suppose another student M joins, scoring 50, and is inserted in the correct position. Recalculate the median score for the new group.