Mathematics
Daily Exam Challenge: Maths (Higher)
Instructions
- • Use black ink or black ball-point pen. Draw diagrams in pencil.
- • Answer all questions in the spaces provided.
- • Do all rough work in this question paper. Cross through any work you do not want to be marked.
- • Show all your working out — marks may be awarded for correct working even if the answer is wrong.
Information
- • The total mark for this paper is 32.
- • The marks for each question are shown in brackets — use this as a guide as to how much time to spend on each question.
- • Questions labelled with an asterisk (*) are where the quality of your written communication will be assessed.
Answer all questions in the spaces provided.
Prove algebraically that the sum of the squares of any two consecutive odd numbers is always 2 more than a multiple of 8.
A circle has equation x² + y² = 25. A tangent to the circle at the point (3, 4) meets the x-axis at point P. Find the coordinates of P.
The first three terms of a geometric sequence are (k+4), k, and (k-3) where k is a positive integer. (a) Show that k² - 7k + 12 = 0 by removing common factors, not by cross multiplying. (b) Find the two possible values of k. (c) For each value of k, find the common ratio and state whether the sequence converges.
A frustum is formed by removing a cone of height 4cm from a cone of height 12cm. The radius of the large base is 9cm. Calculate the volume of the frustum in terms of π.
Solve the simultaneous equations: x² + y² = 25 y = 2x + 1
A bag contains n red beads and 5 blue beads. Two beads are taken at random without replacement. The probability they are both red is 1/3. Show that n² - n - 30 = 0 and find n.
End of Questions
Total marks: 32