coordinate geometry

July 2016
A1 Pure Mathematics and Statistics
F.M.: 35 Class Test Time: 50 minutes
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Q. N. 1: The diagram shows points A, B and C lying on the line 2y = x + 4. The point A lies on the y-axis and AB = BC. The line from D(10, -3) to B is perpendicular to AC. Calculate the coordinates of B and C. [7]Q. N. 2: The coordinates of A are (-3, 2) and the coordinates of C are (5, 6). The midpoint of AC is M and the perpendicular bisector of AC cuts the x-axis at B.
(i) Find the equation of MB and the coordinates of B. [5]
(ii) Show that AB is perpendicular to BC. [2]
(iii) Given that ABCD is a square, find the coordinates of D and the length of AD. [2]
Q. N. 3: The diagram shows a triangle in which A has coordinates (1, 3), B has coordinates (5, 11) and angle ABC is 900. The point X(4, 4) lies on AC. Find the equation of BC. [3]
Q. N. 4: For n values of the variable x, it is given that = 216 and . Find the value of n. [3]
Q. N. 5: The time taken, t hours, to deliver letters on a particular route each day is measured on 250 working days. The mean time taken is 2.8 hours. Given that = 96.1, find the standard deviation of the times taken. [3]
Q. N. 6: 120 people were asked to read an article in a newspaper. The times taken, to the nearest second, by the people to read the article are summarized in the following table.
Calculate estimates of the mean and standard deviation of the reading times. [5]
Q. N. 7: Seventy samples of fertilizer were collected and the nitrogen content was measured for each sample. The cumulative frequency distribution is shown in the table.
Nitrogen content
3.5
3.8
4.0
4.2
4.5
4.8
Cumulative frequency
0
6
18
41
62
70

Construct a histogram to represent the given data. [5]

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