The table shows the distribution of marks scored by students in a test.

(a) Construct a cumulative frequency table for the distribution.

(b) Draw a cumulative frequency curve for the distribution.

(c) Use the curve to estimate the:

(i) median;

(ii) probability that a student selected at random obtained distinction, if the lowest mark for distinction is 75%.

 

A container, in the form of a cone resting on its vertex, is full when 4.158 litres of water is poured into it.

(a) If the radius of its base is 21 cm,

(i) represent the information in a diagram;

(ii) calculate the height of the container.

(b) A certain amount of water is drawn out of the container such that the surface diameter of the water drops to 28 cm. Calculate the volume of the water drawn out. (Take \(\pi\) = \(\frac{22}{7}\))

A man starts from a point X and walk 285 m to Y on a bearing of 078\(^o\). He then walks due South to a point Z which is 307 m from X.

(a) Illustrate the information on a diagram.

(b) Find, correct to the nearest whole number, the:

(i) bearing of X from Z;
(ii) distance between Y and Z.
 

(a) Using a scale of 2cm to 2units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for - 10 \(\leq\) x \(\leq\) 10  and -10 \(\leq\) y \(\leq\)10

(b) Given the points P(3, 2). Q(-1. 5). R(0. 8) and S(3, 7). draw on the same graph, indicating clearly the vertices and their coordinates, the:

(i) quadrilateral PQRS;

(ii) image P\(_1\)Q\(_1\)R\(_1\)S\(_1\) of PQRS under an anticlockwise rotation of 90\(^o\) about the origin where P \(\to\) P\(_1\), Q \(\to\) Q\(_{1}\), R \(\to\) R\(_{1}\) and S \(\to\) S\(_{1}\)

(iii) image P\(_2\)Q\(_2\)R\(_2\)S\(_2\) of P\(_1\)Q\(_1\)R\(_1\)S\(_1\) under a reflection in the line y - x = 0 where P\(_1\) \(\to\) P\(_2\), Q\(_1\) \(\to\) Q\(_{2}\), R\(_1\) \(\to\) R\(_{2}\) and S\(_1\) \(\to\) S\(_{2}\)

(c) Describe precisely the single transformation T for which T : PQRS \(\to\)  P\(_2\)Q\(_2\)R\(_2\)S\(_2\)

(d) The side P\(_1\)Q\(_1\) of the quadrilateral P\(_1\)Q\(_1\)R\(_1\)S\(_1\) cuts the x-axis at the point W. What type of quadrilateral is P\(_1\)S\(_1\)R\(_1\)W?

(a) Solve the inequality: \(\frac{1 + 4x}{2}\) -\(\frac{5 + 2x}{7}\) < x -2

(b) If x: y = 3: 5, find the value of \(\frac{2x^2 - y^2}{y^2 - x^2}\)