The data shows the marks obtained by students in a biology test
52 | 56 | 25 | 56 | 68 | 73 | 66 | 64 | 56 | 48 |
20 | 39 | 9 | 50 | 46 | 54 | 54 | 40 | 50 | 96 |
36 | 44 | 18 | 97 | 65 | 21 | 60 | 44 | 54 | 32 |
92 | 49 | 37 | 94 | 72 | 88 | 89 | 35 | 59 | 34 |
15 | 88 | 53 | 16 | 84 | 52 | 72 | 46 | 60 | 42 |
(a) Construct a frequency distribution table using the class interval 0 - 9, 10 - 19, 19, 20, 29...
(b) Draw a cumulative frequency curve for the distribution
(c) Use the graph to estimate the;
(i) median
(ii) Percentage of students who scored at least 66 marks, correct to the nearest whole number.
(a) Solve the inequality \(\frac{1}{3}x - \frac{1}{4} (x + 2) \geq 3x - 1\frac{1}{3}\)
(b)
In the diagram, ABC is right-angled triangle on a horizontal ground. |AD| is a vertical tower. < BAC = 90\(^o\), < ACB = 35\(^o\), < ABD = 52\(^o\) and |BC| = 66cm.
Find, correct to two decimal places:
(I) the height of the tower
(ii) the angle of elevation of the top of the tower from C
(a) Copy and complete the table of values for y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) x \(\geq\) 360\(^o\)
x | 0\(^o\) | 60\(^0\) | 120\(^o\) | 180\(^o\) | 240\(^o\) | 300\(^o\) | 360\(^o\) |
y | 2.0 | - 3.6 |
(b) Using a scale of 2cm to 60\(^o\) on the x-axis and 2cm to 1 unit in the y-axis, draw the graph of y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) 360\(^o\)
(c) Using the graph,
(i) Solve 2 cos x + 3 sin x = -1
(ii) Find, correct to one decimal place, the value of y when x = 342\(^o\)
A woman bought 130 kg of tomatoes for 52,000.00. She sold half of the tomatoes at a profit of 30%. The rest of the tomatoes began to go bad, she then reduced the selling price per kg by 12%. Calculate:
(a) the new selling price per kg;
(ii) the percentage profit on the entire sales if she threw away 5 kg of bad tomatoes.
(a) The third and sixth terms of a Geometric Progression (G.P) are and \(\frac{1}{4}\) and \(\frac{1}{32}\) respectively.
Find:
(i) the first term and the common ratio;
(ii) the seventh term.
(b) Given that 2 and -3 are the roots of the equation ax\(^2\) ± bx + c = 0, find the values of a, b and c.