The table shows the distribution of marks obtained by some students in a test
| Marks | 0-9 | 10-19 | 20-29 | 30-39 | 40-49 |
| Frequency | 4 | 12 | 16 | 6 | 2 |
What is the upper class boundary of the upper quartile class?
49.5
39.5
29.5
19.5
Correct answer is C
£f = 4 + 12 + 16 + 6 +2 = 40
Upper quartile class
= 3/4 of 40 = 30th position
Counting from the distribution table to the 30th position,
the upper class boundary is 29.5
If \(\frac{15 - 2x}{(x+4)(x-3)}\) = \(\frac{R}{(x+4)}\) \(\frac{9}{7(x-3)}\), find the value of R
\(\frac{-32}{7}\)
\(\frac{-23}{7}\)
\(\frac{23}{7}\)
\(\frac{32}{7}\)
Correct answer is C
\(\frac{15 - 2x}{(x+4)(x-3)}\) = \(\frac{R}{(x+4)}\) + \(\frac{9}{7(x-3)}\)
15-2x = R(x - 3) +9(x +4)/7
Put x =-4, we have 15 -2(-4) = -7R
23 -7R;
R = 23/7
{21, 91, 221}
{21, 91, 221, 381}
{1,21, 91, 221}
{1,21, 91, 221,381}
Correct answer is A
multiples of 5 less than 20 = 5, 10 and 15
= [ 5, 10 and 15 ]x\(^2\) - x + 1
x\(^2\) - x + 1
when x = 5
5\(^2\) - 5 + 1; 25 - 5 + 1 --> 21
when x = 10
10\(^2\) - 10 + 1
100 - 9 = 91
when x = 15
15\(^2\) - 15 + 1
225 - 15 + 1 = 211
Find the radius of the circle 2x\(^2\) - 4x + 2y\(^2\) - 6y -2 = 0.
17/4
17/2
17/√2
√17/2
Correct answer is C
2x\(^3\) - 4x + 2y\(^2\) - 6y - 2 = 0
Divide through by 2: x\(^2\) - 2x + y\(^2\) -3y -1 = 0
x\(^2\) -2x + y\(^2\) - 3y = 1
x\(^2\) -2x + 1 + y\(^2\) - 3y + 9/4
= 1+ 1 + 9/4
= (x- 1)\(^2\) (y - 3/2)\(^2\)
= √[17/4]
r = √17/2
Find the value of the derivative of y = 3x\(^2\) (2x +1) with respect to x at the point x = 2.
72
84
96
120
Correct answer is B
y 3x\(^2\) (2x +1) = 6x\(^3\) + 3x\(^2\)
dy/dx = 18x\(^2\) + 6x
At x = 2, 18(2)\(^2\) + 6(2)
= 72 + 12 = 84