F.6 DSE Paper 2

If p and q are constant such that  $x^2\ +p\equiv\left(x+2\right)\left(x+q\right)+10$  , then p = 

• -4

• -2

• 6

• 10

If k is a constant such that  $x^3+^{ }4x^{2\ }+\ kx\ -\ 12$  is divisible by  $x+3$  , then k = 

• -25

• -1

• 1

• 17

Mary performs a typing task for 7 hours. Her average typing speeds for the first 3 hours and the last 4 hours are 63 per minute and 56 per minute respectively. Find her average typing speed for the 7 hours.

• 17 words per minute

• 35 words per minute

• 59 words per minute

• 60 words per minute

0.0322515 =

• 0.032 (correct to 3 significant figures).

• 0.0322 (correct to 4 decimal places).

• 0.03225 (correct to 5 significant figures).

• 0.032252 (correct to 6 decimal places).

The length of a piece of thin string is measured as 25m correct to the nearest m. If the string is cut into n pieces such that the length of each piece is measured as 5 cm correct to the nearest cm, find the greatest possible value of n.

• 445

• 566

• 567

• 650

The solution of  $x-\frac{x-1}{2}>5$  or  $1<x-11$  is

•  $x>9.$  

•  $x>10.$  

•  $x>11.$  

•  $x>12.$  

The actual area of a playground is 900 $m^2$  . If the area of the playground on a map is 36  $cm^2$  , then the scale of the map is

• 1:25

• 1:50

• 1:500

• 1:250 000

The figure shows the graph of the straight line  $x+ay+b=0$  . Which of the following are true?
I.  a < 0
II. b < 0
III. a < b

• I and II only

• I and III only

• II and III only

• I, II and III

In the figure, the solid consists of a right circular cone and a hemisphere with a common base. The base radius and the height of the circular cone are 3 cm and 4 cm respectively. Find the total surface area of the solid.

• 30 $\pi\ cm^2$

• 33 $\pi\ cm^2$

• 48 $\pi\ cm^2$

• 51 $\pi\ cm^2$

In the figure, ABCD is a circle. AC and BD intersect at E. If AB = AD and AD // BC , then $\angle$  BAE =

• 53 $\degree$  

• 57 $\degree$  

• 69 $\degree$  

• 74 $\degree$