G12 mathematics test 2

Simplify  2a – 7b – 2(a-3b) 

Two tins are geometrically similar. If the ratio of their volumes is 27:64, find the ratio of their curved surface areas.

(a)      For the sequence 11, 13,  15,  17, …, find the 13″ term.

(b)     If the arithmetic mean of 5 and c is 11, what is the value of c?

(a)      A soccer match kicked off at 14 00 hours at A(20N, 30E). What would be the kick off time of the soccer match at B(20N,  15°w) ?

(b) Two towns P and Qare  on the same longitude. Given that Pis (40°N,  15°w)

and PQ is 7 200nm, find the position of Q

A die and a coin are rolled and tossed, respectively. What is the probability of getting a five and a tail? Wriete your answer as a fraction 

In the diagram below, points A, B, C and D are on a circle. BD is the diameter of the circle. AC =42°, CAD = 33° and the lines AC and BD intersect at X.

Find

(a)      CBD,

(b)      ACD,

(c)      AXB.

14       The table below shows the relationship  between two variables x andy. It is given that y varies inversely as the square root of x, where x is positive.

(a)      Write an expression  for y in terms of x and the constant of variation k.  (no mark)

(b)      Find the value of

(i)       k,

(ii)     a.

Maphone Manufacturing Company paid a total dividend of K12 600.00 at the end of 2015 on 6 000 shares. If Magula owned 200 shares in the company, how much was paid out in dividends to her?

The diagram below shows triangle ABC in which AC= 18cm, CAB = 30° and ABC = 90°.

Calculate the length of BC.

The curved surface area of a cone is 88 cm. Given that the base radius is 4 cm, calculate the slant height of the cone. ( ℼ=22/7     A = ℼrl) 

A bag ofpotatoes has mass (15.4 ± 0.05)kg

Find the tolerance of this mass.

A, B and C are three points on level ground. B is on a bearing of 070° from A and

C is on a bearing of 130° from B

Calculate the bearing of

(i) A from B,

(ii) B from C

The diagram below shows a Cartesian plane with points A(6, 6), B(O, -2), C(O, 6)

and D(6, 0).

Find the

(a) equation of the line CD,

(b) distance AB.

The diagram below shows the speed-time graph of a 1 00m sprinter who accelerates uniformly for 3 seconds until he reaches a speed of 12m/s. He maintains the speed for 7 seconds and then uniformly retards for a further 4 seconds and comes to a stop

Calculate the

(a)       acceleration during the first 3 seconds,

(b)       retardation at the end of his race,

(c)       distance he covered in the first 10 seconds

Given that

Find the value of x

Solve the equation  25^x = 5