WAEC Mathematics Question 2015 ( Essay Question Four 4b )

QUESTION 4b

4b. The height, h m, of a dock above sea level is given by  $,0<p<6$. Find :

(i) the value of h when p = 4 ; 

(ii) correct to two significant figures, the value of p when h = 9m

SOLUTION

(i) Given the equation;

with p = 4

Substituting the valiie of p into the equation, we have;

h=6+4cos(15 x 4)°

h=6+4cos60°

But cos60° = 

  h=6+4 (  )

 h=6+2

 h= 8m ANSWERED

(ii) Given the equation;

h=6+4cos(15p)°

with h=9m

Substituting h=9 into into the equation. we have;

9=6+4cos(15p)°

9 - 6 = 4cos(15p)°

3 = 4cos(15p)°

Dividing both sides by 4

cos(15p)°

0.75 = cos(15p)°

or cos(15p)° = 0.75

p°=41.415

p°=2.76°

$$p ≊ 2.8° (2 significant figures).ANSWERED

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WAEC Mathematics Question 2015 ( Essay Question Four 4a )

4a. By how much is the sum of   less than 7?

 

SOLUTION

Let the sum of    and   be k.

And how much is the sum of  and  less than 7 be 7-k.

Hence; The sum of   and  which is k will be expressed as

Converting the mixed fractions to improper fraction, we have

The LCM of 3 and 5 is 15

 

Therefore, how much sum of  and  is less than 7 which is expressed as 7-k becomes  

The LCM of 1 and 15 = 15

Simplifying further;

    ANSWER

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WAEC Mathematics Question 2015 ( Essay Question Three 3b )

3b. The diagram shows a circle PQRS with centre O, < UQR = 68°, < TPS = 74° and < QSR = 40°. Calculate the value of < PRS.

SOLUTION

From the diagram above, we deduce that PSR = 68° (The Interior Angle of a Cyclic Quadrilateral = Opposite Exterior Angle)

Therefore, ° + 40° = 68°

                 ° = 68 - 40

                 ° = 28°

Since ° = 28°, we can conclude that PRQ = 28° (Angles in the same segment are equal)

Also, SRQ = 74° (Interior Angles of  a Cyclic Quadrilateral = Opposite Exterior Angle)

Therefore, to obtain PRS, we have;

PRS = 74° - 28°

PRS = 46°  ANSWER

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WAEC Mathematics Question 2015 ( Essay Question Three 3a )

The ratio of the interior angle to the exterior angle of a regular polygon is 5:2.

Find the number of sides of the polygon.

 

Solution

Given ratio of interior angle to exterior angle as 5:2, we have;

But the interior angle of a regular polygon is given as   and the exterior angle as 

Hence, 

Simplifying, we have

changing the division sign to multiplication sign, we have

2(n-2) = 5 x 2 

2n - 4 = 10

2n = 10 + 4

2n = 14

Making  n the subject of the formular in the equation we have to divide both side by 2

n = 7

ANSWERED

 The number (n) of sides of the polygon is 7

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