Q1. (a) A supplier buys 80 items, all at the same price. He sells 50 of them at a profit of 30% on each. He sells the remainder at a profit of 15 % on each.
Calculate the overall profit he made on the sale of the 80 items. (8)
(b) A car is driven for 5 hours without stopping from town A to town B. The return journey on the same route took only three hours. The return average speed was 26 mph faster than the first journey.
Determine the average speed of the journeys in each direction. (8)
Q2. (a) Factorise completely EACH of the following:
(i) 100 - 100t - 64t2+ 64t3 (5)
(ii) 2sin2 A+5sinA cosA-12 cos2 A (3)
(b) Given: Z = √(R2+(ωL-1/ωC)2 )
Make C the subject of the formula. (8)
Q3. (a) Given: E = 0.36V((D-0.7)/D)3
Calculate the value of D when E = 0.64 and V = 12. (6)
(b) Solve the following system of equations for a, b and c: (10)
2a + 3b + 4c = 32
3a - 2b + 3c = 23
7a + 5b - 8c = 13
Q4. (a) Evaluate without using tables or calculator: (5)
(5log25 - log125 + 1/2 log125)/3log5
(b) Solve for t in the following equation: (5)
log2t3- logt = log16 + logt
(c) The value £C of a piece of machinery after t years is given by:
C = 28000 e-0.115t
Calculate the number of complete years before its value is less than £10000. (6)
Q5. Table Q5 indicates the various temperatures T°C, of a cooling liquid after t minutes as recorded in an experiment.
The relationship between T and t is given by the formula:
T = T0 eat where a and T0 are constants.
(a) Draw a graph to verify this relationship. (8)
(b) Use the graph drawn in Q5(a) to determine EACH of the following:
(i) approximate values of a and T0; (4)
(ii) the temperature after 23 minutes; (2)
(iii) the time it takes for the temperature to fall to 25°C. (2)
Suggested scale: horizontal axis 2 cm = 5
vertical axis 2 cm = 0.2
Q6. (a) Calculate the size of θ° using the dimensions in Fig Q6(a). (8)
Note: the figure is not drawn to scale
(b) Determine the values of ∅ in the range 0 ≤ ∅ ≤ 2π which satisfy the following equation: (8)
8 sin2∅- 10 sin∅ - 3 = 0
Q7. (a) Given V = (2t - 1)2 (3t-2)
(i) express V as a polynomial in descending powers of t; (3)
(ii) determine dV/dt (3)
(b) Determine the coordinates of the turning points on the function: (10)
y = x2 + 16/x2
Q8. (a) Fig Q8(a) shows the graphs of the functions y = x2 +1 and y - 7 -x.
Calculate the area enclosed by the two functions. (8)
(b) Given (d2 y)/(dx2 ) = 2-3 sinx+5 cosx and when x = 0, dy/dx = 4 and y = 5.
Express y as a function of x. (8)
Q9. (a) Fig Q9(a) shows the cross section of a regular hexagonal nut which is 8 mm thick.
Determine the number of these nuts which can be cast from a block of metal having dimensions of 5 cm × 4 cm × 12 cm, allowing for 9.2% wastage. (10)
(b) A solid conic frustum made of aluminium has end diameters 120 mm and 180 mm and a vertical height of 120 mm.
The density of the aluminium is 2.7 × 103 kg/m3.
Determine the mass of the frustum. (6)
Username or email address *Required
Password *Required
Note: Entering wrong username in the login form will ban your IP address immediately. Entering wrong password multiple times will also ban your IP address temporarily.
Log in
Lost your password? Remember me
No account yet?
