MB
H
(0 25, B II)
UNIVERSITIES
OF MANCHESTER LIVERPOOL
LEEDS SHEFFIELD AND
BIRMINGHAM
JOINT
MATRICULATION BOARD
GENERAL
CERTIFICATE OF EDUCATION
MATHEMATICS
(025)
SYLLABUS
B, PAPER II
ORDINARY
Friday 21 June 1963 2— 430
Negligently presented or slovenly work will be
penalized.
Mathematical tables will be provided.
Answer all questions in Section A and any three questions from Section B.
In each question necessary
details of working, including rough work, must be shown with the answer.
Section A
A 1. (a) A hot water system in a building uses 70 lb.
of
coke per day. It is used for only 200 days in the
year. Calculate the cost of coke for the year at
£8 8s. 0d. per ton.
(b) Factorize
completely _{}.
(c) In an isosceles triangle the
angles are in the proportion 1 :2 :2. Calculate one of the equal angles.
[Turn
over
2
A 2. (a) After paying tax at
3s. 3d. in the £ a man had £1,005 left. What had he paid in tax?
(b)
Simplify
_{}
(c) For
what value of x on the curve _{}^{ }is the tangent parallel to the xaxis?
A 3. (a) Solve the simultaneous equations
_{}
(b) Express _{}as a fraction of
9 ft. 9 in. giving your
answer in its lowest terms.
(c) The bisector of
the exterior angle at A of the triangle ABC meets BC
produced at D. Given that
AB=6
in., BC= CD =4 in., calculate AC.
A 4. (a) The
chord DC of a circle is produced to a point X and the secant XAB
meets the circle at A and B. If DC = CX = 6 cm. and AB = 1 cm., calculate the length
of AX.
(b) In the triangle ABC
the angle ABC = 60°, the angle ACB = 72° and AC = l5.2l in. Calculate the
length of AB.
3

A5. (a) By how much does_{} exceed _{} ? .
(b)

The
figure represents a square ABCD with vertices A and D
lying on the lines OY and OX which are at
right angles. OA = 12 in. and OD = 5 in.
Calculate _{}OAD and find the perpendicular
distance of N from OY.
A 6. (a) Solve the equation
_{}
giving your answers correct to one place of decimals.
(b) Two
places A and B have the same latitude and both lie in the
northern hemisphere. The longitude of A is 5° W and the longitude
of B is 95° E. If the distance AB measured
along the circle of latitude is 3,300 miles calculate (i) the radius of the
circle of latitude, (ii) the latitude of the two places. (Take the radius of
the earth to be 3,960 miles and take _{} as _{}
Section B
Answer three questions from this section.
B 7. A bookseller had 600 books for sale at 9s. 0d.
each at a profit of 35 per cent on the cost price. After selling 500 books he
reduced the remainder to 6s. 0d. each. Supposing he had sold all these books at
this price, calculate the percentage profit on cost price he would have made on
the whole transaction.
He actually sold 70 of these
books and he had to reduce the price again to clear the remaining 30 books.
When he had sold all the books his percentage profit on his cost price for the
whole transaction was 25. Find the reduced price of each of the last 30
books.
B 8. An aeroplane which flies at a
speed of v m.p.h. in still air flies from A to B, a
distance of b miles, with a following wind of u m.p.h. and then
flies from B to A flying directly into the wind. Obtain
and simplify an expression for the difference between the times for the two
parts of the journey.
If the return journey takes t minutes longer than the outward
journey prove that
_{}
Calculate
the value of v when u = 30, b = 120 and t =6.
[Turn over
5
B 9. Construct a triangle ABC in
which AC = 8 cm., BC= 7 cm. and _{}ACB = 90°. Construct
(i) the circle on AB as diameter,
(ii) a point X on AB
dividing AB internally in the proportion 3: 2,
(iii)
two points on the circumference of the circle each of which is equidistant from
XC and XA.
B 10. A box in the shape of a triangular prism stands with its base on a
horizontal table. The base DEF and the lid ABC are
both equilateral triangles of side 6 in. The other three rectangular faces ABED,
BCFE and ACFD are at right angles to the base and the
height of the box is 8 in. Calculate the angle between the planes CDE and
DEF.
The
lid ABC is hinged about AB and is opened into the position
ABC' through an angle of 36°. Calculate (i) the height of C' above
the table, (ii) the distance CC'.
B 11. A particle P moves
on a straight line. At time t sec. its velocity is v ft. per sec. and its
distance from a fixed point in the line is s ft. Given that
_{} find
(i) the acceleration of P when _{} explaining the significance of the sign of
this answer,
(ii) the distance P travels
in the third second,
(iii)
the minimum velocity of P.