Crescent Girls School
Secondary 3 Mathematics D
Past Years Examination Questions
(1997 – 2001)
Topic: Inequalities
1(a)
(b)
2(a)
(b)
3.
Find the smallest prime number y which satisfies
y
y
 6   10  y  5 .
2
4
1 x 1
Solve the inequality 
< 4.
3
2
Find the range of values of x such that 1 2x < 2  8  3x .
1
Given that 31  1 x  20 , find the least integer value of x.
2
(2000 Mid SA Q12)
(2000 Final SA Q9)
Find the range of values of x such that
5x  7  x  11  2x .
(1997 Mid SA Q7b)
4(a)
(b)
Express 3x  2  7  2x  9 in the form a  x  b .
Find the integers x for which 3< x  2 < 8 and 9< 2x  1 <17.
(1999 Mid SA Q11)
5.
(i)
(ii)
It is given that 2  x  9 and  5  y  3 . Find
the largest possible value of x  y and
the smallest possible value of x 3  y 2 .
(1999 Final SA Q4)
6.
It is given that  8  x  3 and  5  y  4 . Find
x
the smallest possible value of 2 ,
y
(a)
(b)
the largest possible value of x 2  y 2 .
81898411
(2000 Final SA Q4)
1
7(a)
It is given that 6  x  8 and 0.2  y  0.5 . If z 
x
, find the limits in which z
y
must lie.
(b) Given that x and y are integers and  8  x  4 and  3  y  2 , find
(i) the greatest value of x  y
(ii) the least value of xy
y
(iii)the least value of
x
(iv) the greatest value of ( x 2  y 2 )
x
(v) the least value of
(2000 Mid SB Q3b,c)
y
8.
(a)
(b)
To the nearest 10 centimetres, a table top is of length 140 cm and width 110 cm.
Between what limits must the length lie?
What is the greatest possible value of the area of the table top? (1997 Final SA Q2)
9(a)
Each 50-cent coin has a radius of 11 mm and a thickness of 2 mm, both measured
correct to the nearest millimetre.
(i) Express, as a multiple of , the smallest possible area of the circular surface of
each coin.
(ii) If ten 50-cent coins are stacked up, find the largest possible value of the height of
the stack of coins.
(b)
When an aircraft from Singapore was reaching New York, the temperature
outside the aircraft was -58°C and the ground temperature in New York was
16°C. Both temperatures are given correct to the nearest degree.
(i) Calculate the largest possible value for the difference between these temperatures.
(ii) The aircraft was 12 000 km above the ground.
Given that the temperature changed uniformly with height, calculate, based on the
result from part (i), the height of the aircraft above the ground at which the
temperature was 0°C.
(c) It is given that 2  x  9 and  5  y  3 . Find
(i) the largest possible value of x  y and
(ii) the smallest possible value of x 2  y 2 .
10.
(1997 Mid SB Q4)
Solve the following inequalities, illustrating the solution on a number line.
3x  1
2<
 2 x  1
(2001 Final SA Q8)
3
81898411
2
11(a) Measured to the nearest metre, the lengths of the sides of a rectangular field
are 305 metres and 411 metres.
(i) Find the difference between the greatest and the least possible value of the area of
the field.
(ii) Find the upper bound for the perimeter of the field.
(b) Given that x and y are integers and 2  x  6 and  5  y  2 , find
(i) the greatest possible value of xy ,
(ii) the smallest possible value of x  y ,
x
(iii)the smallest possible value of
and
y
(iv) the largest possible value of ( x 2  y 2 ) .
(1999 Mid SB Q2)
12.
(i)
(ii)
Raymond's weight is 68.9kg.
Rosamund's weight is 56.4kg.
Beatrice's weight is 51.7kg.
If all their weights have been measured correct to the nearest 1 decimal place, find
the lower bound for the total weights of Raymond and Beatrice,
the least possible ratio of Rosamond's weight to Beatrice's weight.
(1999 Final SA Q8)
13.
(a)
(b)
(c)
14.
1
Given that  4  x   and  1  y  7 , find,
2
the smallest possible value of x  y ,
the greatest possible value of x 2  y 2 and
y
the smallest possible value of
.
2x
Find the smallest integer such that
81898411
3n n  4

5 .
2
3
(2001 Final SA Q9)
(1999 Final SA Q2b)
3