Page 82 - Mathematics_Form_Two

Algebra

(m) (x − ) 5 = 2 25 10. The concentration y in mg/l of a
drug in the bloodstream is given by
(n) b + 2 2b + 1 = 0 t 2
5 25 the equation y = − + 2 ,t , where t
2 1 10
(o) c + 2 c + = 0 is the time in hours administration.
7 ) 9 − 2 36 0= 49 After how many hours will the
FOR ONLINE READING ONLY
Mathematics for Secondary Schools (q) 9x = 12x − 4 Solving quadratic equations by
concentration reach 10 mg/l?
(p) (x−
2
1
completing the square
(r)
a
10
2
a + +=
4
In the previous section, a method for
(s)
2
14r
the middle term was discussed. However,
(t) 4r −= 25 = 0 solving quadratic equations by splitting
5x +
x −
not all quadratic equations can be factored.
2
4 For instance, in case of x + 5x + 14 = 0, no
2
4. The product of two consecutive whole two whole numbers add to 5 and multiply
numbers is 42. Find the numbers. to give 14. For such equations, methods
5. A projectile is launched from the such as completing the square and
quadratic formula can be used.
ground with an initial velocity of 20
m/s. Its height h after t seconds is given Completing the square is a technique
( )
2
by the equation ht = − 5t + 20 .t used to solve quadratic equations by
Find the time when the projectile will transforming the left-hand side of the
hit the ground. equation into a perfect square. The
6. A garden has a rectangular area of steps involved are demonstrated in the
following examples.
length 3 metres more than its width.
The area of the garden is 40 square Example 4�34
metres. Find the dimensions of the
2
garden. What must be added to x + 10x to
7. The difference between two positive make the expression a perfect square?
numbers is 8 and the products of the Solution
numbers is 105. Find the smaller The term to be added must be the square
number. of half the coefficient of x.
8. The base of the triangle is 5 cm less The coefficient of x is 10.
2
than its height. If its area is 33 cm , 1
5
10
( ) =
find the length of the base. Half of 10 is (10) = 5.
2
9. The perimeter of a rectangular garden The square of 5 is 25.
2
is 60 m and its area is 209 m . Find Therefore, 25 must be added to
the dimensions of the garden. x + 10x to make it a perfect square.
2
76
Student's Book Form Two

11/10/2024 20:12:01
MATHEMATIC F2 v5.indd 76
MATHEMATIC F2 v5.indd 76 11/10/2024 20:12:01