Page 88 - Mathematics_Form_Two

Algebra

Exercise 4�8 21. The ages of a man and his son are 35
and 9 years, respectively. How many
Solve the following quadratic equations years ago was the product of their
using the quadratic formula ages 87 years?

2
30
1. x − 4x += 22. A square garden of side 20 metres is
surrounded by a path whose area is
FOR ONLINE READING ONLY
2
x +
3x +
1 0=
the same as that of the garden. Find
2.
Mathematics for Secondary Schools 3. 3x − 6x −= 23. A piece of wire 40 cm long is cut
the width of the path.
2
20
into two parts and each part is then
2
2x +
20
3x −=
4.
bent into a square. If the sum of the
areas of these squares is 68 square
2
30
2x −
7x +=
5.
centimetres, find the lengths of the
2
10
6.
7. (x + 3x − ) 3 = 2x −= two pieces of wire.
2
20
Chapter summary
8. − 22n − 2 15n + 27 0= 1. A binary operation is rule for
combining two quantities to produce
( −
9. 3xx ) 1 = 4 a unique quantity from the same set.
)(
10. ( xx + 3 ) (x= − 12x − ) 1 2. An expression whose highest
power of the variable is 2 is called a
11. 2x − −= quadratic expression.
30
2
x
3. Factorisation is the process of
6 0
2
12. − 145p + 97p −= writing an expression as a product
of two or more factors.
13. x + 2x −= 4. A quadratic equation is formed when
2
30
14. − 12m + 2 36m− 27 0= a quadratic expression is equal to a
specific value, typically zero.
15. 400 20tt+ - 2 = 0 5. The solutions of quadratic equations
are known as roots.
16. 2e += 6
2
e
17. 6x + 2 12x = 0 Revision exercise 4
1. Solve each of the following quadratic
x 2 4 equations by the factorization method:
18.  1  =
−
 1 − x  (2 x ) (a) x + 2 3x = 0
 2 
(b) 3x 2 15x - = 0
19. Find two consecutive numbers whose (c) x = 3x 2
product is 132.
2
20. Find two consecutive even numbers (d) 2x = 3x
whose product is 80. (e) x (5 x− ) 0=
82
Student's Book Form Two
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MATHEMATIC F2 v5.indd 82 11/10/2024 20:12:08
MATHEMATIC F2 v5.indd 82