Elementary Mathematics Revision Worksheet 20
1
2
The garden in Mr Smith’s house is in the shape of a right-angled triangle. The lengths of this garden are
x  2 m, 5x  1 m and 5x  m. The area of this garden would not exceed 10m2.
a)
Form an equation in x and show that it reduces to x 2  6 x  5  0.
b)
Solve the equation x 2  6 x  5  0 .
x =1 or x = 5
c)
Find the area of the garden.
6 m2
a)
Find the fraction that is exactly halfway between
4
3
and .
9
8
59
144
b)
Make a the subject of the formula c  b 
a
2a
.
c
c 3  2bc 2  b 2 c
2
3
It takes 20 students 55 days to finish a project. Half the students quit after 20 days. Find the number of days
required for the remaining students to finish the project, assuming all students work at the same rate.
70 days
4
Solve the inequality

5
x
x3
.
 1  2x 
4
5
4
1
x
7
3
a)
Express 156 as a product of its prime factors.
156  2 2  3  13
b)
Find the LCM and HCF of 156 and 144.
LCM = 1872 HCF = 12
c)
Find the smallest value of n such that 144n is a multiple of 156.
n = 13