Everything Maths Grade 10

7.Solve forh:A= 2rh+ 2r.

8.Makethe subject of the formula:t=

D

f 

.

9.Solve form:E=mgh+^12 mv^2.

10.Solve forx:x^2 +x(a+b) +ab= 0.

11.Solve forb:c=

p

a^2 +b^2.

12.MakeUthe subject of the formula:

1

V

=

1

U

+

1

W

.

13.Solve forr:A=R^2 r^2.

14.F=^95 C+32°is the formula for converting temperature in degrees Celsius to degrees Fahrenheit. Derive

a formula for converting degrees Fahrenheit to degrees Celcius.

15.V=^43 r^3 is the formula for determining the volume of a soccer ball. Express the radius in terms of the

volume.

16.Solve forxin:x^2 ax 3 x= 4 +a

17.Solve forxin:ax^2  4 a+bx^2  4 b= 0

18.Solve forxinv^2 =u^2 + 2axifv= 2,u=0,3,a=0,5

19.Solve foruinf′=f

v

vu

ifv= 13,f= 40,f′= 50

20.Solve forhinI=

bh^2

12

ifb= 18,I= 384

21.Solve forr 2 in

1

R

=

1

r 1

+

1

r 2

ifR=^32 ,r 1 = 2

For more exercises, visit http://www.everythingmaths.co.za and click on ’Practise Maths’.

1.2FFR 2.2FFS 3.2FFT 4.2FFV 5.2FFW 6.2FFX 7.2FFY 8.2FFZ

9.2FG2 10.2FG3 11.2FG4 12.2FG5 13.2FG6 14.2FG7 15.2FG8 16.2FG9

17.2FGB 18.2FGC 19.2FGD 20.2FGF 21.2FGG

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4.7 Solving linear inequalities EMA3H

A linear inequality is similar to a linear equation in that the largest exponent of a variable is 1. The following
are examples of linear inequalities.

2 x+ 2 1

2 x

3 x+ 1

 2

4

3

x 6 < 7 x+ 2

The methods used to solve linear inequalities are similar to those used to solve linear equations. The only
difference occurs when there is a multiplication or a division that involves a minus sign. For example, we
know that 8 > 6. If both sides of the inequality are divided by2, then we get 4 > 3 , which is not true.
Therefore, the inequality sign must be switched around, giving 4 < 3.

In order to compare an inequality to a normal equation, we shall solve an equation first.

96 4.7. Solving linear inequalities