4 Substitution
In all of the earlier exercises you have been given a formula, substituted the given values
and calculated the answer. This is using algebra which defines the rules about what
symbols mean and the order in which operations are carried out.
The key is to substitute the numbers in the correct places and then carry out the
calculations in the correct order. If you are using a calculator, make sure you know
how it works!
Some Examples: a=3, b=5, c=4, d=2, e=1
1. P=a+b 2.q=ab . 3. R=2a+c. 4. s=3c+4d 5. V=(bd)²÷(c+e)
P=3+5 q=3x5 R=2x3+4 s=(3x4)+(4x2) V=(5x2)²÷(4+1)
P=8 q=15 R=10 s=12+8 V=10²÷5
s=20 V=100÷5
V=20
4A Given that f=6, g=4, h=3, j=1, evaluate
1. A=gh 6. K=3(h+2) 11. Q=f² 16. v=f÷h
2. b=g-h 7. L=5(f-j) 12. R=4h² 17. W=(3h)÷(f+h)
3. c=4h-j 8. m=h(g-2) 13. s=(4h)² 18. x=2(h+g)÷(h+g)
4. D=fg-h 9. n=2(3f-8) 14. t=g²+7 19. y=(2h²+3j)÷(h+g)
5. e=5j-2g 10. P=4(2h-2j) 15. u=2f²-13 20. z=((3g)²+6)÷(2f+h)
4B
1. The area of a trapezium is given by A=(a+b)h÷2 where a and b are the lengths of the
parallel sides and h is the height. Find A when a=7, b=9, and h=5
2. The speed of a train is given by s=d÷t. Find the speed of a train which travels a
distance of 150 miles in 2 hours.
3. The volume of a cone is V=pr²h÷3. Find the volume of a cone which has a radius
of 5cm and a height of 13cm.
4. The surface area of a cylinder is given by S=2pr(r+h). Find the surface area of a
cylinder which has a radius of 3cm and a height of 12cm
5. The temperature outside an aircraft flying at an altitude of a feet when the temperature
at ground level is g°C is given by T=g-(a÷500). Work out the temperature outside an
aircraft which is flying at 32000 feet when the ground temperature is 21°C.