Everything Maths Grade 10

b)Tn= 3n 1

c) 89

17. a)T 1 = 4
    b) 3
    c)Tn= 3n+ 1
    d)76 matchsticks


18. 10


19. a)d= 3y+ 3
    b)T 1 = 7 andT 2 = 1


20. a)^13
    b)^16 ;^32 and^196
    21.T 85 =7227 blocks


21. a) 29

b)Tn= (n+ 1)^2 +n

c)T 14 = 239blocks

23.77 parts

24. a) 7
    b) 0
    c) 4

4 Equations and inequalities

Exercise 4 – 1:

1. 5
   2. 8
   3. 1
   4. 3


2. 0
   6.^78


3. 12


4. 11
   9.^21720


5. 15


6. 109


7. ^5013


8. 1


9. 3


10. 6
    16.^1712
    17.^203


11. 26


12. 5


13. 4
    21.^3611


14. 8


15. 5


16. 24


17. 10
    26.^226


18. 6
    28. 2
    29.12,5
    30.^280451
    31.^22345


19. 12


20. ^1713
    34. 19
    35.^16

Exercise 4 – 2:

1. a) 5 r^2 + 16r= 0
   b) 6 r^2 25 r+ 39 = 0
   c) 2 d^2 + 15d+ 17 = 0


2. a)x= 5 orx= 3
   b)p= 2 orp= 9
   c)x=^23 orx=^43
   d)x=^95 orx= 6
   e)z= 2 orz= 1
   f)b= 3orb= 4
   g)a= 3ora= 6:
   h)y=^32 ory=^32
   i)x=^12 orx=^92
   j)^32
   k)m= 0orm=^45

l)x=^32 orx= 4

m)x=^65 orx=^83

n)x= 4orx= 11

o) 2

p)x=^35 orx= 3

q)t= 0ort= 3

r) 5

s)x=

p

18 orx=

p

18

t)p= 7orp= 1

u)x=^114 orx= 7

v)x=^67 orx=^12

w)x= 3orx= 2

x)a=^12 ora=3,5

y)x= 11orx= 1

3. a)y= 3ory= 3
   b)z=^15 orz=^12
   c)x= 3orx= 6
   d)y=^14 ory= 4
   e)b=^13 borb= 4
   f)y=^43 ory= 1
   g)x= 4orx= 4
   h)z= 1orz= 1
   i)b= 2 orb= 3
   j)a=^438 ora= 1
   k)x= 3
   l)x= 4
   m)a= 2
   n)a= 0ora=^23

Exercise 4 – 3:

1.x= 2 andy= 3

2.there is no solution toxandy

3.x= 2andy= 3

4. a)x= 101 andy=^4350
   b)x= 7 andy=^32
   c)x= 5andy= 3
   d)x= 1 andy= 1
   e)x= 13andy= 1

f)x= 11andy= 5

g)x= 9andy= 2

h)a=^163 andb=^43

i)x= 101 andy= 2

j)x=^75 andy=^85

k)x=^17 andy=^14

l)xcan be any real number,^12 

y < 2

m)aandbcan be any real number

except for 0.

5. a)x= 1 andy= 2
   b)x= 9andy= 4
   c)x= 1 andy= 4
   d)x= 2andy= 1
   e)x=1,5 andy=3,5

Exercise 4 – 4:

1.2 hours

2.1 hour

3.Zwelibanzi achieved 80 marks and Jessica

achieved 68 marks.

4.18 large shirts and 2 small shirts

6. 34

7.a milkshake costs R 34 and a wrap costs

R 27.

8. 30 °and 60 °
   9.b=8 cm andl= 2b=16 cm
   10.7 or 3
   11.length: 6 cm, width: 4 cm
   12.^1950 litres
   13.9 and 11
   14.^12

15.8 years old

16.7 and 35 years old.

17.x=^12

18.x= 2orx= 3

19. 15


20. 34


21. 48 blue beads, 96 red beads and 36 purple beads,

Exercise 4 – 5:

1.x= 1 2 y

2.2(st 2 ut)=a

3. RTpV=n

4.x=^2 b

2

1  2 b

5.

√

hV =r

6. Ec =h
   7. A 2 r^2 r=h
   8.=Dtf
   9.gh+E 1
   2 v^2

=m

502 Solutions