Everything Maths Grade 10

19.Write the following irrational numbers to 3 decimal places and then write each one as a rational number
to get an approximation of the irrational number.
a) 3,141592654... b)1,618033989...
c) 1,41421356... d)2,71828182845904523536...

20.Determine between which two consecutive integers the following irrational numbers lie, without using
a calculator.
a)

p

5 b)

p

10 c)

p

20 d)

p

30 e)^3

p

5 f)^3

p

10

g)^3

p

20 h)^3

p

30 i)

p

90 j)

p

72 k)^3

p

58 l)^3

p

118

21.Estimate the following surds to the nearest 1 decimal place, without using a calculator.

a)

p

14 b)

p

110 c)

p

48 d)

p

57

22.Expand the following products:

a) (a+ 5)^2 b)(n+ 12)^2 c) (d4)^2

d)(7w+ 2)(7w2) e)(12q+ 1)(12q1) f) (x2)(x+ 2)

g) (5k4)(5k+ 4) h) (5f+ 4)(2f+ 2) i)(3n+ 6)(6n+ 5)

j) (2g+ 6)(g+ 6) k)(4y+ 1)(4y+ 8) l)(d3)(7d+ 2)

m) (6z4)(z2) n) (5w11)^2 o) (5s1)^2

p)(3d8)^2 q) 5 f^2 (3f+ 5) + 7f(3f^2 + 7) r) 8 d(4d^3 + 2) + 6d^2 (7d^2 + 4)

s) 5 x^2 ( 2 x+ 2 ) + 7 x( 7 x^2 + 7 )

23.Expand the following:

a) (y^4 + 3y^2 +y)(y+ 1)(y2) b)(x+ 1)^2 (x1)^2

c) (x^2 + 2x+ 1)(x^2  2 x+ 1) d)(4a 3 b)(16a^2 + 12ab+ 9b^2 )

e) 2(x+ 3y)(x^2 xyy^2 ) f)(3a 5 b)(3a+ 5b)(a^2 +abb^2 )

g)

(

y

1

y

) (

y+

1

y

)

h)

(

a

3

3

a

) (

a

3

+

3

a

)

i)

1

3

(12x 9 y) +

1

6

(12x+ 18y) j)(x+ 2)(x2)(x+ 2)^2

24.What is the value ofein(x4)(x+e) =x^2 16?

25.In(x+ 2)(x+k) =x^2 +bx+c:

a)For which of these values ofkwillbbe positive?

6 ;1 ; 0 ; 1 ; 6

b)For which of these values ofkwillcbe positive?

6 ;1 ; 0 ; 1 ; 6

c)For what values ofkwillcbe positive?

d)For what values ofkwillbbe positive?

26.Answer the following:

a)Expand:

(

3 a

1

2 a

) 2

b)Expand:

(

3 a

1

2 a

) (

9 a^2 +

3

2

+

1

4 a^2

)

c)Given that 3 a

1

2 a

= 7, determine the value of 27 a^3 

1

8 a^3

without solving fora.

38 1.9. Chapter summary