MATHS OBJ

1EAACBAECBE

11CDABECBCCA

21AEDCBACEDE

31ADADCCDABD

41BCEBDCEABE

51DBAECBECBE

1a

(6y²)³ / 2+y^6

= 6³y^6 / 24y^6

=6³*y^6/24*y^6

= 216/24

=9

1b

Log10(2m²+5m-2)=1

2m²+5m-2=10

2m²+5m-2-10=0

2m²+5m-12=0

Using m=-b+-√b²-4ac/2a

a=2

b=5

c=-12

m=-5+-√5²-4*2*(-12)/2*2

m=-5+-√2+96/4

m=-5+-√98/4

m=-5+-9.9/4

m=-5+9.9/4 or m=-5-9.9/4

M=1.225 or -3.725

2a)

W~ 3√D

Let our constant be K

W= K×3√D

10= K × 3√27

10/3= 3k/3

K= 10 /3

W when D= 64

W= 10/3 × 3√64

W= 10/3 × 4

W= 40/3

W= 13.3

==========

2a)

w*3√D

W=k 3√D

10=k*3√27

10/3 =k*3/3 k=10/3

W=10/3*3√64 = 10/3*4*40/3=13 1/3

2b)

X/2 + y/6 = 2/3

L.C.M = 6

Rx + y = 4 ---(1)

X/3 - y/2 = 5/3

L.C.M = 6

2x - 3y = 10 -----(2)

From eq (1)

3x + y = 4

Y= 4 - 3x ---- (3)

Sub for y in eq (2)

2x - 3(4-3x) = 10

2x - 12 + 9x = 10

11x = 22

X=2

Sub for x in eq (3)

Y = 4-3(1)

Y = 4-3-

Y = 1

===========

3a)

Sn = a(r^n - 1)

a = 5

r = 3

n= 8

5(3^8 - 1)/ (3-1) = 5(6561-1)/2

= 32800/2 = 164000

4a)

V=2/3Πr

1527.4=2/3*22/7*r

1527.4=44r/21

32075.4=44r

r=32075.4/44

r=728.98

=729cm

4b

3^3y+1 = 81^-y

3^3y= 3^-4y

3y+1=-4y

1=-4y-3y

1=-7y

Y= - 1/7

===============

5a)

Red=4

Green = 6

Black= 10

Total=20

1)p(Red) = 4/20 = 1/5

2)p(green)= 6/20 = 3/10

3) p (black)= 10/20= 1/2

5b)

( X-1)(X-8)+12=0

X²-8x-X+8+12=0

X²-9x+20=0

X= -b +√b²-4ai

X= 9+/-√-9²-4×1×20÷ 2×1

X=9+/-√81-80÷2

X=9+/-√1÷2

X= 9+1/2 or 9-1/2

X= 10/2 or 8/2

X= 5 or 4

============

8b)

Let the pocket money be x

2x/5 =stations

X/4=school levies

X/6= food

X-(24x/5+x/4+x/6)=55

X-(24x+15x+10x)/60 =55

X-49x/60 =55

60*x-60-49x/60 = 55*60

60x-49x=#3,300

11x/11=3300/11

X=#300

The pocket money =#300

10a.

1/27^(x-2)=9^(2-x)

3^3(x-2)-1=3^2(2-x)

3-1(x-2)=4-2x

2x-4=4-2x

2x+2x=4+4

4x=8

X=8/4

X=2

10b

5x+y/x+5y= 3/1

5x+y= 3(x+5y)

5x+y=3x+15y

5x-3x=15y-y

2x=14y

X/y= 14/2 =7, y/x= 1/7

X2-y2/4xy

Divide all through by my

(X²- y²/) ÷(4xy/xy)

Xy- xy

(X/y- y/x) ÷4

(7- 1/7)÷4 ~~~49-1/7×1/4

48/7× 1/4= 24/7

= 4

11a)

A=(1 7,3 2) and B=(2 5,4 6)

i)A^-1=1/det(2 -7,-3 1)

Det= 2 -21=-19

A^-1=1/-19(2 -7,-3 1)

-1/19(2 -7,-3 1)

ii)B^T =(2 -4,5 6)

iii)AB =(1 7,3 2) (2 5,4 6)

(2 -28,6-8, 5+46,15+12)

(-26,-2, 51,27,)

11b)

7x^2 + 12x + 5 = 0

7x^2/7 + 12x/7 = -5/7

X^2 + 12x/7 = -5/7

X^2 12x/7 + (6/7)^2 - -5/7 + (6/7)2

(X+6/7)^2= -5/7 + 36/49

(X+6/7)^2 = -35+36/49

(X +6/7)^2 = 1/49

(X +6/7) = + and - √1/19

X+ 6/7 = + and - 1/7

X = -6/7 + and - 1/7

X = -6+1/7 or -6-1/7

X= -5/7 or -7/7

X = -5/7 or -1

1EAACBAECBE

11CDABECBCCA

21AEDCBACEDE

31ADADCCDABD

41BCEBDCEABE

51DBAECBECBE

1a

(6y²)³ / 2+y^6

= 6³y^6 / 24y^6

=6³*y^6/24*y^6

= 216/24

=9

1b

Log10(2m²+5m-2)=1

2m²+5m-2=10

2m²+5m-2-10=0

2m²+5m-12=0

Using m=-b+-√b²-4ac/2a

a=2

b=5

c=-12

m=-5+-√5²-4*2*(-12)/2*2

m=-5+-√2+96/4

m=-5+-√98/4

m=-5+-9.9/4

m=-5+9.9/4 or m=-5-9.9/4

M=1.225 or -3.725

2a)

W~ 3√D

Let our constant be K

W= K×3√D

10= K × 3√27

10/3= 3k/3

K= 10 /3

W when D= 64

W= 10/3 × 3√64

W= 10/3 × 4

W= 40/3

W= 13.3

==========

2a)

w*3√D

W=k 3√D

10=k*3√27

10/3 =k*3/3 k=10/3

W=10/3*3√64 = 10/3*4*40/3=13 1/3

2b)

X/2 + y/6 = 2/3

L.C.M = 6

Rx + y = 4 ---(1)

X/3 - y/2 = 5/3

L.C.M = 6

2x - 3y = 10 -----(2)

From eq (1)

3x + y = 4

Y= 4 - 3x ---- (3)

Sub for y in eq (2)

2x - 3(4-3x) = 10

2x - 12 + 9x = 10

11x = 22

X=2

Sub for x in eq (3)

Y = 4-3(1)

Y = 4-3-

Y = 1

===========

3a)

Sn = a(r^n - 1)

a = 5

r = 3

n= 8

5(3^8 - 1)/ (3-1) = 5(6561-1)/2

= 32800/2 = 164000

4a)

V=2/3Πr

1527.4=2/3*22/7*r

1527.4=44r/21

32075.4=44r

r=32075.4/44

r=728.98

=729cm

4b

3^3y+1 = 81^-y

3^3y= 3^-4y

3y+1=-4y

1=-4y-3y

1=-7y

Y= - 1/7

===============

5a)

Red=4

Green = 6

Black= 10

Total=20

1)p(Red) = 4/20 = 1/5

2)p(green)= 6/20 = 3/10

3) p (black)= 10/20= 1/2

5b)

( X-1)(X-8)+12=0

X²-8x-X+8+12=0

X²-9x+20=0

X= -b +√b²-4ai

X= 9+/-√-9²-4×1×20÷ 2×1

X=9+/-√81-80÷2

X=9+/-√1÷2

X= 9+1/2 or 9-1/2

X= 10/2 or 8/2

X= 5 or 4

============

8b)

Let the pocket money be x

2x/5 =stations

X/4=school levies

X/6= food

X-(24x/5+x/4+x/6)=55

X-(24x+15x+10x)/60 =55

X-49x/60 =55

60*x-60-49x/60 = 55*60

60x-49x=#3,300

11x/11=3300/11

X=#300

The pocket money =#300

10a.

1/27^(x-2)=9^(2-x)

3^3(x-2)-1=3^2(2-x)

3-1(x-2)=4-2x

2x-4=4-2x

2x+2x=4+4

4x=8

X=8/4

X=2

10b

5x+y/x+5y= 3/1

5x+y= 3(x+5y)

5x+y=3x+15y

5x-3x=15y-y

2x=14y

X/y= 14/2 =7, y/x= 1/7

X2-y2/4xy

Divide all through by my

(X²- y²/) ÷(4xy/xy)

Xy- xy

(X/y- y/x) ÷4

(7- 1/7)÷4 ~~~49-1/7×1/4

48/7× 1/4= 24/7

= 4

11a)

A=(1 7,3 2) and B=(2 5,4 6)

i)A^-1=1/det(2 -7,-3 1)

Det= 2 -21=-19

A^-1=1/-19(2 -7,-3 1)

-1/19(2 -7,-3 1)

ii)B^T =(2 -4,5 6)

iii)AB =(1 7,3 2) (2 5,4 6)

(2 -28,6-8, 5+46,15+12)

(-26,-2, 51,27,)

11b)

7x^2 + 12x + 5 = 0

7x^2/7 + 12x/7 = -5/7

X^2 + 12x/7 = -5/7

X^2 12x/7 + (6/7)^2 - -5/7 + (6/7)2

(X+6/7)^2= -5/7 + 36/49

(X+6/7)^2 = -35+36/49

(X +6/7)^2 = 1/49

(X +6/7) = + and - √1/19

X+ 6/7 = + and - 1/7

X = -6/7 + and - 1/7

X = -6+1/7 or -6-1/7

X= -5/7 or -7/7

X = -5/7 or -1

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