Test: Algebra III - Challenging

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Question 1:   If x= 2 3 , solve: x1 x+1
2 9
1 1 2
5
1
Question 2:   Solve: a a3 3 =4+3a
a= 9 11
a= 9 11
a=2 1 7
a=1 2 7
Question 3:   Expand: ( 2x 2 1 )( 3x2 2 )
6 x 2 2 5x+ 2
5 x 2 2 11x+2 2 1
6 x 2 2 11x+2 2
5x 2 +2 2
Question 4:   Expand: 2( a 3 )( 3 3 +a )
2 a 2 3a 3 3 3
a 2 2a 3 +9
2 a 2 +4a 3 18
4a 3 18
Question 5:   Expand: 1 3 ( 3x+6 ) 2
9 x 2 +36x+6
2 x 2 +12x+4
6 x 2 +18x+3
3 x 2 +12x+12
Question 6:   Expand: ( x5 ) ( x+2 ) 2
x 3 x 2 16x20
16x+20
x 3 2 x 2 24x20
2 x 3 16x20
Question 7:   Expand: ( 3a2 ) 2 ( a2 )
9 a 3 6 a 2 +20a8
9 a 3 +6 a 2 +20a8
9 a 3 -30 a 2 +28a8
9 a 3 +30 a 2 -14a1
Question 8:   Expand: 4 x 2 ( x 2 1 )( x 2 +3 )( x 2 2 )
3 x 4 +5 x 2 6
3 x 4 5 x 2 +6
5 x 4 3 x 2 6
5 x 4 3 x 2 +6
Question 9:   Rearrange the formula to make y the subject: x y = ab c
y= xc ab
y= ab xc
y= x( ab ) c
y=cx( ab )
Question 10:   Formula for the volume of a cylinder is: V=π r 2 h Rearrange the formula to make r the subject
r= h V π
r= V πh
r= π V h 3
r= πh V