Year 11 Mathematics Extension 1 algebra 1.1 practice-answer

1.1 practice-answer

2

Year 11 Mathematics Extension 1

Question 1 x 2

2

x 1 3 x 1 x 1

2

x x 1 3 x 1

x x 1 3 x 1 0

2

3 x 1 x x 1 0

2

x 1 3 x 1 x 0

x 1 2 x 3 0 algebra 3

x 1

2

3

x 1 , since x 1

2

Question 2

y 3 y 1 2 y 1

2

2 y 1 y 3 y 1 0

y 1 2 y 1 y 3

y 1 y 5 0

2

y 1, y 5

Question 3

2 x 3x 2 0

x 0, x

2

3

Question 4

2 x 3 5x 3 6 5x 3

5x 3 28x 21 0

2

6 5x 3 2 x 3 5x 3 0 5x 3 30 x 18 2 x 3 0

2

3

3

x

4

5

Question 5

2

2

5 x 7 3x 5

4 x2 25x 6 0

4 x 1 x 6 0 x 6 or x 0.25

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1.1 practice-answer

3

Year 11 Mathematics Extension 1

Question 6 y 2x 1 2 x 2 5

5

, or divide 2 x 1 by x 2

2 x2 x2 x2 thus x 2

Question 7

2 5x 2 2

4 5x 0

4

x0

5

Question 8

algebra

3x 7 y y

2x 8 y x

3x2 5xy 8 y 2 0

2

x

x

3 5 8 0

y

y x 8

,1 y 3

1 1 2 1 1 2

1 1 2 1 1 2

Question 9

2

Question 10 x40 x2 6 x 7 0 or x 4 0 x2 6 x 7 0

The second case could not hold simultaneously,

4 x 1, x 7

Question 11

2

(a)

x2

(b)

x3

1

1

x 2 92 7

2

x x

3

(c)

1

1

1

x 3 x 27 9 18

3

x x x

1

2 1 3 1 5 1

x 2 x 3 x 5 x …