l1 starters a links starter 11starter 11 starter 11 solnsstarter 11 solns starter 12starter 12...

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L1 Starters A Links Starter 11 Starter 11 Solns Starter 12 Starter 12 Solns Starter 13 Starter 13 Solns Starter 14 Starter 14 Solns Starter 15 Starter 15 Solns Starter 16 Starter 16 Solns Starter 17 Starter 17 Solns These starters focus on ‘Merit’ problems. A mixture of Number, Algebra, Graphs, Trigonometry, & Probability

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Page 1: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

L1 Starters ALinks

Starter 11 Starter 11 Solns

Starter 12 Starter 12 Solns

Starter 13 Starter 13 Solns

Starter 14 Starter 14 Solns

Starter 15 Starter 15 Solns

Starter 16 Starter 16 Solns

Starter 17 Starter 17 Solns

Starter 18 Starter 18 Solns

Starter 19 Starter 19 Solns

Starter 20 Starter 20 Solns

These starters focus on ‘Merit’ problems.

A mixture of Number, Algebra, Graphs, Trigonometry, &

Probability

Page 2: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 11 1st slide1)

2)

5)

6)

7)

8)

9)

10)

3)

4)

26% of A is $128. Find A

Simplify

Expand (2x + 1)(x – 6) =

Solve

Solve 3(x – 9) ≥ 2x

What is the gradient of the line 2y + 6x = 12

Sketch the graph of y = (x + 2)2 – 4

13 × Cos 38º =

What is the probability of 4 heads when flipping a coin 4 times?

Find the reciprocal of 0.02

14649 yx

752

xx

Page 3: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 11 Soln A1)

2)

5)

3)

4)

26% of A is $128. Find A

Expand (2x + 1)(x – 6) =

Find the reciprocal of 0.02

Simplify 14649 yx

Solve 752

xx

1st slide

Page 4: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 11 Soln B6)

7)

8)

9)

10)

Solve 3(x – 9) ≥ 2x

What is the gradient of the line 2y + 6x = 12

Sketch the graph of y = (x + 2)2 – 4

13 × Cos 38º =

What is the probability of 4 heads when flipping a coin 4 times?

y

x

1

1

2

2

– 1

– 1

– 2

– 2

– 3

– 3

– 4

– 4

– 5

– 5

1

1

– 1

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– 2

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– 5

1st slide

Page 5: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 121)

2)

5)

6)

7)

8)

9)

10)

3)

4)

Find GST (12.5%) component of a shirt selling for $48

Make ‘x’ the subject of y = 4x + 6

Factorise 7x2 + 42x +35

Solve 4(x + 3) < 3x + 1

Solve (x + 1)(x – 1) = 8

What is the y intercept of the line y = 7x − 9

Sketch the graph of y = 2x2 − 3

0.24 ÷ Tan 62º (to 3dp) =

A 12 sided die, P(more than 8) =

Simplify the ratio 0.02 : 0.81st slide1st slide

Page 6: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 12 Soln A1)

2)

5)

3)

4)

Find GST (12.5%) component of a shirt selling for $48

Make ‘x’ the subject of y = 4x + 6

Factorise 7x2 + 42x +35

Solve 4(x + 3) < 3x + 1

Simplify the ratio 0.02 : 0.81st slide

Page 7: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 12 Soln B6)

7)

8)

9)

10)

Solve (x + 1)(x – 1) = 8

What is the y intercept of the line y = 7x − 9

Sketch the graph of y = 2x2 − 3

0.24 ÷ Tan 62º (to 3dp) =

A 12 sided die, P(more than 8) =

y

x

1

1

2

2

3

3

– 1

– 1

– 2

– 2

– 3

– 3

1

1

2

2

3

3

– 1

– 1

– 2

– 2

– 3

– 3

1st slide

Page 8: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 131)

2)

5)

6)

7)

8)

9)

10)

3)

4)

Solve x2 = 2x + 15

Factorise 3x2 – 2x – 8

Solve simultaneously: x + y = 14 3x – y = 10

Solve (x + 1)(x – 7) = 3x – 7

What is the equation the graph.

Sketch the graph of y = 0.5x2 + 2

Sin 215º =

A pack of 52 cards, P(card with a red 3) =

A bottle has 120mL of juice in it. It is 74% full. What is volume of the full bottle?

Calculate 3 61072 x.

y

x

1

1

2

2

– 1

– 1

– 2

– 2

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– 4

1

1

– 1

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– 5

1st slide

Page 9: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 13 Sol A1)

2)

5)

3)

4)

Solve x2 = 2x + 15

Factorise 3x2 – 2x – 8

Solve simultaneously: x + y = 14 3x – y = 10

A bottle has 120mL of juice in it. It is 74% full. What is volume of the full bottle?

Calculate 3 61072 x.

1st slide

Page 10: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 13 Soln B6)

7)

8)

9)

10)

Solve (x + 1)(x – 7) = 3x – 7

What is the equation the graph.

Sketch the graph of y = 0.5x2 + 2

Sin 215º =

A pack of 52 cards, P(card with a red 3) =

y

x

1

1

2

2

– 1

– 1

– 2

– 2

– 3

– 3

– 4

– 4

1

1

– 1

– 1

– 2

– 2

– 3

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– 4

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– 5

– 5

1st slide

Page 11: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 141)

2)

5)

6)

7)

8)

9)

10)

3)

4)

740 boys are about 54% of the school roll. How many students total?

Simplify 5(x + 6) − 3(x + 4)

Factorise x2 + 9x + 14 =

Solve 3(x + 2) = 10x − 5

Solve x2 + 6x + 5 = 0

Sketch y = 4 − 2x2

Sketch the graph of y = (x + 1)(x − 3)

A 12 sided die, P(no more than 5) =

(3.84 × 1014) ÷ (2.24 × 10-16 )

4.9 3.6 22

1st slide

Page 12: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 14 Soln A1)

2)

5)

3)

4)

740 boys are about 54% of the school roll. How many students total?

Simplify 5(x + 6) − 3(x + 4)

Factorise x2 + 9x + 14 =

Solve 3(x + 2) = 10x − 5

(3.84 × 1014) ÷ (2.24 × 10-16 )1st slide

Page 13: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 14 Soln B6)

7)

8)

9)

10)

Solve x2 + 6x + 5 = 0

Sketch y = 4 − 2x2

Sketch the graph of y = (x + 1)(x − 3)

A 12 sided die, P(no more than 5) =

4.9 3.6 22

1st slide

Page 14: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 151)

2)

5)

6)

7)

8)

9)

10)

3)

4)

Two fifths of a class of 25 were away sick. A quarter of the rest were wagging. How many were left in class?

Simplify (3x3y4)2 =

Expand (x – 5)(x – 9) =

Factorise x2 – 2x – 35

Solve 4x(x – 9) = 0

Sketch y = -(x + 2)2 + 3

Sketch the graph of y = (x + 2)2

Roll two 6 sided dice, adding the result. P(Sum of 6 or less)

The ratio of A:B is 3:5 If there is 6.4 kg of A, how heavy is B?

22 61084 ..

1st slide

Page 15: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 15 Soln A1)

2)

5)

3)

4)

Two fifths of a class of 25 were away sick. A quarter of the rest were wagging. How many were left in class?

Simplify (3x3y4)2 =

Expand (x – 5)(x – 9) =

Factorise x2 – 2x – 35

The ratio of A:B is 3:5 If there is 6.4 kg of A, how heavy is B?

1st slide

Page 16: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 15 Soln B6)

7)

8)

9)

10)

Solve 4x(x – 9) = 0

Sketch the graph of y = (x + 2)2

Roll two 6 sided dice, adding the result. P(Sum of 6 or less)

22 61084 ..

Sketch y = -(x + 2)2 + 3

1st slide

Page 17: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 161)

2)

5)

6)

7)

8)

9)

10)

3)

4)

A price drops by 15 % then increases by 10%. Find the total % change

Simplify (5x8)3 =

Expand (2x – 3)2 =

Factorise x2 + x – 20

Solve x2 + 3x = 4

Sketch y = -0.25x2 + 2

Write the equation for this graph

A 12 sided die, P(A factor of 12) =

What $650 invested for 2 yr at 8% per year simple interest is?

y

x

1

1

2

2

– 1

– 1

– 2

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1

1

2

2

3

3

4

4

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6m

1.4m x?

1st slide

Page 18: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 16 Soln A1)

2)

5)

3)

4)

A price drops by 15 % then increases by 10%. Find the total % change

Simplify (5x8)3 =

Expand (2x – 3)2 =

Factorise x2 + x – 20

What $650 invested for 2 yr at 8% per year simple interest is?

1st slide

Page 19: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 16 Soln B

6)

7)

8)

9)

10)

Solve x2 + 3x = 4

Sketch y = -0.25x2 + 2

Write the equation for this graph

A 12 sided die, P(A factor of 12) =

y

x

1

1

2

2

– 1

– 1

– 2

– 2

– 3

– 3

– 4

– 4

1

1

2

2

3

3

4

4

– 1

– 1

– 2

– 2

– 3

– 3

– 4

– 4

– 5

– 5

6m

1.4m x?

y

x

1

1

2

2

3

3

4

4

– 1

– 1

– 2

– 2

– 3

– 3

– 4

– 4

1

1

2

2

3

3

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– 3

1st slide

Page 20: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 171)

2)

5)

6)

7)

8)

9)

10)

3)

4)

¾ of students do homework. 60% of these work. 40% of the rest work.What fraction of all students work?

Expand (10x + 1)2 =

Factorise x2 + x – 56

Sketch y = 5 – x2

Sketch the graph of y = 3 – (x + 2)2

Roll 2 six sided dice, adding the scores. P(At most 8) =

18% of days have rain. 34% of the rest are cloudy. What % are sunny?

12 ÷ Cos 41º =

Solve 42525

.x

Simplify (2m5)3 × (5m3)2 =

1st slide

Page 21: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 17 Soln A1)

2)

5)

3)

4)

¾ of students do homework. 60% of these work. 40% of the rest work.What fraction of all students work?

Expand (10x + 1)2 =

Factorise x2 + x – 56

18% of days have rain. 34% of the rest are cloudy. What % are sunny?

Simplify (2m5)3 × (5m3)2 =

1st slide

Page 22: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 17 Soln B6)

7)

8)

9)

10)

Sketch the graph of y = 3 – (x + 2)2

Roll 2 six sided dice, adding the scores. P(At most 8) =

12 ÷ Cos 41º =

Solve 42525

.x

Sketch y = 5 – x2

1st slide

Page 23: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 181)

2)

5)

6)

7)

8)

9)

10)

3)

4)

$20 000 invested at 12% for ‘N’ years gives a total of $8400 interest. Find ‘N’

Factorise 36 – 49x2

Factorise 4x2 + 20x – 96

Solve 2x2 + 4x = 30

Sketch y = 3(x – 2)2 – 3

Sketch the graph of y = 5 – (x – 2)2

A bag of 6 lollies, 4 are red. If 3 red were eaten find the probability ofanother red being randomly selected.

Increase 8.4 × 1012 km by 38%

If e = 4, g = 5 find942 ge

Sin-1 0.8 = Hint: ‘Shift’ ‘Sin’

1st slide

Page 24: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 18 Soln A1)

2)

5)

3)

4)

$20 000 invested at 12% for ‘N’ years gives a total of $8400 interest. Find ‘N’

Factorise 36 – 49x2

Factorise 4x2 + 20x – 96

Increase 8.4 × 1012 km by 38%

If e = 4, g = 5 find942 ge

1st slide

Page 25: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 18 Soln B6)

7)

8)

9)

10)

Solve 2x2 + 4x = 30

Sketch y = 3(x – 2)2 – 3

Sketch the graph of y = 5 – (x – 2)2

A bag of 6 lollies, 4 are red. If 3 red were eaten find the probability ofanother red being randomly selected.

Sin-1 0.8 = Hint: ‘Shift’ ‘Sin’

1st slide

Page 26: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 191)

2)

5)

6)

7)

8)

9)

10)

3)

4) Expand fully 2(5x + 2)2 =

Factorise 3x2 – 6x – 72

Solve -6x + 18 ≥ -3x + 2

Sketch 2y + 3x – 6 = 0

Sketch the graph of y = (x + 2)(4 – x)

Flip a coin 3 times. If the first flip is a ‘H’ find the probability of ‘HHH’

0.4% of N is 2.4 × 1014 Find N

Sin-1 0.34 =

When a tank is full it contains 64litres. How many litres are neededto make it full?

1513

32

Simplify 62 182 ww

1st slide

Page 27: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 19 Soln A1)

2)

5)

3)

4) Expand fully 2(5x + 2)2 =

Factorise 3x2 – 6x – 72

0.4% of N is 2.4 × 1014 Find N

When a tank is full it contains 64litres. How many litres are neededto make it full?

1513

32

Simplify 62 182 ww

1st slide

Page 28: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 19 Soln B6)

7)

8)

9)

10)

Solve -6x + 18 ≥ -3x + 2

Sketch 2y + 3x – 6 = 0

Sketch the graph of y = (x + 2)(4 – x)

Flip a coin 3 times. If the first flip is a ‘H’ find the probability of ‘HHH’

Sin-1 0.34 =

1st slide

Page 29: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 201)

2)

5)

6)

7)

8)

9)

10)

3)

4)

Half of a third of a quarter was eaten. What fraction is left?

Factorise 4x2 – 81y8

Factorise 6x2 + 7x + 2

Solve x2 = 35 – 2x

Sketch 3y + 6 – 2x = 0

Sketch the graph of y = 0.5(x – 2)2 – 4

It rains 0.25 of days. I am late 60% of rainy days, and 15% of the restWhat is the probability I am late? Hint: draw a probability tree.

Add GST (12.5%) and then a 24% profit. What is the % increase?

Cos-1 0.184 =

Simplify ww 8232

1st slide

Page 30: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 20 Soln A1)

2)

5)

3)

4)

Half of a third of a quarter was eaten. What fraction is left?

Factorise 4x2 – 81y8

Factorise 6x2 + 7x + 2

Add GST (12.5%) and then a 24% profit. What is the % increase?

Simplify ww 8232

1st slide

Page 31: L1 Starters A Links Starter 11Starter 11 Starter 11 SolnsStarter 11 Solns Starter 12Starter 12 Starter 12 SolnsStarter 12 Solns Starter 13Starter 13 Starter

Starter 20 Soln B6)

7)

8)

9)

10)

Solve x2 = 35 – 2x

Sketch 3y + 6 – 2x = 0

Sketch the graph of y = 0.5(x – 2)2 – 4

It rains 0.25 of days. I am late 60% of rainy days, and 15% of the restWhat is the probability I am late? Hint: draw a probability tree.

Cos-1 0.184 =

1st slide