INTERMEDIATE 2 ADDITIONAL QUESTION BANK

1
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
Algebraic Operations
Quadratic Functions
UNIT 3
Further Trig
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INTERMEDIATE 2 ADDITIONAL QUESTION BANK
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Algebraic Operations
UNIT 3
Please choose a question to attempt from the
following
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3
ALGEBRAIC OPERATIONS Question 1
Express (m ? -7) as a single
fraction in its simplest form.
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ALGEBRAIC OPERATIONS Question 1
Express (m ? -7) as a single
fraction in its simplest form.
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5
ALGEBRAIC OPERATIONS Question 1
Express (m ? -7) as a single
fraction in its simplest form.
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6
Question 1
Express
(m ? -7) as a single fraction in
its simplest form.
m (m 7)
- (2 x 4m)

2 (m 7)
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To add or subtract fractions use the results
m (m 7)
- (2 x 4m)
2 (m 7)
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ALGEBRAIC OPERATIONS Question 1B
Express (t ? 3) as a single
fraction in its simplest form.
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9
ALGEBRAIC OPERATIONS Question 1B
Express (t ? 3) as a single
fraction in its simplest form.
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ALGEBRAIC OPERATIONS Question 1B
Express (t ? 3) as a single
fraction in its simplest form.
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Question 1B
Express
(t ? 3) as a single fraction in
its simplest form.
7t (t 3)
(10 x 4t)

10 (t 3)
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Continue Solution
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Comments
To add or subtract fractions use the results
7t (t 3)
(10 x 4t)

10 (t 3)
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Comments
Note Always check that you have cancelled as
far as possible. This is the final result, it
does not cancel further.
7t (t 3)
(10 x 4t)

10 (t 3)
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ALGEBRAIC OPERATIONS Question 2
Express as a single fraction in its
simplest form.
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15
ALGEBRAIC OPERATIONS Question 2
Express as a single fraction in its
simplest form.
Multiply top line then bottom line.
Cancel numbers then letters in alphabetical
order.
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16
ALGEBRAIC OPERATIONS Question 2
Express as a single fraction in its
simplest form.
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17
Question 2
1. Multiply top line then bottom line.
Express as a
single fraction in its simplest form.
3
b
2
a
2. Cancel numbers then letters in alphabetical
order.
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Comments
To multiply fractions use the result
1. Multiply top line then bottom line.
3
b
2
a
2. Cancel numbers then letters in alphabetical
order.
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Comments
To simplify final answer write out in full and
cancel
1. Multiply top line then bottom line.
30.a.a.b.b 20.a.a.a.b
3
b
2
a
2. Cancel numbers then letters in alphabetical
order.
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ALGEBRAIC OPERATIONS Question 2B
Express as a single fraction in its
simplest form.
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21
ALGEBRAIC OPERATIONS Question 2B
To divide by a fraction turn it upside down
and multiply.
Express as a single fraction in its
simplest form.
Multiply top line then bottom line.
Cancel numbers then letters in alphabetical
order.
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22
ALGEBRAIC OPERATIONS Question 2B
Express as a single fraction in its
simplest form.
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Question 2B

• To divide by a fraction turn it upside down and
  multiply.

Express as a
single fraction in its simplest form.
2. Multiply top line then bottom line.
v
1
w2
3
Begin Solution
3. Cancel numbers then letters in alphabetical
order.
Continue Solution
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Comments
To divide fractions use the result

• To divide by a fraction turn it upside down and
  multiply.

2. Multiply top line then bottom line.
v
1
w2
3
3. Cancel numbers then letters in alphabetical
order.
Next Comment
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25
Comments
To simplify final answer write out in full and
cancel

• To divide by a fraction turn it upside down and
  multiply.

2. Multiply top line then bottom line.
v
1
w2
3
3. Cancel numbers then letters in alphabetical
order.
Next Comment
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ALGEBRAIC OPERATIONS Question 3
Simplify
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ALGEBRAIC OPERATIONS Question 3
Deal with numbers and then apply laws of
indices when dividing subtract the powers.
Simplify
Remember subtracting negative is like adding.
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28
ALGEBRAIC OPERATIONS Question 3
3d2
Simplify
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29
Question 3
1. Deal with numbers and then apply laws of
indices when dividing subtract the powers.
Simplify .
24d5/4 ? 8d3/4
3d5/4-(3/4)
2. Remember subtracting negative is like adding.
3d8/4
3d2
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Comments
Learn Laws of Indices
1. Deal with numbers and then apply laws of
indices when dividing subtract the powers.
24d5/4 ? 8d3/4
e.g.
3d5/4-(3/4)
2. Remember subtracting negative is like adding.
3d8/4
3d2
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ALGEBRAIC OPERATIONS Question 3B
Simplify
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32
ALGEBRAIC OPERATIONS Question 3B
Deal with top row first. Apply laws of indices
when dividing subtract the powers when
multiplying add powers.
Simplify
Now divide remembering subtracting negative is
like adding.
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33
ALGEBRAIC OPERATIONS Question 3B
Simplify
a3
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Question 3B
1. Deal with top row first. Apply laws of
indices when dividing subtract the powers when
multiplying add powers.
Simplify .
2. Now divide remembering subtracting negative is
like adding.
Begin Solution
a1-(-2)
Continue Solution
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a3
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Comments
Learn Laws of Indices
1. Deal with top row first. Apply laws of
indices when dividing subtract the powers when
multiplying add powers.
e.g.
2. Now divide remembering subtracting negative is
like adding.
Next Comment
a1-(-2)
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Comments
Learn Laws of Indices
1. Deal with top row first. Apply laws of
indices when dividing subtract the powers when
multiplying add powers.
e.g.
2. Now divide remembering subtracting negative is
like adding.
Next Comment
a1-(-2)
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a3
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37
ALGEBRAIC OPERATIONS Question 4
Simplify
giving your answer with positive indices.
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38
ALGEBRAIC OPERATIONS Question 4
Deal with numbers and then apply laws of
indices when dividing subtract the powers.
Simplify
giving your answer with positive indices.
Remember subtracting negative is like adding.
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39
ALGEBRAIC OPERATIONS Question 4
Simplify
giving your answer with positive indices.
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40
Question 4
1. Multiply out brackets remembering to apply
laws of indices when multiplying add the powers.
Simplify
giving your answer with positive indices.
m1/3( m5/3 m-4/3 )
m6/3 m-3/3
m2 m-1
2. Negative powers become positive on bottom line.
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Comments
Learn Laws of Indices
1. Multiply out brackets remembering to apply
laws of indices when multiplying add the powers.
m1/3( m5/3 m-4/3 )
m6/3 m-3/3
e.g.
m2 m-1
2. Negative powers become positive on bottom line.
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ALGEBRAIC OPERATIONS Question 4B
Simplify
giving your answer without indices.
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43
ALGEBRAIC OPERATIONS Question 4B
Multiply out brackets remembering to apply
laws of indices when multiplying add the powers.
Simplify
giving your answer without indices.
Zero power is 1 and ½ power is square root.
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44
ALGEBRAIC OPERATIONS Question 4B
1 - ?w
Simplify
giving your answer without indices.
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45
Question 4B
1. Multiply out brackets remembering to apply
laws of indices when multiplying add the powers.
Simplify
giving your answer without indices.
w-1/4( w1/4 - w3/4 )
w-1/41/4 - w-1/43/4
w0 - w1/2
2. Zero power is 1 and ½ power is square root.
1 - ?w
Begin Solution
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Comments
Learn Laws of Indices
1. Multiply out brackets remembering to apply
laws of indices when multiplying add the powers.
w-1/4( w1/4 - w3/4 )
w-1/41/4 - w-1/43/4
w0 - w1/2
e.g.
2. Zero power is 1 and ½ power is square root.
1 - ?w
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ALGEBRAIC OPERATIONS Question 5
Evaluate 7c3/4 when c 16
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48
ALGEBRAIC OPERATIONS Question 5
Deal with indices first. Power ¾ is 4th root
cubed.
Evaluate 7c3/4 when c 16
Evaluate root before power
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49
ALGEBRAIC OPERATIONS Question 5
Evaluate 7c3/4 when c 16
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Question 5

• Deal with indices first. Power ¾ is 4th root
  cubed.

Evaluate 7c3/4 when c 16
c3/4
(4?c)3
(4?16)3
(2)3
8
So 7c3/4
7 x 8
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Comments
Learn Laws of Indices

• Deal with indices first. Power ¾ is 4th root
  cubed.

(4?c)3
Think Flower Power
(4?16)3
(2)3
Power on top
8
Root at bottom
So 7c3/4
7 x 8
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Comments
Learn Laws of Indices

• Deal with indices first. Power ¾ is 4th root
  cubed.

(4?c)3
e.g.
(4?16)3
(2)3
8
Always find root before power
So 7c3/4
7 x 8
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ALGEBRAIC OPERATIONS Question 5B
Evaluate 10f -1/2 when f 25
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54
ALGEBRAIC OPERATIONS Question 5B
Evaluate 10f -1/2 when f 25
Deal with indices first. Power ½ is square
root on bottom line.
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55
ALGEBRAIC OPERATIONS Question 5B
2
Evaluate 10f -1/2 when f 25
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56
Question 5B

• Deal with indices first. Power ½ is square root
  on bottom line.

Evaluate 10f -1/2 when f 25
10f -1/2
2
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Learn Laws of Indices

• Deal with indices first. Power ½ is square root
  on bottom line.

10f -1/2
e.g.
2
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58
ALGEBRAIC OPERATIONS Question 6
f(x) 7x1/2 . Find the value of x if f(x)
63.
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59
ALGEBRAIC OPERATIONS Question 6
f(x) 7x1/2 . Find the value of x if f(x)
63.
Equate both things that are equal to f(x).
To get rid of square roots square both sides.
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60
ALGEBRAIC OPERATIONS Question 6
f(x) 7x1/2 . Find the value of x if f(x)
63.
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61
Question 6
1. Equate both things that are equal to f(x).
f(x) 7x1/2 . Find the value of x if
f(x) 63.
7x1/2 63
(?7)
so x1/2 9
2. Remember power ½ is the square root.
so ?x 9
3. Now square each side.
Begin Solution
so x 92
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ie x 81
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Comments
Learn Laws of Indices
1. Equate both things that are equal to f(x).
7x1/2 63
(?7)
Note In solving the equation Square both sides
so x1/2 9
2. Remember power ½ is the square root.
so ?x 9
3. Now square each side.
so x 92
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ie x 81
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63
ALGEBRAIC OPERATIONS Question 6B
f(x) 2x1/3 . Find the value of x if f(x)
20.
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64
ALGEBRAIC OPERATIONS Question 6B
f(x) 2x1/3 . Find the value of x if f(x)
20.
Equate both things that are equal to f(x).
To get rid of cube roots cube both sides.
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65
ALGEBRAIC OPERATIONS Question 6B
f(x) 2x1/3 . Find the value of x if f(x)
20.
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66
Question 6B
1. Equate both things that are equal to f(x).
f(x) 2x1/3 . Find the value of x if
f(x) 20.
2x1/3 20
(?2)
so x1/3 10
2. Remember power 1/3 is the cube root.
so 3?x 10
3. Now cube each side.
Begin Solution
so x 103
Continue Solution
ie x 1000
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Comments
Learn Laws of Indices
1. Equate both things that are equal to f(x).
2x1/3 20
(?2)
Note In solving the equation cube both sides
so x1/3 10
2. Remember power 1/3 is the cube root.
so 3?x 10
3. Now cube each side.
so x 103
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ie x 1000
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ALGEBRAIC OPERATIONS Question 7
Simplify ?75 - ?27 ?48
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69
ALGEBRAIC OPERATIONS Question 7
Simplify ?75 - ?27 ?48
Find the largest perfect square factor of each
of the numbers!
Collect identical surds in same way as you would
letters. .
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70
ALGEBRAIC OPERATIONS Question 7
Simplify ?75 - ?27 ?48
6?3
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71
Question 7
1. Find the largest perfect square factor of
each of the numbers!
Simplify ?75 - ?27 ?48
?75 - ?27 ?48
?25 x ?3 -
?9 x ?3
?16 x ?3
5?3 - 3?3 4?3
2. Collect identical surds in same way as you
would letters.
6?3
5x 3x 4x 6x
Begin Solution
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Comments
Learn Laws of Indices
1. Find the largest perfect square factor of
each of the numbers!
?25 x ?3 -
?9 x ?3
?16 x ?3
5?3 - 3?3 4?3
e.g.
2. Collect identical surds in same way as you
would letters.
6?3
5x 3x 4x 6x
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Comments
The key to these simplification questions is that
all of the individual terms can be reduced to a
multiple of the same basic surd.
1. Find the largest perfect square factor of
each of the numbers!
?25 x ?3 -
?9 x ?3
?16 x ?3
So check that once you have taken perfect
squares all terms have the same basic surd. If
not you may not have used the highest perfect
square for a term.
5?3 - 3?3 4?3
2. Collect identical surds in same way as you
would letters.
6?3
5x 3x 4x 6x
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ALGEBRAIC OPERATIONS Question 7B
Simplify ?80 ?45 - ?180
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75
ALGEBRAIC OPERATIONS Question 7B
Simplify ?80 ?45 - ?180
Find the largest perfect square factor of each
of the numbers!
Collect identical surds in same way as you would
letters. .
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76
ALGEBRAIC OPERATIONS Question 7B
Simplify ?80 ?45 - ?180
?5
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77
Question 7B
1. Find the largest perfect square factor of
each of the numbers!
Simplify ?80 ?45 - ?180
?80 ?45 - ?180
?16 x ?5
?9 x ?5 -
?36 x ?5
4?5 3?5 - 6?5
2. Collect identical surds in same way as you
would letters.
?5
4x 3x 6x x
Begin Solution
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Comments
Learn Laws of Indices
1. Find the largest perfect square factor of
each of the numbers!
?80 ?45 - ?180
e.g.
?16 x ?5
?9 x ?5 -
?36 x ?5
4?5 3?5 - 6?5
2. Collect identical surds in same way as you
would letters.
?5
4x 3x 6x x
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79
Comments
The key to these simplification questions is that
all of the individual terms can be reduced to a
multiple of the same basic surd.
1. Find the largest perfect square factor of
each of the numbers!
?80 ?45 - ?180
So check that once you have taken perfect
squares all terms have the same basic surd. If
not you may not have used the highest perfect
square for a term.
?16 x ?5
?9 x ?5 -
?36 x ?5
4?5 3?5 - 6?5
2. Collect identical surds in same way as you
would letters.
?5
4x 3x 6x x
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80
ALGEBRAIC OPERATIONS Question 7C
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81
ALGEBRAIC OPERATIONS Question 7C
Deal with top and bottom lines separately.
For each, find the largest perfect square
factor of each of the numbers!
Now bring both parts together again. Cancel out
where the same basic surd is in evidence on both
top and bottom.
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82
ALGEBRAIC OPERATIONS Question 7C

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83
Question 7C
1. Deal with top and bottom lines separately. For
each, find the largest perfect square factor of
each of the numbers!
Simplify ?75 - ?27 ?48
Top Line
?75 - ?27 ?48
?25 x ?3 -
?9 x ?3
?16 x ?3
?300 - ?12
5?3 - 3?3 4?3
6?3
5x - 3x 4x 6x
Begin Solution
Continue Solution
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Question 7C
1. Deal with top and bottom lines seperately. For
each, find the largest perfect square factor of
each of the numbers!
Simplify ?75 - ?27 ?48
Bottom Line
?300 - ?12
?100 x ?3 -
?4 x ?3
?300 - ?12
10?3 - 2?3
8?3
10x - 2x 8x
Begin Solution
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Question 7C
2. Now bring both parts together again. Cancel
out where the same basic surd is in evidence on
both top and bottom.
Simplify ?75 - ?27 ?48
?75 - ?27 ?48
?300 - ?12
?300 - ?12
3

4

Begin Solution
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86
Comments
Learn Laws of Indices
1. Deal with top and bottom lines seperately. For
each, find the largest perfect square factor of
each of the numbers!
Top Line
e.g.
?75 - ?27 ?48
?25 x ?3 -
?9 x ?3
?16 x ?3
5?3 - 3?3 4?3
6?3
5x - 3x 4x 6x
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87
Comments
In questions involving fractions always treat
each line separately. Reduce each line to its
simplest form before dividing.
2. Now bring both parts together again. Cancel
out where the same basic surd is in evidence on
both top and bottom.
?75 - ?27 ?48
The key to these simplification questions is that
all of the individual terms can be reduced to a
multiple of the same basic surd. In fractions
these will then often cancel.
?300 - ?12

Remember to cancel numbers too!!

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88
ALGEBRAIC OPERATIONS Question 8
Express
with a rational denominator.
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89
ALGEBRAIC OPERATIONS Question 8
Express
with a rational denominator.
To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?6.
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90
ALGEBRAIC OPERATIONS Question 8
Express
with a rational denominator.
2?6
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91
Question 8
1. To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?6.
Express
with a rational denominator.
2
1
2?6
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92
Comments
Learn Laws of Surds
1. To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?6.
Rationalising the denominator
Multiply top and bottom by
2?6
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93
Comments
Learn Laws of Surds
1. To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?6.
Rationalising the denominator
e.g.
2?6
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94
ALGEBRAIC OPERATIONS Question 8B
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95
ALGEBRAIC OPERATIONS Question 8B
Find the largest perfect square factor of each
of the numbers!
Collect identical surds in same way as you would
letters. .
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96
ALGEBRAIC OPERATIONS Question 8B
2?7
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97
Question 8B
1. Re-write expression using laws of surds
?28
?4 x ?7
2?7
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98
Comments
Learn Laws of Surds
1. Re-write expression using laws of surds
e.g.
?28
?4 x ?7
2?7
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99
Comments
Learn Laws of Surds
1. Re-write expression using laws of surds
e.g.
?28
?4 x ?7
2?7
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100
ALGEBRAIC OPERATIONS Question 8C
Find the value of tanx giving your answer as a
fraction with a rational denominator.
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101
ALGEBRAIC OPERATIONS Question 8C
Find the value of tanx giving your answer as a
fraction with a rational denominator.
When dealing with fractions check that you have
simplified as far as possible.
To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?2.
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102
ALGEBRAIC OPERATIONS Question 8C
Find the value of tanx giving your answer as a
fraction with a rational denominator.
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103
Question 8C
1. To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?2.
Find the value of tanx giving your answer as a
fraction with a rational denominator.
tanx
1
Simplify!!!
Begin Solution
4
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104
Comments
Learn Laws of Surds
1. To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?2.
Rationalising the denominator
tanx
Multiply top and bottom by
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105
Comments
Learn Laws of Surds
1. To change the look of a fraction but not the
value multiply top bottom by the same amount
ie ?2.
e.g.
tanx
In questions involving fractions make sure you
have simplified as far as possible.
Simplify!!!
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106
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Further Trig
UNIT 3
Please choose a question to attempt from the
following
1
2
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107
Further Trig Question 1
The graph below shows a curve with equation in
the form y asinbx . Write down the values
of a and b.
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y asinbx
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108
Further Trig Question 1
The graph below shows a curve with equation in
the form y asinbx . Write down the values
of a and b.
a amplitude ½ vertical extent.
b no. of waves in 3600
y asinbx
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109
Further Trig Question 1
The graph below shows a curve with equation in
the form y asinbx . Write down the values
of a and b.
a 2
b 3
y asinbx
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110
Question 1
1. a amplitude ½ vertical extent.
y asinbx
max /min 2 so
a 2
2. b no. of waves in 3600
3 complete waves from 0 to 360
so b 3
Write down the values of a and b.
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111
Comments
Learn basic trig graphs
1. a amplitude ½ vertical extent.
i.e. y sinx
max /min 2 so
a 2
2. b no. of waves in 3600
3 complete waves from 0 to 360
so b 3
Max. 1 Min. -1 One cycle in 360
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112
Comments
Learn basic trig graphs
1. a amplitude ½ vertical extent.
i.e. y sinx
max /min 2 so
a 2
2. b no. of waves in 3600
One cycle
3 complete waves from 0 to 360
y asinx
y sinbx
so b 3
Stretch factor
Number of cycles in 360
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113
Further Trig Question 1B
The graph below shows a curve with equation in
the form y acosbx . Write down the values
of a and b.
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114
Further Trig Question 1B
The graph below shows a curve with equation in
the form y acosbx . Write down the values
of a and b.
a amplitude ½ vertical extent.
b no. of waves in 3600
y acosbx
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900
1800
3600
2700
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115
Further Trig Question 1B
The graph below shows a curve with equation in
the form y acosbx . Write down the values
of a and b.
a 5
b 2
y acosbx
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900
1800
3600
2700
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116
Question 1B
1. a amplitude ½ vertical extent.
max /min 5 so
a 5
2. b no. of waves in 3600
2 complete waves from 0 to 360
so b 2
Write down the values of a and b.
Begin Solution
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117
Comments
Learn basic trig graphs
1. a amplitude ½ vertical extent.
i.e. y cosx
max /min 5 so
a 5
2. b no. of waves in 3600
2 complete waves from 0 to 360
so b 2
Max. 1 Min. -1 One cycle in 360
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118
Comments
Learn basic trig graphs
1. a amplitude ½ vertical extent.
i.e. y cosx
max /min 2 so
a 2
2. b no. of waves in 3600
One cycle
3 complete waves from 0 to 360
y acosx
y cosbx
so b 3
Stretch factor
Number of cycles in 360
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119
Further Trig Question 2
Solve 5sinx - 1 1 where 0ltxlt360
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120
Further Trig Question 2
Solve 5sinx - 1 1 where 0ltxlt360
What would you like to do now?
Always re-arrange given equation to sin x
cosx tan x
Use CAST diagram to decide which quadrants angles
lie.
Reveal answer only
Remember that answers to trig equations come in
pairs.
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121
Further Trig Question 2
Solve 5sinx - 1 1 where 0ltxlt360
x 23.6
x 156.4
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122
Question 2
1. Always re-arrange to sinx0 ...
Solve 5sinx - 1 1 where 0ltxlt360
5sinx - 1 1
5sinx 2
sinx? 0.4
Q1 or Q2
2. Use the CAST diagram to decide which quadrant
angles lie in.
Where is sin positive?
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123
Question 2
1. Always re-arrange to sinx0 ...
Solve 5sinx - 1 1 where 0ltxlt360
5sinx - 1 1
5sinx 2
sinx? 0.4
Q1 or Q2
3. Calculate angles remembering that answers to
trig equations come in pairs.
sin-1 0.4 23.6?
Q1 angle 23.6
Begin Solution
Q2 angle 180 - 23.6
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156.4
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124
Comments
We are finding the two angles at which the sine
curve reaches a height of 0.4
1. Always re-arrange to sinx0 ...
5sinx - 1 1
5sinx 2
sinx? 0.4
Q1 or Q2
0.4
3. Calculate angles remembering that answers to
trig equations come in pairs.
sin-1 0.4 23.6?
Q1 angle 23.6
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Q2 angle 180 - 23.6
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125
Further Trig Question 2B
Solve 3tanx 7 2 where 0ltxlt360
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126
Further Trig Question 2B
Solve 3tanx 7 2 where 0ltxlt360
Always re-arrange given equation to sin x
cosx tan x
What would you like to do now?
Use CAST diagram to decide which quadrants angles
lie.
Reveal answer only
Remember that answers to trig equations come in
pairs.
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127
Further Trig Question 2B
Solve 3tanx 7 2 where 0ltxlt360
x 121.0
x 301.0
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128
Question 2B
1. Always re-arrange to tanx0 ...
Solve 3tanx 7 2 where 0ltxlt360
3tanx 7 2
3tanx -5
tanx? -5/3
Q2 or Q4
2. Use the CAST diagram to decide which quadrant
angles lie in.
Where is tan negative?
Begin Solution
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129
Question 2B
1. Always re-arrange to tanx0 ...
Solve 3tanx 7 2 where 0ltxlt360
3tanx 7 2
3tanx -5
tanx? -5/3
Q2 or Q4
3. Calculate angles remembering that answers to
trig equations come in pairs.
tan-1 (5?3) 59.0?
What would you like to do now?
Q2 angle 180 - 59.0
Begin Solution
121.0
Continue Solution
Q4 angle 360 - 59.0
Comments
301.0
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130
Comments
We are finding the two angles at which the tan
graph reaches a height of
1. Always re-arrange to tanx0 ...
3tanx 7 2
3tanx -5
tanx? -5/3
3. Calculate angles remembering that answers to
trig equations come in pairs.
tan-1 (5?3) 59.0?
Q2 angle 180 - 59.0
121.0
Next Comment
Q4 angle 360 - 59.0
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131
Comments
Note Never put a negative value into the
inverse trig function
1. Always re-arrange to tanx0 ...
3tanx 7 2
3tanx -5
tanx? -5/3
3. Calculate angles remembering that answers to
trig equations come in pairs.
DO
tan-1 (5?3) 59.0?
then CAST diagram
Q2 angle 180 - 59.0
121.0
Next Comment
Q4 angle 360 - 59.0
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132
INTERMEDIATE 2 ADDITIONAL QUESTION BANK
You have chosen to study
Quadratic Functions
UNIT 3
Please choose a question to attempt from the
following
1
2
3
4
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133
Quadratic Functions Question 1
Solve the equation x2 6x 7 0 giving
your answers to 2 decimal places.
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134
Quadratic Functions Question 1
Solve the equation x2 6x 7 0 giving
your answers to 2 decimal places.
Write down values of a, b c.
What would you like to do now?
Evaluate b2 4ac .
Now use quadratic formula, remembering that you
should get two answers.
Remember to round.
Reveal answer only
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135
Quadratic Functions Question 1
Solve the equation x2 6x 7 0 giving
your answers to 2 decimal places.
x 4.41 or 1.59
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136
Question 1
1. Write down values of a, b c.
x2 6x 7 0
Solve the equation x2 6x 7 0 giving
your answers to 2 decimal places.
a 1 b (-6) c 7
2. Evaluate b2 4ac .
b2 4ac (-6)2 (4x1x7)
36 28
8
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137
Question 1
1. Write down values of a, b c.
x2 6x 7 0
Solve the equation x2 6x 7 0 giving
your answers to 2 decimal places.
a 1 b -6 c 7
3. Now use quadratic formula.
Begin Solution
4. Rewrite with brackets and now use calculator.
Continue Solution
Comments
(6 ?8) ? 2 or (6 - ?8) ? 2
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138
Question 1
1. Write down values of a, b c.
x2 6x 7 0
Solve the equation x2 6x 7 0 giving
your answers to 2 decimal places.
a 1 b -6 c 7
4. Rewrite with brackets and now use calculator.
(6 ?8) ? 2 or (6 - ?8) ? 2
4.414 or 1.585..
5. Remember to round.
Begin Solution
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x 4.41 or 1.59
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139
Comments
For any question involving a quadratic in which
you are asked to give your answer to a given
number of decimal places
OR a given number of significant
figures THINK QUADRATIC FORMULA!!
1. Write down values of a, b c.
x2 6x 7 0
a 1 b -6 c 7
3. Now use quadratic formula.
Next Comment
4. Rewrite with brackets and now use calculator.
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(6 ?8) ? 2 or (6 - ?8) ? 2
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140
Comments
Refer to the Formula Sheet
1. Write down values of a, b c.
ax2 bx c 0
x2 6x 7 0
Quadratic Formula
a 1 b -6 c 7
3. Now use quadratic formula.
Next Comment
4. Rewrite with brackets and now use calculator.
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(6 ?8) ? 2 or (6 - ?8) ? 2
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141
Comments
Take care when allocating a value to a, b and c.
1. Write down values of a, b c.
x2 6x 7 0
ax2 bx c 0
1x2 - 6x 7 0
a 1 b -6 c 7
3. Now use quadratic formula.
a 1 b (-6) c 7
Next Comment
4. Rewrite with brackets and now use calculator.
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(6 ?8) ? 2 or (6 - ?8) ? 2
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142
Comments
Note Finding first
eases working. Bracket all negative numbers.
Watch out for double negative!
1. Write down values of a, b c.
b2 4ac
x2 6x 7 0
a 1 b -6 c 7
2. Evaluate b2 4ac .
b2 4ac (-6)2 (4x1x7)
36 28
8
Try another
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143
Quadratic Functions Question 1B
Solve the equation 3x2 5x - 1 0 giving
your answers to 2 significant figures.
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144
Quadratic Functions Question 1B
Solve the equation 3x2 5x - 1 0 giving
your answers to 2 significant figures.
Write down values of a, b c.
Evaluate b2 4ac .
Now use quadratic formula, remembering that you
should get two answers.
Remember to round.
What would you like to do now?
Reveal answer only
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145
Quadratic Functions Question 1B
Solve the equation 3x2 5x - 1 0 giving
your answers to 2 significant figures.
x 0.18 or -1.8
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146
Question 1B
1. Write down values of a, b c.
Solve the equation 3x2 5x - 1 0
giving your answers to 2 significant figures.
3x2 5x 1 0
a 3 b 5 c (-1)
2. Evaluate b2 4ac .
b2 4ac (5)2 (4 x 3 x -1)
25 (- 12)
37
Begin Solution
Continue Solution
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147
Question 1B
1. Write down values of a, b c.
Solve the equation 3x2 5x - 1 0
giving your answers to 2 significant figures.
3x2 5x 1 0
a 3 b 5 c (-1)
3. Now use quadratic formula.
Begin Solution
4. Rewrite with brackets and now use calculator.
Continue Solution
Comments
(-5 ?37) ? 2 or (-5 - ?37) ? 2
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148
Question 1B
1. Write down values of a, b c.
Solve the equation 3x2 5x - 1 0
giving your answers to 2 significant figures.
3x2 5x 1 0
a 3 b 5 c (-1)
4. Rewrite with brackets and now use calculator.
(-5 ?37) ? 2 or (-5 - ?37) ? 2
0.180 or -1.847..
5. Remember to round.
Begin Solution
Continue Solution
x 0.18 or -1.8
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149
Comments
For any question involving a quadratic in which
you are asked to give your answer to a given
number of decimal places
OR a given number of significant
figures THINK QUADRATIC FORMULA!!
1. Write down values of a, b c.
3x2 5x 1 0
a 3 b 5 c (-1)
3. Now use quadratic formula.
Next Comment
4. Rewrite with brackets and now use calculator.
Quadratics Menu
(-5 ?37) ? 2 or (-5 - ?37) ? 2
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150
Comments
Refer to the Formula Sheet
1. Write down values of a, b c.
ax2 bx c 0
3x2 5x 1 0
Quadratic Formula
a 3 b 5 c (-1)
3. Now use quadratic formula.
Next Comment
4. Rewrite with brackets and now use calculator.
Quadratics Menu
(-5 ?37) ? 2 or (-5 - ?37) ? 2
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151
Comments
1. Write down values of a, b c.
Take care when allocating a value to a, b and c.
3x2 5x 1 0
ax2 bx c 0
a 3 b 5 c (-1)
3x2 5x - 1 0
3. Now use quadratic formula.
a 3 b 5 c -1
Next Comment
4. Rewrite with brackets and now use calculator.
Quadratics Menu
(-5 ?37) ? 2 or (-5 - ?37) ? 2
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152
Comments
Note Finding first
eases working. Bracket all negative numbers.
Watch out for double negative!
1. Write down values of a, b c.
b2 4ac
3x2 5x 1 0
a 3 b 5 c (-1)
2. Evaluate b2 4ac .
b2 4ac (5)2 (4 x 3 x -1)
25 (- 12)
37
Next Comment
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153
Quadratic Functions Question 2
Solve the equation 3x2 x 1 giving your
answers to 2 decimal places.
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154
Quadratic Functions Question 2
Solve the equation 3x2 x 1 giving your
answers to 2 decimal places.
Write down values of a, b c.
Re-write quadratic make it equal to zero before
solving.
Evaluate b2 4ac .
Now use quadratic formula, remembering that you
should get two answers.
Remember to round.
What would you like to do now?
Reveal answer only
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155
Quadratic Functions Question 2
Solve the equation 3x2 x 1 giving your
answers to 2 decimal places.
x 0.77 or -0.43
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156
Question 2
1. Rearrange in quadratic form.
3x2 x 1
Solve the equation 3x2 x 1 giving your
answers to 2 decimal places.
3x2 x 1 0
a 3 b (-1) c (-1)
2. Write down values of a, b c.
3. Evaluate b2 4ac .
b2 4ac (-1)2 (4 x 3 x -1)
Begin Solution
1 (