Transcript File

CAT Practice
Merit 2
Question One
• Expand and simplify
Question One
a
( 2x + 1) ( x - 3)
b 3( y + 5 ) - 2 ( y - 8 )
c 12 - 2 ( x + 2 )
Answers Question One
a
( 2x + 1) ( x - 3)
= 2x - 5x - 3
2
b 3( y + 5 ) - 2 ( y - 8 ) = y + 31
c 12 - 2 ( x + 2 ) = -2x + 8
Question Two
• Factorise
a x + 9x - 36
2
b x - 14 x + 49
2
Answer Question Two
• Factorise
a x + 9x - 36 = ( x +12 ) ( x - 3)
2
b x - 14x + 49 = ( x - 7 )
2
2
Question Three
a
( 2x )
b
(4y )
3
4
2
3
Answer Question Three
a
( 2x )
= 8x
b
( 4y )
= 16y
4 3
2
3
12
6
Question Four
• Solve for x
a x = -64
3
b 2 = 64
x
Answer Question Four
• Solve for x
a x = -64, x = -4
3
b 2 = 64, x = 6
x
Question Five
• Simplify
a
4 x 5x
+
3
8
b
x - 81
2x + 18
c
24 x
8x 3
2
9
Answer Question Five
• Simplify
a
4x 5x 32x + 15x 47x
+
=
=
3
8
24
24
b
x 2 - 81 ( x + 9 ) ( x - 9 ) x - 9
=
=
2x + 18
2 ( x + 9)
2
c
24 x 9
6
=
3x
3
8x
Question Six
• An operation * is defined by
10ab
a *b =
2
( a + b)
• Find the value of 3*-4
Answwer Question Six
10 ´ 3 ´ -4
3* -4 =
= -120
2
( 3- 4 )
Question Seven
• Solve these equations
a 7x + 25 = 5 - x
b 4y ( y + 2 ) = 0
c 3z = 96
5
Answer Question Seven
• Solve these equations
a 7x + 25 = 5 - x Þ 8x = -20 Þ x = -2.5
b 4y ( y + 2 ) = 0 Þ y = 0, -2
c 3z = 96 Þ z = 32 Þ z = 2
5
5
Question Eight
• Factorise fully
a + 3a - 40
2
Answer Question Eight
• Factorise fully
a + 3a - 40
2
= ( a + 8)( a - 5)
Question Nine
• Write in simplest form
a + 3a - 40
2
a + 8a
2
Answer Question Nine
• Write in simplest form
a + 3a - 40 ( a + 8 ) ( a - 5 )
=
2
a (a + 8)
a + 8a
2
a-5
=
a
Question Ten
• What is the value of k if:
( 2a )
4
´ a = 16a
k
8
Answer Question Ten
• What is the value of k if:
( 2a )
4
k=4
´ a = 16a
k
8
Question Eleven
• Expand and simplify
(2a + 4)( a -1)
Answer Question Eleven
• Expand and simplify
( 2a + 4 )( a -1)
= 2a + 2a - 4
2
Question Twelve
Question Twelve
15 + 9 ) h
(
36 =
2
72 = 24h
3cm = h
Question Thirteen
• Clearly state the range and possible
• values of a if (2a + 8)(a - 2) < 4a + 2
Answer Question Thirteen
2a + 4a - 16 < 4a + 2
2 the range and possible
• Clearly state
• values of a if (2a + 8)(a - 2) < 4a + 2
2
2a - 18 < 0
a -9<0
2
( a + 3) ( a - 3) < 0
-3 < a < 3
Question Fourteen
• A rectangular swimming pool is
• 30 metres × 10 metres. Around the pool is a
concrete path that is w metres wide. The total
area of the pool and surrounding path is 800
m2.
• Using the information form an equation and
solve it to find the width (w) of the path
around the pool.
Question Fourteen
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• A rectangular30
swimming
+ 2w pool
10 +is 2w = 800
• 30 metres × 10 metres.
Around the pool is a
2
4w
- 500
= The
0 total
concrete path
that+is80w
w metres
wide.
area of the pool
2 and surrounding path is 800
w
+
20w
125
=
0
2
m.
• Using the information
w + 25 form
w -an5equation
= 0 and
solve it to find the width (w) of the path
w = 5m, w ¹ -25
around the pool.
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Question Fifteen
• Last year the Mahobe Football club sold pizzas.
There were 250 pizzas sold for a total raised of $1730.
• Large pizzas sold for $8 each and small ones sold for $5
each.
There were y large pizzas and x small pizzas.
Solve the simultaneous equations below to find the
number of each sized pizza that was sold.
•
• x + y = 250
• 5x + 8y = 1730
Answer Question Fifteen
• Last year the Mahobe Football club sold pizzas.
There were 250 pizzas sold for a total raised of $1730.
• Large pizzas sold for $8 each and small ones sold for $5
each.5x + 5y = 1250
There were y large pizzas and x small pizzas.
8y = 1730
Solve5x
the +
simultaneous
equations below to find the
number of each sized pizza that was sold.
3y = 480
•
• x + y = 250
large
y
=
160,
small
x
=
90
• 5x + 8y = 1730
Question Sixteen
• There are many interesting properties of consecutive
numbers.
• Consecutive numbers are numbers such as 21, 22, 23,
24.
For example, choose any 5 consecutive numbers. Take
the middle number and multiply it by 5. The answer
will be the same as if you summed all 5 of the
numbers.
Write an expression that represents five consecutive
numbers and use this expression to show that if you
multiply the middle number by five you get a result the
same as if you summed all five numbers.
Answer Question Sixteen
• There are many interesting properties of consecutive
numbers.
• Consecutive numbers are numbers such as 21, 22, 23,
24.
For example, choose any 5 consecutive numbers. Take
the middle number and multiply it by 5. The answer
will be the same as if you summed all 5 of the
numbers.
Write an expression that represents five consecutive
numbers and use this expression to show that if you
multiply the middle number by five you get a result the
same as if you summed all five numbers.
n + ( n + 1) + ( n + 2 ) + ( n + 3) + ( n + 4 )
= 5n + 10
= 5 (n + 2)
Question Seventeen
• In another example take three consecutive whole
numbers.
• Square each number and sum the three squares.
• Subtract two from the sum and divide the result
by three. Write down an expression to represent
any three consecutive numbers. Use this
expression to show that if you follow the steps
outlined above with any set of three consecutive
numbers you will always get as a result the
square of the second of the numbers that you
first started with.
Answer Question Seventeen
• In another example take three consecutive whole
numbers.
2
2
2
n +each
n +number
1 + and
n + sum
2 the
- 2three squares.
• Square
• Subtract two from3the sum and divide the result
by three. Write down an expression to represent
2 consecutive numbers. Use this
any three
3n + 6n + 3
2
2
expression
to show that
follow
=
= nif you
+ 2n
+ 1 =thensteps
+1
outlined above
3 with any set of three consecutive
numbers you will always get as a result the
square of the second of the numbers that you
first started with.
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Question Eighteen
• To find Sung’s birth month multiply it by 4.
Add to this product the difference between 12
and his birth month. Subtract from this result
twice the sum of 5 and his birth month. If you
successfully follow this equation you should
end up with 10. What must Sung’s birth
month be?
Answer Question Eighteen
• To find Sung’s birth month multiply it by 4.
4nAdd
+12
- nproduct
- 2 nthe
+ 5difference
= n + 2between
= 10 12
to this
and his birth month. Subtract from this result
n twice
= 8 the sum of 5 and his birth month. If you
successfully follow this equation you should
end up with 10. What must Sung’s birth
month be?
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