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Section 1

36% of 175g
\(=36 \div 100 \times 175\)
\(=63\)

\( 2. \frac {4} {9} - \frac {5} {12} \)
Times the left fraction by the right fractions denominator and then visa versa
\( = \frac {48} {108} - \frac {45} {108} \)

150L increasedby 43
\(=143 \div 100 \times 150\)
= 214L

Highest Common Factor of 36 an 24
36: 1,2,3,4,6,12 and 36
24: 1,2,3,4,6,12 and 24
The highest common factor is 12

Write Down the first 5 terms of a sequence with the formula. \(n^{th} =6n-5\)
1,7,13,19 and 25

For the sequence for 2,9,16,23,30
a) The formula that generates it.
\(n^{th} =7n-5\)
b) The value of the \(40^{th}\) term
=280

Find the value of \(x\) in the following equations
a) \(3x-5=16\) || (\(-5\))
\(3x=11\) || (\(\div 3\))
\(x= \frac {11} {3}\)

b) \(2x+11=19\) || \(-11\)
\(2x=8\) || \(\div2\)
\(x=4\)
c) \(3(x+11)=21\) || Claw method
d) \(4x+3=x+18\) || \(-x\)
\(3x+3 =18\) || \(-3\)
\(3x=15\) \(\div 3\)
\(x=5\)

Section 2

Phil buys 4 bags of sweets and eats 15 single sweets.
Jamie has 2 bags of sweets and finds 7 more down the side of the sofa.
If they have the same number of sweets. How many sweets are in the bag

Solve the following question
\(2x+5(3-x)=4(x+6)\)
\(2x+15-5x=4x+24\)
\(-3x+15=4x+24 || +3x\)
\(7x+24=15 ||-24\)
\(7x=-9 ||\div 7\)
\(x + \frac{9} {7}\)

For the patterns find a formula for posts and a formula for the wires
e.g.
1st section: 2 posts 2 wires
2nd section: 4 posts 6 wires
Formula:

Box

||

\(Perimeter = 50cm\)
\(Area=144cm^2\)

Put it into an equation.
\(2(x+2)+2(3x-5)=50\)
\(2x+4+6x-10 = 50\)
\(8x-6=50 || +6\)
\(8x=56 || \div 8\)
\(x=7\)

Area

\( Circumference = \pi \times Diameter\)
\( Area = \pi r^2\)

Section 3

Expand the following expressions.
\(5(x-7)\)
\(5x-35 || \div 5\)
\(x=-7\)

\(x+2\)
\(9\)

\(3x-5\)
\(16\)