- Calculate \(\sum _ { r = 1 } ^ { 20 } 5 + 2 r\)
- Find \(\int 5 x + 3 \sqrt { x } d x\)
- (a) Express \(\sqrt { } 80\) in the form \(a \sqrt { } 5\), where \(a\) is an integer.
(b) Express \(( 4 - \sqrt { 5 } ) ^ { 2 }\) in the form \(b + c \sqrt { 5 }\), where \(b\) and \(c\) are integers. - The points \(A\) and \(B\) have coordinates \(( 3,4 )\) and \(( 7 , - 6 )\) respectively. The straight line \(l\) passes through \(A\) and is perpendicular to \(A B\). Find an equation for \(l\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers. (5)
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\caption{Figure 1}
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Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\).
The curve crosses the coordinate axes at the points \(( 0,1 )\) and \(( 3,0 )\). The maximum point on the curve is \(( 1,2 )\).
On separate diagrams, sketch the curve with equation