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user 2011 May June Paper 21 Q1 Without using a calculator, express (frac{(5+2 sqrt{3})^{2}}{2+sqrt{3}}) in the form (p+q sqrt{3}), where (p) and (q) are integers. 2014 May june Paper 21 Q2 Without using a calculator, express (6(1+sqrt{3})^{-2}) in the form (a+b sqrt{3}), where (a) and (b) are integers to be found. More Similar Questions 2012 Oct … Read more
Question 1 Show that (frac{1}{tan theta+cot theta}=sin theta cos theta). [3] Question 2 Find the coordinates of the points where the line (2 y=x-1) meets the curve (x^{2}+y^{2}=29). [5] Question 3 (i) Express (log _{x} 2) in terms of a logarithm to base 2. [1] (ii) Using the result of part (i), and the substitution … Read more
Question 1 Solve the inequality (x(2 x-1)>15) [3] Question 2 (i) Given that (y=(12-4 x)^{5},) find (frac{ d y}{ d x}). (ii) Hence find the approximate change in (y) as (x) increases from 0.5 to (0.5+p,) where (p) is small. [2] Question 4 Without using a calculator, find the positive root of the equation[(5-2 sqrt{2}) … Read more
Question 1 (i) Given that (A =left(begin{array}{rr}4 & -3 \ 2 & 5end{array}right),) find the inverse matrix (A ^{-1}).(ii) Use your answer to part (i) to solve the simultaneous equations[begin{array}{l}4 x-3 y=-10 \2 x+5 y=21end{array}] Question 2 A cuboid has a square base of side ((2+sqrt{3}) cm) and a volume of ((16+9 sqrt{3}) cm ^{3}). … Read more
Download pdf The equation of a curve is \(\quad y=2 x^{2}-20 x+37\). Express \(y\) in the form \(a(x+b)^{2}+c,\) where \(a, b\) and \(c\) are integers. Write down the coordinates of the stationary point on the curve. A function \(f\) is defined by \(f : x \mapsto 2 x^{2}-20 x+37\) for \(x>k\). Given that the function … Read more
1. Show that (frac{1}{1-cos theta}+frac{1}{1+cos theta}=2 operatorname{cosec}^{2} theta). [3] Answer 2. Express (lg a+3 lg b-3) as a single logarithm. [3] Answer 3. (a) Shade the region corresponding to the set given below each Venn diagram. (b) Given that (P=left{p: tan p=1right.) for (left.0^{circ} leqslant p leqslant 540^{circ}right}), find (n (P)). Answer 4. (a) Solve … Read more
Show that \(\frac{1}{1-\cos \theta}+\frac{1}{1+\cos \theta}=2 \operatorname{cosec}^{2} \theta\).
Answer only one of the following two alternatives. EITHER A function \(f\) is such that \(f (x)=\ln (5 x-10),\) for \(x>2\) (i) State the range of \(f\). (ii) Find \(f ^{-1}(x)\). (iii) State the range of \(f ^{-1}\). (iv) Solve \(f(x)=0\). A function \(g\) is such that \(g (x)=2 x-\ln 2,\) for \(x \in R\). … Read more
Magnesium carbonate reacts with hydrochloric acid to form calcium chloride, carbon dioxide and water. Complete the symbol equation for this reaction.MgCO₃ + HCl → MgCl₂ + __ + H₂O MgCO₃ + 2HCl → MgCl₂ + CO2 + H₂O b. Magnesium reacts with steam. Mg(s) + H2O(g) MgO(s) + H2(g) Write a word equation for … Read more
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