Expanding Bracket with Surds
2014 May June Paper 23 Q5(i) Do not use a calculator in this question.(i) Show that ((2 sqrt{2}+4)^{2}-8(2 sqrt{2}+3)=0).
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Solving Equation with Indices – Same Base
2012 Oct Nov Paper 22 Q6 (i) Given that (frac{2^{x-3}}{8^{2 y-3}}=16^{x-y}), show that (3 x+2 y=6).(ii) Given also that (frac{5^{y}}{125^{x-2}}=25), find the value of (x) and of (y).
Surds Word Problem
2012 May June Paper 21/23 Q2 A cuboid has a square base of side ((2+sqrt{3}) cm) and a volume of ((16+9 sqrt{3}) cm ^{3}). Without using a calculator, find the height of the cuboid in the form ((a+b sqrt{3}) cm), where (a) and (b) are integers. 2015 May June Paper 22 Q3 Do not use … Read more
Solving Quadratic Equation with Surd
2011 Oct Nov Paper 23 Q4 Without using a calculator, find the positive root of the equation[(5-2 sqrt{2}) x^{2}-(4+2 sqrt{2}) x-2=0,]giving your answer in the form (a+b sqrt{2}), where (a) and (b) are integers. More Similar Questions 2014 May June Paper 23 Q5(ii) Do not use a calculator in this question.(ii) Solve the equation ((2 … Read more
Rationalise the Denominator
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
Cambridge Additional Mathematics 2011 Past Paper Oct Nov Paper 12
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
Cambridge Additional Mathematics 2011 Past Paper Oct Nov Paper 23
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
Cambridge Additional Mathematics 2012 Past Paper May June Paper 21 | 23
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
Add Maths 2012 May-June Paper 21 23 Q12
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