## Finding Quadratic/Cubic Expression from Graph

2020 May June Paper 11 Q1 The diagram shows the graph of a cubic curve y = f(x). (a) Find an expression for f(x). (b) Solve f(x) ≤ 0.  2020 Oct Nov Paper 12 Q2 The diagram shows the graph of y = f(x), where f(x) is a cubic polynomial.  (a) Find f(x). (b) … Read more

## Solving Simultaneous Equations with Surd

2015 Oct Nov Paper 23 Q4 Solve the following simultaneous equations, giving your answers for both (x) and (y) in the form (a+b sqrt{3}), where (a) and (b) are integers.[begin{array}{r}2 x+y=9 \sqrt{3} x+2 y=5end{array}]

## Finding UnKnown By Comparing Equation with Surd

2014 Oct Nov Paper 21 & 22 Q9 Integers (a) and (b) are such that ((a+3 sqrt{5})^{2}+a-b sqrt{5}=51). Find the possible values of (a) and the corresponding values of (b). 2016 Oct Nov Paper 21 & 22 Q2 Without using a calculator, find the integers (a) and (b) such that (frac{a}{sqrt{3}+1}+frac{b}{sqrt{3}-1}=sqrt{3}-3). More Similar Questions 2016 … Read more

## 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).

## 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

## Cambridge Additional Mathematics 2011 Past Paper Oct Nov Paper 12

Question 1 Show that (frac{1}{tan theta+cot theta}=sin theta cos theta).  Question 2 Find the coordinates of the points where the line (2 y=x-1) meets the curve (x^{2}+y^{2}=29).   Question 3 (i) Express (log _{x} 2) in terms of a logarithm to base 2.  (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)   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.  Question 4 Without using a calculator, find the positive root of the equation[(5-2 sqrt{2}) … Read more

## Add Maths 2010 May-June Paper 11

1. Show that (frac{1}{1-cos theta}+frac{1}{1+cos theta}=2 operatorname{cosec}^{2} theta).  Answer 2. Express (lg a+3 lg b-3) as a single logarithm.  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