Official 2016 Paper 1
20 questions · 75 min · Difficulty 41
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Questions in this paper
- Question 1It is given that the expansion of (ax+b)^3 is 8x^3-px^2+18x-3√(3), where a, b and p are real constants. What is the value of p?
- Question 2The expression 3x^3+13x^2+8x+a, where a is a constant, has (x+2) as a factor. Which one of the following is a complete factorisation of the…
- Question 3A line is drawn normal to the curve y=(2)/(x^2) at the point on the curve where x=1. This line cuts the x-axis at P and the y-axis at Q…
- Question 4The sequence a_n is defined by the rule: a_n=(-1)^n-(-1)^(n-1)+(-1)^(n+2) n≥1. Find the value of Σ_(n=1)^(39)a_n
- Question 5What is the total area enclosed between the curve y=x^2-1, the x-axis and the lines x=-2 and x=2?
- Question 6P, Q, and R are each mixtures of red and white paint. The percentage by volume of red paint in P is 30%. The percentage by volume of red…
- Question 760% of a sports club's members are women and the remainder are men. This sports club offers the opportunity to play tennis or cricket…
- Question 8Find the maximum angle x in the range 0°≤ x≤360°which satisfies the equation cos^2(2x)+√(3)sin(2x)-(7)/(4)=0
- Question 9The line segment joining the points (3,3) and (7,5) is a diameter of a circle. This circle is translated by 3 units in the negative…
- Question 10How many solutions does the equation xtan x=1 have in the interval -2π≤ x≤2π?
- Question 11The real roots of the equation 4^(2x)+12=2^(2x+3) are p and q, where p>q. The value of p-q can be expressed as
- Question 12A right circular cylinder is contained within a sphere of radius 5 cm in such a way that the whole of the circumferences of both ends of…
- Question 13How many real roots does the equation 3x^5-10x^3-120x+30=0 have?
- Question 14The terms of an infinite series S are formed by adding together the corresponding terms in two infinite geometric series, T and U. The…
- Question 15The least possible value of the gradient of the curve y=(2x+a)(x-2a)^2 at the point where x=1, as a varies, is
- Question 16Given the simultaneous equations log_(10)2+log_(10)(y-1)&=2log_(10)x log_(10)(y+3-3x)&=0 the values of y are
- Question 17It is given that y=(1+2cos x)cos2x 0<x<π The complete set of values of x for which y is negative is
- Question 18The function dfrac1-x√[3]x^2 is defined for all x≠0. The complete set of values of x for which the function is decreasing is
- Question 19The coefficient of x^3 in the expansion of (1+2x+3x^2)^6 is equal to twice the coefficient of x^4 in the expansion of (1-ax^2)^5. Find all…
- Question 20The diagram shows a square-based pyramid with base PQRS and vertex O. All the edges of the pyramid are of length 20 metres. Find the…