Official 2017 Paper 1
20 questions · 75 min · Difficulty 37
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Questions in this paper
- Question 1Given that (d y)/(d x)=3x^2-(2-3x)/(x^3), x≠0 and y=5 when x=1, find y in terms of x.
- Question 2The function f is given by f(x)=(frac2x-frac12x^2)^2 (x≠0) What is the value of f"(1)?
- Question 3A line l has equation y=6-2x. A second line is perpendicular to l and passes through the point (-6,0). Find the area of the region enclosed…
- Question 4When (3x^2+8x-3) is multiplied by (px-1) and the resulting product is divided by (x+1), the remainder is 24. What is the value of p?
- Question 5S is the complete set of values of x which satisfy both the inequalities x^2-8x+12 9 The set S can also be represented as a single…
- Question 6A tangent to the circle x^2+y^2=144 passes through the point (20,0) and crosses the positive y-axis. What is the value of y at the point…
- Question 7The first three terms of an arithmetic progression are p, q and p^2 respectively, where p<0. The first three terms of a geometric…
- Question 8Find the complete set of values of x, with 0≤ x≤π, for which (1-2sin x)cos x≥0
- Question 9A circle has equation x^2+y^2-18x-22y+178=0. A regular hexagon is drawn inside this circle so that the vertices of the hexagon touch the…
- Question 10A curve C has equation y=f(x) where f(x)=p^3-6p^2x+3px^2-x^3 and p is real. The gradient of the normal to the curve C at the point where…
- Question 11The sequence x_n is defined by the rules x_1=7 x_(n+1)=(23x_n-53)/(5x_n+1) The first three terms in the sequence are 7, 3, 1. What is the…
- Question 12The polynomial function f(x) is such that f(x)>0 for all values of x. Given ∫_2^4f(x) d x=A, which one of the following statements must be…
- Question 13In the expansion of (a+bx)^5 the coefficient of x^4 is 8 times the coefficient of x^2. Given that a and b are non-zero positive integers…
- Question 14The solution of the simultaneous equations 2^x+3×2^y=3 2^(2x)-9×2^(2y)=6 is x=p, y=q. Find the value of p-q.
- Question 15It is given that f(x)=-2x^2+10. Consider the following three curves: - (1) y=f(x) - (2) y=f(x+1) - (3) the curve y=f(x+1) reflected in the…
- Question 16The functions f and g are given by f(x)=3x^2+12x+4 and g(x)=x^3+6x^2+9x-8. What is the complete set of values of x for which one of the…
- Question 17The two functions F(n) and G(n) are defined as follows for positive integers n: F(n)=frac1n∫_0^n(n-x) d x G(n)=Σ_(r=1)^nF(r) What is the…
- Question 18The graph of y=log_(10)x is translated in the positive y-direction by 2 units. This translation is equivalent to a stretch of factor k…
- Question 19The set of solutions to the inequality x^2+bx+c<0 is the interval p<x<q where b, c, p and q are real constants with c<0. In terms of p, q…
- Question 20The lengths of the sides QR, RP and PQ in triangle PQR are a, a+d and a+2d respectively, where a and d are positive and such that 3d>2a…