Official 2018 Paper 1
20 questions · 75 min · Difficulty 34
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
Questions in this paper
- Question 1Find the value of ∫_1^4(3-2x)/(x√ x) d x
- Question 2An arithmetic progression has first term a and common difference d. The sum of the first 5 terms is equal to the sum of the first 8 terms…
- Question 3Find the shortest distance between the two circles with equations: (x+2)^2+(y-3)^2=18 (x-7)^2+(y+6)^2=2
- Question 4Consider the simultaneous equations 3x^2+2xy=4 x+y=a where a is a real constant. Find the complete set of values of a for which the…
- Question 5The function f is defined by f(x)=x^3+ax^2+bx+c. a, b and c take the values 1, 2 and 3 with no two of them being equal and not necessarily…
- Question 6Find the number of solutions of the equation xsin2x=cos2x with 0≤ x≤2π.
- Question 7The non-zero constant k is chosen so that the coefficients of x^6 in the expansions of (1+kx^2)^7 and (k+x)^(10) are equal. What is the…
- Question 8The sum to infinity of a geometric progression is 6. The sum to infinity of the squares of each term in the progression is 12. Find the sum…
- Question 9Find the complete set of values of the constant c for which the cubic equation 2x^3-3x^2-12x+c=0 has three distinct real solutions.
- Question 10x and y satisfy |2-x|≤6 and |y+2|≤4. What is the greatest possible value of |xy|?
- Question 11The line y=mx+5, where m>0, is normal to the curve y=10-x^2 at the point (p,q). What is the value of p?
- Question 12A curve has equation y=f(x), where f(x)=x(x-p)(x-q)(r-x) with 0<p<q<r. You are given that: ∫_0^r f(x) d x=0 ∫_0^q f(x) d x=-2 ∫_p^r f(x) d…
- Question 13The function f(x) has derivative f'(x). The diagram below shows the graph of y=f'(x). Which point corresponds to a local minimum of f(x)?
- Question 14The line y=mx+4 passes through the points (3,log_2 p) and (log_2 p,4). What are the possible values of p?
- Question 15Find the sum of the real solutions of the equation: 3^x-(√3)^(x+4)+20=0
- Question 16The curve C has equation y=x^2+bx+2, where b≥0. Find the value of b that minimises the distance between the origin and the stationary point…
- Question 17There are two sets of data: the mean of the first set is 15, and the mean of the second set is 20. One of the pieces of data from the first…
- Question 18What is the smallest positive value of a for which the line x=a is a line of symmetry of the graph of y=sin(2x-frac4π3)?
- Question 19A triangle ABC is to be drawn with AB=10 cm, BC=7 cm and the angle at A equal to θ, where θ is a certain specified angle. Of the two…
- Question 20Find the value of &sin^2 0°+sin^2 1°+sin^2 2°+sin^2 3°+… & +sin^2 87°+sin^2 88°+sin^2 89°+sin^2 90°