← All paperstmua.fyi · Paper 1

tmua.fyi Mock Paper 1 (2)

20 questions · 75 min · Difficulty 13 · by tmua.fyi

Read the questions freely. Sign in to answer them, start a timed paper and save your progress.

Question paper ↗

Questions in this paper

  1. Question 1An arithmetic sequence has first term 5 and common difference 3. What is the sum of its first 20 terms?
  2. Question 2Find the equation of the normal to the curve y=x^2-3x at the point where x=2.
  3. Question 3A fair six-sided die is rolled three times. What is the probability that the three numbers obtained are strictly increasing?
  4. Question 4An open-topped box is made from a square sheet of card of side 12 cm by cutting a square of side x cm from each corner and folding up the…
  5. Question 5How many positive integers are divisors of 720?
  6. Question 6Two circles have equations x^2+y^2=4 and (x-6)^2+(y-8)^2=9. Find the shortest distance between them.
  7. Question 7Find the term independent of x in the expansion of (2x-frac1x^2)^6.
  8. Question 8A sequence is defined by u_1=1 and u_(n+1)=frac6u_n+1. Given that it converges, find its limit.
  9. Question 9What is the maximum value of f(x)=3sin x+4cos x?
  10. Question 10The line y=kx-2 is a tangent to the curve y=x^2-3x+2 for two values of k. Find the sum of those two values.
  11. Question 11The graph of y=√ x is transformed, in order, first by a translation of 3 in the positive x-direction and then by a stretch of scale factor…
  12. Question 12The cubic f(x)=x^3+ax^2+bx-6 has both (x-1) and (x-2) as factors. What is its third root?
  13. Question 13Which of the following is the largest?
  14. Question 14Given that sinθ+cosθ=frac12, find the value of sinθcosθ.
  15. Question 15Evaluate ∫_0^3lfloor xrfloor d x, where lfloor xrfloor denotes the greatest integer not exceeding x.
  16. Question 16Solve log_2 x+log_2(x-2)=3 for x>2.
  17. Question 17The sum of the first n terms of a sequence is S_n=n^2+2n. Find the tenth term of the sequence.
  18. Question 18The points (1,2) and (5,8) are the endpoints of a diameter of a circle. Find the radius of the circle.
  19. Question 19In how many ways can 8 identical balls be placed into 3 distinct boxes so that no box is empty?
  20. Question 20How many ordered pairs of positive integers (x,y) satisfy frac1x+frac1y=frac16?