tmua.me Medium Set F Paper 1
20 questions · 75 min · Difficulty 49 · by tmua.me
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Questions in this paper
- Question 1The graph of y=x^2+px+q, where p and q are real constants, is translated by 1 unit in the positive x-direction. The resulting graph has…
- Question 2The derivative f' of a function f is continuous for 1≤ x≤6, and ∫_1^3 f'(x) dx=8, ∫_3^6 f'(x) dx=-3. What is the gradient of the straight…
- Question 3The first nine terms u_1,u_2,…,u_9 of an arithmetic progression are all positive. It is given that u_2u_8=40 u_4u_6=48. What is…
- Question 4Packet A contains 25\% more rice than packet B, and its total price is 10\% higher than the total price of packet B. The price per 100…
- Question 5Triangle ABC has ∠ BAC=120°, BC=2√7, AB=AC+2. What is the length of AB?
- Question 6A circle passes through O=(0,0) and P=(4,2). Its centre lies on the line y=2x. The circle meets the x-axis again at Q. What is the equation…
- Question 7Real numbers x, y and z satisfy xy+x+y=5, yz+y+z=11, zx+z+x=7. What is the sum of all the distinct possible values of xyz?
- Question 8A list of 15 real numbers has median 7 and range 6. A new list is formed by replacing every number x in the original list by 20-2x. What is…
- Question 9The real numbers x and y satisfy 2^(x+y)=16, 4^x+4^y=40. What is |x-y|?
- Question 10A point P lies on the curve y=x^2+3+frac1x, x>0. The origin is O. What is the least possible gradient of the straight line OP?
- Question 11Box A contains one counter, and boxes B and C each contain two counters. Three counters are removed, one at a time. Before each removal…
- Question 12The points A=(0,0), B=(4,0) and C=(2,t), where t>0, are three vertices of a parallelogram. They are not necessarily consecutive vertices…
- Question 13A geometric progression u_1,u_2,u_3,… has a negative common ratio. It is given that u_3=8, u_5=2. What is u_4+u_6?
- Question 14The points A, B and C lie in that order on a horizontal straight line, with AB=BC=3 m. A vertical pole of positive height has its base P on…
- Question 15For each real number k, consider the equation (3x^2+4x+1)/(x^2+1)=k. What is the sum of all the values of k for which this equation has…
- Question 16A positive integer n has exactly six positive divisors, including 1 and n. The sum of these six divisors is 434. What is the sum of all…
- Question 17The sequence with nth term u_n=2^n-1 can be generated by starting with 1 and repeatedly doubling the previous term and adding 1. A student…
- Question 18The points A=(1,2) and B=(4,6) are adjacent vertices of a square. The centre of the square has x-coordinate less than 1. What are the…
- Question 19The function f is a quadratic polynomial. The tangent to y=f(x) at the point where x=1 has equation y=2x+1. It is also given that ∫_0^2…
- Question 20For each real number x, let m(x) be the smaller of the two numbers (x-1)^2+2 10-(x+1)^2. What is the greatest possible value of m(x)?