tmua.me Medium Set B Paper 1
20 questions · 75 min · Difficulty 40 · by tmua.me
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Questions in this paper
- Question 1The function f is defined by f(x)=2x^2-3x+1. A real number a satisfies f(a+1)-f(a)=9. What is the value of f(a-1)-f(a)?
- Question 2A jug contains 900 mL of a drink made from concentrate and water in the volume ratio 1:4. The drink is mixed thoroughly, and 300 mL is…
- Question 3The line 3x+4y=15 meets the circle x^2+y^2=25 at A and B. The point O is the origin. What is the area of triangle OAB?
- Question 4In the expansion of (1+x)^5(1+ax), where a is a real constant, the coefficient of x^2 is zero. What is the coefficient of x^3?
- Question 5What is the sum of all the positive real solutions of (x^2-3x)^2=2x^2-6x+8 ?
- Question 6A drone is at a point T vertically above a point O on horizontal ground. Points A and B lie on a straight line on the ground, with A…
- Question 7A cubic polynomial f satisfies f'(0)=f'(4)=9 f(4)-f(0)=4. What is the positive difference between the x-coordinates of the two stationary…
- Question 8Eight cards are numbered 1,2,3,…,8. Two cards are selected at random without replacement, with every pair equally likely. Given that the…
- Question 9The curve y=frac(x-1)^2√(x), x>0, and the lines x=1, x=4 and y=0 bound a region. What is the area of this region?
- Question 10Triangle ABC is right-angled at C. The perpendicular from C to AB meets AB at D, where AD=9 and DB=16. What is the area of triangle ABC?
- Question 11For which real values of k does the equation x^2-kx+k=0 have two distinct real roots, both satisfying 0<x<4?
- Question 12A geometric progression has positive terms u_1,u_2,u_3,… and satisfies u_1+u_2+u_3=21, u_4+u_5+u_6=168. What is the value of…
- Question 13The angles α and β satisfy 0<α<β<fracπ2, sinα+cosα=sinβ+cosβ, tanα+tanβ=4. What is the value of sinβ-sinα?
- Question 14The length and width of a rectangle, each rounded to the nearest centimetre, are 12 cm and 8 cm respectively. What is the least integer N…
- Question 15The function f is defined by f(x)=(x^2+2x+5)/(x^2+2x+2), -3<x<0. Which inequality describes the complete set of values of y=f(x)?
- Question 16The vertices A, B, C and D of a convex quadrilateral lie, in that order, on a circle. Its side lengths are AB=3, BC=4, CD=5, DA=6. What is…
- Question 17A histogram represents journey times t, in minutes. Its classes and frequency densities are shown below, where k>0. c|ccc Journey time & 0≤…
- Question 18During the first 3 minutes after a tap is opened, the volume of water in a tank is modelled by V(t)=t^3+3, where V is measured in litres…
- Question 19The numbers a_0,a_1,…,a_9 are defined by (1+x)^9=a_0+a_1x+…+a_9x^9. Which of the following is equal to a_0a_1+a_1a_2+…+a_8a_9 ?
- Question 20The real numbers x and y satisfy x^2+y^2=13, x^3+y^3=35. What is the sum of all the distinct possible values of xy?