tmua.me Medium Set C Paper 1
20 questions · 75 min · Difficulty 47 · by tmua.me
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Questions in this paper
- Question 1A map has scale 1:25 000. It is enlarged so that every length on the new map is 20\% greater than the corresponding length on the original…
- Question 2The function f is defined by f(x)=x^2+ax+b, where a and b are real constants. It satisfies f(0)=f(4) f(f(1))=1. What is the sum of all…
- Question 3A point P lies on the curve y=√(x), x>0. The normal to the curve at P meets the x-axis at (dfrac92,0). What is the y-coordinate of P?
- Question 4A circular sector with centre O has area 24π cm^2. The length of its curved arc from A to B is 8π cm. What is the length of the straight…
- Question 5The points A and B have coordinates (0,0) and (5,0), respectively. There are two points on the line y=x/2 whose distance from A is twice…
- Question 6A sequence is defined by u_1=2 and u_(n+1)=√(u_n^2+5) (n≥1). What is the least value of n for which u_n>8?
- Question 7The function f is defined by f(x)=ax^2+bx+c, where a, b and c are real constants; a is allowed to be zero. For every real number x…
- Question 8A coin has a fixed probability of landing heads, and successive tosses are independent. The probability that two tosses give different…
- Question 9When a polynomial P(x) is divided by x^2-x-1, the remainder is 3x+2. What is the remainder when (x-1)P(x) is divided by x^2-x-1?
- Question 10Triangle ABC has AB=6 and area 18. The points M and N are the midpoints of BC and CA, respectively, and AM is perpendicular to BN. What is…
- Question 11The function F is defined by F(x)=∫_0^x (t^2-2t) dt, -1≤ x≤4. Which of the following describes the range of F?
- Question 12A sequence is defined by u_1=3, u_(n+1)=u_n(u_n+1) (n≥1). Let M=u_(10). Which of the following is equal to frac1u_1+1+fr…
- Question 13A list of eight numbers has mean 10 and range 12. The smallest number is accidentally recorded a second time. The resulting list of nine…
- Question 14The angle θ satisfies π/2<θ<π and 3sin^2θ+4sinθcosθ=4cos^2θ. What is the value of frac1sinθcosθ ?
- Question 15For which values of the real constant a does x^2+(1)/(x^2)-2a(x+(1)/(x))+6a-3≥0 hold for every positive real number x?
- Question 16In trapezium ABCD, the sides AB and DC are parallel, with AB=6, DC=2. The points E and F lie on AD and BC, respectively. The segment EF is…
- Question 17For each real number a, the curve C_a has equation y=frac14x^4-frac32x^2+ax, 0≤ x≤3. Let M(a) be the greatest absolute value of the…
- Question 18The polynomial P is defined by P(x)=(x+2)^5. What is the coefficient of x^2 in (1-x)P(2x-1)?
- Question 19A positive divisor d of 360 is chosen at random, with every positive divisor equally likely. What is the probability that the highest…
- Question 20For a real constant a, consider the equation | x^2-a|=| x-2|. What is the sum of all values of a for which this equation has exactly three…