Rosie's Papers Set A Paper 1
20 questions · 75 min · Difficulty 47 · by Rosie's Papers
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Questions in this paper
- Question 1A geometric series with n terms is denoted by S, where S=i+i^2+i^3+…+i^n, and i=√(-1). Find an expression for the sum of all the unique…
- Question 2lfloor xrfloor is defined as the greatest integer less than or equal to x, e.g. lfloor6.7rfloor=6, lfloor5rfloor=5, lfloorπrfloor=3. Hence…
- Question 3A group of 6 students, 4 girls and 2 boys, are sat around a circular table discussing how much they hate Stats. How many ways can the…
- Question 4Find the product of all the real roots of the equation x^4-4x^2+2=0.
- Question 5Given that function f satisfies 3f(x)+2f((x+2)/(x-1))=x+2, x∈mathbb R and x≠1. Find the value of f(4).
- Question 6Find the simplified value given by the below sum, where x is in degrees. Σ_(x=1)^(90)cos4x.
- Question 7Two circles, C_1 and C_2, are defined below: C_1:x^2+y^2=8, C_2:x^2+y^2-6x+8y=-22. Find the shortest distance between them.
- Question 8The curve below is shown roughly between 0≤ x≤2π. The curve passes through (0,0), (π,0) and (2π,0). It is also strictly bounded between…
- Question 9f(x) is given by f(x)=ax^b-cx^d, where b and d are positive integers with b<d, and f(x) is also given to have these below properties: ∫_0^1…
- Question 10A function f(x) is defined by f(x)=x^2-4x. A real constant c with 0<c<4 satisfies the equation ∫_0^c f(x) dx=∫_c^4 f(x) dx. Hence find the…
- Question 11It is given that the expression dfrac3√[3]4-1 can be rewritten as √[3]a+√[3]b+1. Hence find the sum of a and b.
- Question 12How many solutions does (sin x+cos x)cos^2x=0 have in the domain 0≤ x≤π?
- Question 13Find the coefficient of xy^2z^3 in the expansion of (7x+2y+3z)^6.
- Question 14A student taking the S.T.E.P. maths exam asks n of their friends also sitting the exam what they think they'll get on the first paper and…
- Question 15A line with equation y=mx+c, where m>0, and a curve with equation y=x^2+2 both lie on the xy plane, with the line being a tangent to the…
- Question 16A recurrence relation is given by x_(n+1)=(x_n^2+1)/(2), where x_1=0.75. Choose the closest estimate to x_(1000).
- Question 17A student named James Chen is approximating the value of the below integral using the Trapezium rule with n strips. ∫_0^2 x^3-3x^2 dx. The…
- Question 18A circle C has a radius of r and is centred at the origin (0,0). A fixed point P lies outside the circle at the coordinates (d,0), where…
- Question 19A polynomial P(x) leaves a remainder of 3 when divided by (x-1), and a remainder of -1 when divided by (x+3). Let R(x) be the remainder…
- Question 20An arithmetic progression has a non-zero common difference d. The 1st term, 4th term and the 10th term of this arithmetic progression form…