NSMQ 2024 Mathematics Fundamentals Round

Given that two circles with the given equations touch each other externally, find the radius R.

Find the coordinates of the stationary points of the given curve.

Solve the compound linear inequality.

Find the largest value and the least value of…

Express Y in terms of X, assuming θ is acute given…

Find the equation of a curve with gradient dy/dx and passing through A(1, 5).

Simplify…

Find the coordinates of the points of intersection of the quadratic curve and the line.

Find the area in terms of π of the circle with the given equation.

Find the length of the side of a rhombus if the diagonals have lengths…

Solve for real x.

Find the equation of the circle touching the x-axis and passing through the points…

A linear transformation T: (X, Y) → (2X+3Y, 2X−3Y). Find the coordinates of P…

Find the constants A and B…

Find the inverse of the function f(x).

A binary operation m * n = m√2 + n√5. Evaluate…

Find the values of the constants A, B, and C given…

Find an equation in x and y from the given parametric equations.

Find a natural number N such that…

Solve the quadratic inequality.

Find the image of point A when reflected in the point P(2, 1).

Find the exact value of the given expression.

Find the equation of the circle touching the y-axis and passing through the points…

Find the least value and the greatest value of the quadratic expression.

Find the area of the region between two concentric circles of radii R₁ and R₂.

Find the equation of a straight line in intercept form with x-intercept A and y-intercept B.

Factorise completely the cubic expression.

Find the least value and the greatest value of the quadratic expression.

Find the equation of the perpendicular bisector of line segment AB.

How many three-letter arrangements can be made from A, B, C, D, E, F, G, H if…

Solve the logarithmic equation for x.

Find coordinates of a point on the curve at which the gradient has the given value.

Find the coordinates of the point of inflection of the given curve.

Simplify…

Committee of 3 from 5 girls and 3 boys. Find the probability…

Solve the radical equation.

Find the volume of the frustum formed by rotating y = f(x) from x=1 to x=2.

Express B in terms of A, given A and B are positive and distinct.

Biased coin tossed thrice. P(H) = 5/9. Find the probability of…

Solve for real X given…

Find the least and greatest value of the expression and the corresponding x values.

y = x² − 2x − 3. Find x values where graph is strictly between x-axis and the line…

Evaluate sin 2A given A is obtuse and…

Find constants A and B in the velocity function V(t)…

Find the greatest value and the least value of the given expression.

Find the equation of the locus of P(x, y) equidistant from A and B.

Solve the trig equation for x in the interval 0 < x < π.

Find A and B given the cubic polynomial is divisible by a perfect square factor.

Find the equation of the curve with gradient dy/dx passing through A.

Given that… evaluate the trig expression.

Find the coordinates of the stationary points of the given curve.

Solve the simultaneous logarithmic equations for x and y.

Solve the absolute value equation.

Point A is reflected in line L to point B. Find the equation of L.

Solve the logarithmic equation for x.

Bag: 5 black, 4 white, 3 red balls. Two drawn without replacement. Find probability.

sin A = 4/5, sin B = 5/13. Find sin(A+B) given conditions on A and B.

Find the area of an isosceles triangle…

Find dy/dx from the implicit equation…

Find the sum of all coefficients in the binomial expansion of…

Side of cube increasing at 0.1 cm/s. Find rate of increase of volume.

Find all three-digit palindromic numbers…

Find the locus of P(x, y) equidistant from an axis and a point.

Find the solution set of the rational inequality.

Solve the cubic inequality.

Solve the simultaneous exponential equations.

Find the length of the tangent from P to the circle.

Find the solution set of the compound inequality.

Find B, C, D of the cubic with a stationary point at P and inflection at Q.

Completely identify the curve defined by the parametric equations.

Find the matrix product of a 3×2 and a 2×3 matrix.

Find the number of possible mappings from A into B.

Express the given number as a difference of two squares.

Find the equation of a quadratic curve y = A(x-h)² + k with a stationary point at…

Find U₃, U₄, U₅ of the sequence defined by the recurrence relation.

Find the cubic curve whose gradient dy/dx = 3x² - 2Ax + B.

Cubic y = Ax³ + Bx² + Cx + D has stationary P and inflection Q. Find constants.

Find all possible real roots of the given equation.

Find the product of the first n terms of the given series.

Solve the cubic inequality.

Solve for a natural number N from the given equation.

Evaluate the definite integral.

Find the gradient of the curve at the given point.

Find the completely factorised equation of a cubic curve with…

Find x and y given trig conditions and 0 < x, y < π/3.