Practice 20 questions on MATH1101 - Specialist Mathematics at Mount Lawley Senior High School. Free AI-generated quiz on uNotes — track your score, retake anytime.
1In a cyclic quadrilateral ABCD, if the angle $\angle DAB = 70^{\circ}$, what is the measure of the opposite angle $\angle BCD$?
2When proving that opposite angles of a cyclic quadrilateral are supplementary, which fundamental circle theorem is directly applied to relate angles at the circumference to angles at the center?
3A tangent DE touches a circle at point C. A chord AC is drawn. If $\angle DCA = 70^{\circ}$, what is the measure of the angle in the alternate segment, $\angle ABC$?
4Points P, Q, and R lie on a circle with centre O. If the minor angle $\angle POR = 150^{\circ}$, what is the measure of $\angle PQR$?
5From an external point P, a tangent PA of length 12 cm is drawn to a circle. A secant PB intersects the circle at D and B, such that PD = 8 cm. Determine the length of the chord BD.
6For what value of $\beta$ are the vectors $(4, -6)$ and $(3, \beta)$ perpendicular?
7Particle A has velocity $\mathbf{v}_A = (2\mathbf{i} - 5\mathbf{j})$ m/s and particle B has velocity $\mathbf{v}_B = (-3\mathbf{i} + \mathbf{j})$ m/s. What is the velocity of A relative to B?
8A particle C is moving with velocity $(8\mathbf{i} - 3\mathbf{j})$ m/s. What is its exact speed?
9For a trapezium OPQR with $OP = \mathbf{a}$ and $PQ = \mathbf{b}$, and $|OR| = k|PQ|$, the scalar product of the diagonals $\vec{OQ} \cdot \vec{PR}$ is given by $k|\mathbf{b}|^2 - |\mathbf{a}|^2 + (k-1)\mathbf{a} \cdot \mathbf{b}$. If the trapezium is a parallelogram (i.e., $k=1$) and $\mathbf{a} = \mathbf{i} + \mathbf{j}$ and $\mathbf{b} = 3\mathbf{i} - 2\sqrt{2}\mathbf{j}$, what is the value of this scalar product?
10Particle A is moving with velocity $\mathbf{u} = (-5\mathbf{i} + 9\mathbf{j})$ m/s and particle B is moving with velocity $\mathbf{v} = (3\mathbf{i} + 4\mathbf{j})$ m/s. What is the cosine of the angle between their velocities?
