Ten-Year-Series (TYS) Solutions | Past Year Exam Questions

1994 A Level H2 Math

These Ten-Year-Series (TYS) worked solutions with video explanations for 1994 A Level H2 Mathematics are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.

Select Year
1994 A Level H2 Math Paper 1 Question 14

In the diagram, $O$ is centre of the square base $ABCD$ of a right pyramid, vertex $V$. Perpendicular unit vectors $\mathbf{i}$, $\mathbf{j}$, $\mathbf{k}$ are parallel to $AB$, $AD$, $OV$ respectively. The length of $AB$ is 4 units and the length of $OV$ is $2h$ units. $P$, $Q$, $M$ and $N$ are mid-points of $AB$, $BC$, $CV$ and $VA$ respectively. The point $O$ is taken as the origin for position vectors.

1994 TYS 1994

(i)

Show that the equation of the line $PM$ may be expressed as $\mathbf{r}=\left( \begin{matrix} 0 \\ -2 \\ 0 \\
\end{matrix} \right)+t\left( \begin{matrix} 1 \\ 3 \\ h \\
\end{matrix} \right)$, where $t$ is a parameter.

[2]

(i) Show that the equation of the line $PM$ may be expressed as $\mathbf{r}=\left( \begin{matrix} 0 \\ -2 \\ 0 \\
\end{matrix} \right)+t\left( \begin{matrix} 1 \\ 3 \\ h \\
\end{matrix} \right)$, where $t$ is a parameter.

[2]

(ii)

Find the equation for the line $QN$.

[2]

(ii) Find the equation for the line $QN$.

[2]

(iii)

Show that the lines $PM$ and $QN$ intersect, and that the position vector $\overrightarrow{OX}$ of their point of intersection is $\left( \begin{matrix}
\frac{1}{2} \\
-\frac{1}{2} \\
\frac{1}{2}h \\
\end{matrix} \right)$.

[3]

(iii) Show that the lines $PM$ and $QN$ intersect, and that the position vector $\overrightarrow{OX}$ of their point of intersection is $\left( \begin{matrix}
\frac{1}{2} \\
-\frac{1}{2} \\
\frac{1}{2}h \\
\end{matrix} \right)$.

[3]

(iv)

Given that $OX$ is perpendicular to $VB$, find the value of $h$ and calculate the acute angle between $PM$ and $QN$, giving your answer correct to the nearest $0.1{}^\circ $.

[4]

(iv) Given that $OX$ is perpendicular to $VB$, find the value of $h$ and calculate the acute angle between $PM$ and $QN$, giving your answer correct to the nearest $0.1{}^\circ $.

[4]

Suggested Handwritten and Video Solutions

1994 TYS 1994

1994 TYS 1994

1994 TYS 1994

1994 TYS 1994

1994 TYS 1994

1994 TYS 1994

1994 TYS 1994

1994 TYS 1994

Share with your friends!

WhatsApp
Telegram
Facebook

H2 Math Free Mini Course

1994 TYS 1994

Sign up for the free mini course and experience learning with us for 30 Days!

Register for FREE H2 Math Mini-course
1994 TYS 1994
Play Video

Join us to gain access to our Question Bank, Student Learning Portal, Recorded Lectures and many more.