Mathematics Paper 1 June 1999

A playing field is in the shape of a regular polygon, each of whose sides is of length 50 m. Themba starts at the centre of one side of the field and walks along all of the sides of the field until he arrives back at his starting point. He turns through $45°$ at each corner of the field.

Calculate the total number of turns he makes.

A playing field is in the shape of a regular polygon, each of whose sides is of length 50 m. Themba starts at the centre of one side of the field and walks along all of the sides of the field until he arrives back at his starting point. He turns through $45°$ at each corner of the field.

Calculate the total distance, in metres, that he walks.

A motorist began a journey at 10 45. The journey took him 2 hours 21 minutes.

Find the time when he arrived, in 24-hour notation.

A motorist began a journey at 10 45. The journey took him 2 hours 21 minutes.

Given that he drove at an average speed of 100 km/h, calculate the distance, in kilometres, that he drove.

In the diagram, $AD$ is the diameter of the circle $ABCD$. Chords $BC$ and $CD$ are equal and $C\hat{A}B = 33°$. The side $CD$ is produced to $E$.

Calculate $B\hat{A}D$, in degrees.

In the diagram, $AD$ is the diameter of the circle $ABCD$. Chords $BC$ and $CD$ are equal and $C\hat{A}B = 33°$. The side $CD$ is produced to $E$.

Calculate $B\hat{C}D$, in degrees.

In the diagram, $AD$ is the diameter of the circle $ABCD$. Chords $BC$ and $CD$ are equal and $C\hat{A}B = 33°$. The side $CD$ is produced to $E$.

Calculate $A\hat{D}E$, in degrees.

At the beginning of an examination the clock in the examination room was set to read 2 p.m. The examination ended at 5 p.m.

Find the angle, in degrees, through which the hour hand turns during the examination.

At the beginning of an examination the clock in the examination room was set to read 2 p.m. The examination ended at 5 p.m.

Find the angle, in degrees, through which the minute hand turns during the examination.

The table shows the results of the games played by the Gweru Giraffes last season and the points awarded in the League Table.

Given that they gained a total of 108 points, calculate the value of $x$.

The table shows the results of the games played by the Gweru Giraffes last season and the points awarded in the League Table.

The Chinhoyi Cheetahs played the same number of games as the Gweru Giraffes. They drew 6 games and won twice as many games as they lost. Calculate the number of points they gained.

The following notice was displayed at an airport.

Temperatures (°C) at Air Zimbabwe International Destinations. Date: 3/1/99.

At which destination was the lowest temperature recorded?

The following notice was displayed at an airport.

Temperatures (°C) at Air Zimbabwe International Destinations. Date: 3/1/99.

At which destination was the greatest range of temperatures recorded?

The following notice was displayed at an airport.

Temperatures (°C) at Air Zimbabwe International Destinations. Date: 3/1/99.

On 4th January the minimum temperature recorded in Frankfurt was 3 °C lower than on 3rd January. Calculate the minimum temperature, in °C, in Frankfurt on 4th January.

All the lengths on a scale drawing are one eighth of their actual lengths.

Calculate the actual length, in centimetres, of a line represented by a line 5,6 cm long on the scale drawing.

All the lengths on a scale drawing are one eighth of their actual lengths.

Calculate the area, in square centimetres, on the scale drawing which represents an actual area of 896 cm$^2$.

The circle $ACD$ has centre $O$ and radius 13 cm. The chord $ABC$ is perpendicular to the straight line $DOB$ and has a total length $AC = 24$ cm.

Calculate the length, in centimetres, of $OB$.

The circle $ACD$ has centre $O$ and radius 13 cm. The chord $ABC$ is perpendicular to the straight line $DOB$ and has a total length $AC = 24$ cm.

Write down, as a fraction, the value of $\cos A\hat{O}D$.

A man estimates that each side of a square floor has a length of 4 metres, correct to the nearest metre.

Find the difference, in square metres, between the largest and smallest possible calculated values of the area of the floor.

Take $\pi$ to be $\frac{22}{7}$.

The diagram shows a pattern used in dressmaking. It consists of six equal circles of radius 3,5 cm inscribed in a rectangle. The sides of the rectangle are tangents to the circles which touch other circles as shown.

Calculate the area, in square centimetres, of the rectangle.

Take $\pi$ to be $\frac{22}{7}$.

The diagram shows a pattern used in dressmaking. It consists of six equal circles of radius 3,5 cm inscribed in a rectangle. The sides of the rectangle are tangents to the circles which touch other circles as shown.

Calculate the area, in square centimetres, of the shaded region.

In the diagram, $ABCD$ and $EFCD$ are parallelograms on the same base $DC$ and between the parallel lines $DC$ and $ABEF$. $DC = 5$ cm, $AD = 12$ cm, $FC = 10$ cm and $E\hat{D}C = 53°$.

Using as much of the information given below as is necessary, calculate the area, in square centimetres, of the parallelogram $EFCD$.

[$\sin 53° = 0,80$; $\cos 53° = 0,60$; $\tan 53° = 1,33$.]

In the diagram, $ABCD$ and $EFCD$ are parallelograms on the same base $DC$ and between the parallel lines $DC$ and $ABEF$. $DC = 5$ cm, $AD = 12$ cm, $FC = 10$ cm and $E\hat{D}C = 53°$.

Using as much of the information given below as is necessary, calculate $\sin B\hat{C}D$, in its lowest terms.

[$\sin 53° = 0,80$; $\cos 53° = 0,60$; $\tan 53° = 1,33$.]

The diagram shows the graph of $f(x) = (2x - 1)(x - 2)(x + 3)$.

Find the coordinates of $A$.

The diagram shows the graph of $f(x) = (2x - 1)(x - 2)(x + 3)$.

Find the coordinates of $B$.

The diagram shows the graph of $f(x) = (2x - 1)(x - 2)(x + 3)$.

The point $P(-2, m)$ lies on the curve. Calculate the value of $m$.

A survey is carried out to find the number of minutes each member of a class takes to finish a multiple choice test. The diagram is an incomplete histogram used to illustrate the results of the survey.

Another way to represent the same information is shown below.

Find the value of $x$.

A survey is carried out to find the number of minutes each member of a class takes to finish a multiple choice test.

Write down the modal time interval.

The strength, $S$, of a beam of metal varies jointly as the square of its depth, $D$, and the inverse of its length, $L$.

Given that $S = 18$ when $D = 3$ and $L = 5$, find the value of $k$, the constant of variation.

The strength, $S$, of a beam of metal varies jointly as the square of its depth, $D$, and the inverse of its length, $L$, so that $S = \frac{kD^2}{L}$ with $k = 10$.

Calculate the value of $D$ when $S = 20$ and $L = 6$, leaving your answer in surd form.

In the diagram, $P$, $Q$ and $R$ represent points on level ground with $PQ = 30$ m, $PR = 24$ m, $P\hat{R}Q = 87°$ and $Q\hat{P}R = 40°$. The bearing of $Q$ from $P$ is $042°$.

Use as much of the information given below as is necessary.

Calculate the bearing of $R$ from $Q$.

[$\sin 42° = 0,67$; $\cos 42° = 0,74$; $\tan 42° = 0,90$.]

In the diagram, $P$, $Q$ and $R$ represent points on level ground with $PQ = 30$ m, $PR = 24$ m, $P\hat{R}Q = 87°$ and $Q\hat{P}R = 40°$. The bearing of $Q$ from $P$ is $042°$.

Calculate how far, in metres, $Q$ is north of $P$.

[$\sin 42° = 0,67$; $\cos 42° = 0,74$; $\tan 42° = 0,90$.]

In the diagram, $P$, $Q$ and $R$ represent points on level ground with $PQ = 30$ m, $PR = 24$ m, $P\hat{R}Q = 87°$ and $Q\hat{P}R = 40°$.

$R$ is the base of a vertical mast $RT$. The angle of elevation of the top of the mast, $T$, from $P$ is also $42°$. Calculate the height, in metres, of the mast $RT$.

[$\sin 42° = 0,67$; $\cos 42° = 0,74$; $\tan 42° = 0,90$.]

In 1999 a television set had a marked price of \$7370,00.

Mr Mogo paid cash and was allowed 15% discount. Calculate the discount, in dollars.

In 1999 a television set had a marked price of \$7370,00.

Mr Dube bought the television set through a lay-by scheme. In this scheme he paid an initial deposit of $\frac{5}{8}$ of the marked price and then 3 equal monthly instalments, before he collected the television set. Calculate each monthly instalment, in dollars.

In 1999 a television set had a marked price of \$7370,00.

The marked price in 1999 was a result of a 10% increase over the marked price of the previous year. Calculate the marked price, in dollars, of the television set in 1998.

Consider the pattern of numbers shown in the incomplete table below.

Write down the value of $x$.

Consider the pattern of numbers shown in the incomplete table below.

Express $y$ in terms of $n$.

The table below shows the first lines of a pattern.

Write down the sum of the terms in line 30 of the table.

A playing field is in the shape of a regular polygon, each of whose sides is of length 50 m. Themba starts at the centre of one side of the field and walks along all of the sides of the field until he arrives back at his starting point. He turns through $45°$ at each corner of the field.

Calculate the total number of turns he makes.

A playing field is in the shape of a regular polygon, each of whose sides is of length 50 m. Themba starts at the centre of one side of the field and walks along all of the sides of the field until he arrives back at his starting point, turning through $45°$ at each corner.

Calculate the total distance, in metres, that he walks.

A motorist began a journey at 10 45. The journey took him 2 hours 21 minutes.

Find the time when he arrived, in 24-hour notation.

A motorist began a journey at 10 45. The journey took him 2 hours 21 minutes.

Given that he drove at an average speed of 100 km/h, calculate the distance, in kilometres, that he drove.

In the diagram, $AD$ is the diameter of the circle $ABCD$. Chords $BC$ and $CD$ are equal and $C\hat{A}B = 33°$. The side $CD$ is produced to $E$.

Calculate $B\hat{A}D$, in degrees.

In the diagram, $AD$ is the diameter of the circle $ABCD$. Chords $BC$ and $CD$ are equal and $C\hat{A}B = 33°$. The side $CD$ is produced to $E$.

Calculate $B\hat{C}D$, in degrees.

In the diagram, $AD$ is the diameter of the circle $ABCD$. Chords $BC$ and $CD$ are equal and $C\hat{A}B = 33°$. The side $CD$ is produced to $E$.

Calculate $A\hat{D}E$, in degrees.

The following notice was displayed at an airport.

Temperatures (°C) at Air Zimbabwe International Destinations. Date: 3/1/99.

At which destination was the lowest temperature recorded?

The following notice was displayed at an airport.

Temperatures (°C) at Air Zimbabwe International Destinations. Date: 3/1/99.

At which destination was the greatest range of temperatures recorded?

The following notice was displayed at an airport.

Temperatures (°C) at Air Zimbabwe International Destinations. Date: 3/1/99.

On 4th January the minimum temperature recorded in Frankfurt was 3 °C lower than on 3rd January. Calculate the minimum temperature, in °C, in Frankfurt on 4th January.

All the lengths on a scale drawing are one eighth of their actual lengths.

Calculate the actual length, in centimetres, of a line represented by a line 5,6 cm long on the scale drawing.

All the lengths on a scale drawing are one eighth of their actual lengths.

Calculate the area, in square centimetres, on the scale drawing which represents an actual area of 896 cm$^2$.

The circle $ACD$ has centre $O$ and radius 13 cm. The chord $ABC$ is perpendicular to the straight line $DOB$ and has a total length $AC = 24$ cm.

Calculate the length, in centimetres, of $OB$.

The circle $ACD$ has centre $O$ and radius 13 cm. The chord $ABC$ is perpendicular to the straight line $DOB$ and has a total length $AC = 24$ cm.

Write down, as a fraction, the value of $\cos A\hat{O}D$.

A man estimates that each side of a square floor has a length of 4 metres, correct to the nearest metre.

Find the difference, in square metres, between the largest and smallest possible calculated values of the area of the floor.

Take $\pi$ to be $\frac{22}{7}$.

The diagram shows a pattern used in dressmaking. It consists of six equal circles of radius 3,5 cm inscribed in a rectangle, arranged three across and two down, with each circle touching its neighbours and the sides of the rectangle.

Calculate the area, in square centimetres, of the rectangle.

Take $\pi$ to be $\frac{22}{7}$.

Six equal circles of radius 3,5 cm are inscribed in a rectangle of area 294 cm2, arranged so that each circle touches its neighbours and the sides of the rectangle.

Calculate the area, in square centimetres, of the region of the rectangle not covered by the circles.

In the diagram, $ABCD$ and $EFCD$ are parallelograms on the same base $DC$ and between the parallel lines $DC$ and $ABEF$. $DC = 5$ cm, $AD = 12$ cm, $FC = 10$ cm and $E\hat{D}C = 53°$.

[$\sin 53° = 0,80$; $\cos 53° = 0,60$; $\tan 53° = 1,33$.]

Calculate the area, in square centimetres, of the parallelogram $EFCD$.

In the diagram, $ABCD$ and $EFCD$ are parallelograms on the same base $DC$ and between the parallel lines $DC$ and $ABEF$. $DC = 5$ cm, $AD = 12$ cm, $FC = 10$ cm and $E\hat{D}C = 53°$.

[$\sin 53° = 0,80$; $\cos 53° = 0,60$; $\tan 53° = 1,33$.]

Calculate $\sin B\hat{C}D$, in its lowest terms.

The diagram shows the graph of $f(x) = (2x - 1)(x - 2)(x + 3)$, which crosses the x-axis at three points, the leftmost of which is labelled $A$.

Find the coordinates of $A$.

The diagram shows the graph of $f(x) = (2x - 1)(x - 2)(x + 3)$. The curve crosses the y-axis at the point $B$.

Find the coordinates of $B$.

The diagram shows the graph of $f(x) = (2x - 1)(x - 2)(x + 3)$. The point $P(-2, m)$ lies on the curve.

Calculate the value of $m$.

A survey is carried out to find the number of minutes each member of a class takes to finish a multiple choice test, summarised in the table below.

Given that 39 pupils took the test, find the value of $x$.

A survey of a class's times (in minutes) to finish a multiple choice test gave the following frequency table.

Write down the modal time interval.

The strength, $S$, of a beam of metal varies jointly as the square of its depth, $D$, and the inverse of its length, $L$, so that $S = \frac{kD^2}{L}$.

Given that $S = 18$ when $D = 3$ and $L = 5$, find the value of $k$, the constant of variation.

The strength, $S$, of a beam of metal varies jointly as the square of its depth, $D$, and the inverse of its length, $L$, so that $S = \frac{kD^2}{L}$ with $k = 10$.

Calculate the value of $D$ when $S = 20$ and $L = 6$, leaving your answer in surd form.

In the diagram, $P$, $Q$ and $R$ represent points on level ground with $PQ = 30$ m, $PR = 24$ m, $P\hat{R}Q = 87°$ and $Q\hat{P}R = 40°$. The bearing of $Q$ from $P$ is $042°$.

[$\sin 42° = 0,67$; $\cos 42° = 0,74$; $\tan 42° = 0,90$.]

Calculate the bearing of $R$ from $Q$.

In the diagram, $P$, $Q$ and $R$ represent points on level ground with $PQ = 30$ m, $PR = 24$ m, $P\hat{R}Q = 87°$ and $Q\hat{P}R = 40°$. The bearing of $Q$ from $P$ is $042°$.

[$\sin 42° = 0,67$; $\cos 42° = 0,74$; $\tan 42° = 0,90$.]

Calculate how far, in metres, $Q$ is north of $P$.

In the diagram, $P$, $Q$ and $R$ represent points on level ground with $PQ = 30$ m, $PR = 24$ m, $P\hat{R}Q = 87°$ and $Q\hat{P}R = 40°$. $R$ is the base of a vertical mast $RT$. The angle of elevation of the top of the mast, $T$, from $P$ is also $42°$.

[$\sin 42° = 0,67$; $\cos 42° = 0,74$; $\tan 42° = 0,90$.]

Calculate the height, in metres, of the mast $RT$.

In 1999 a television set had a marked price of \$7370,00.

Mr Mogo paid cash and was allowed 15% discount. Calculate the discount, in dollars.

In 1999 a television set had a marked price of \$7370,00.

Mr Dube bought the television set through a lay-by scheme. He paid an initial deposit of $\frac{5}{8}$ of the marked price and then 3 equal monthly instalments, before he collected the television set. Calculate each monthly instalment, in dollars.

In 1999 a television set had a marked price of \$7370,00. This marked price was a result of a 10% increase over the marked price of the previous year.

Calculate the marked price, in dollars, of the television set in 1998.

Consider the pattern of numbers shown in the incomplete table below.

Write down the value of $x$.

Consider the pattern of numbers shown in the incomplete table below.

Express $y$ in terms of $n$.

The table below shows the first lines of a pattern.

Write down the sum of the terms in line 30 of the table.