Mathematics Paper 1 November 1999

$ABCD$ is a rhombus whose diagonals meet at $O$.

State the number of lines of symmetry of the rhombus.

$ABCD$ is a rhombus whose diagonals meet at $O$.

State the order of rotational symmetry of the rhombus.

$ABCD$ is a rhombus whose diagonals meet at $O$.

State the size, in degrees, of $A\hat{O}B$.

A solid rectangular block measuring 6 m $\times$ 5 m $\times$ 2 m is made up of metal whose density is 7 850 kg/m$^3$.

Find the mass of the block in tonnes.

The cost of 5 rulers is \$11,25. The cost of 3 rulers and a pen is \$9,35.

Calculate the cost, in dollars, of a ruler.

The cost of 5 rulers is \$11,25. The cost of 3 rulers and a pen is \$9,35.

Calculate the cost, in dollars, of a pen.

The minimum temperatures recorded in degrees Celsius on six consecutive days were as follows:

$$6, \quad 3, \quad -2, \quad 6, \quad -1, \quad 0.$$

Write down the lowest temperature recorded, in °C.

The minimum temperatures recorded in degrees Celsius on six consecutive days were as follows:

$$6, \quad 3, \quad -2, \quad 6, \quad -1, \quad 0.$$

Write down the modal temperature, in °C.

The minimum temperatures recorded in degrees Celsius on six consecutive days were as follows:

$$6, \quad 3, \quad -2, \quad 6, \quad -1, \quad 0.$$

Calculate the median temperature, in °C.

Solve the simultaneous equations

$$3x + 2y = -14,$$
$$3x - 5y = 56.$$

Give the value of $x$.

Solve the simultaneous equations

$$3x + 2y = -14,$$
$$3x - 5y = 56.$$

Give the value of $y$.

The exchange rate on a certain day was 3,8 dollars for 1 rand.

Calculate the equivalent of 150 rands in dollars.

The exchange rate on a certain day was 3,8 dollars for 1 rand.

Calculate the equivalent of 304 dollars in rands.

In the diagram, $Q$ is due north of $R$. $PQR$ is an isosceles triangle with $PQ = PR$ and $Q\hat{P}R = 36°$.

Calculate, giving the answer in three figure notation, the bearing of $Q$ from $P$.

In the diagram, $Q$ is due north of $R$. $PQR$ is an isosceles triangle with $PQ = PR$ and $Q\hat{P}R = 36°$.

Calculate, giving the answer in three figure notation, the bearing of $P$ from $R$.

In the diagram, $Q$ is due north of $R$. $PQR$ is an isosceles triangle with $PQ = PR$ and $Q\hat{P}R = 36°$.

Calculate reflex $Q\hat{P}R$, in degrees.

The scale on a map is such that 6 cm on the map represents 1,5 km on the ground.

Calculate the length, in kilometres, of a road which measures 42 cm on the map.

The scale on a map is such that 6 cm on the map represents 1,5 km on the ground.

Calculate the area on the map, in square centimetres, that represents a lake of area 8 km$^2$.

The diagram shows points $P(4, 8)$, $Q(9, 3)$ and $S(12, 10)$.

Write down $\overrightarrow{PQ}$ in column vector form.

The diagram shows points $P(4, 8)$, $Q(9, 3)$ and $S(12, 10)$.

Write down the coordinates of the point $R$ such that $PQRS$ is a parallelogram.

The diagram shows points $P(4, 8)$, $Q(9, 3)$ and $S(12, 10)$.

Write down the coordinates of the point $T$, the image of $S$ under a clockwise rotation of $90°$ about $P$.

Measured correct to the nearest centimetre, the sides of a kite are 15 cm and 12 cm.

Find the smallest possible perimeter, in centimetres, of the kite.

Two of the angles of a pentagon are $3x°$ and $11x°$ respectively. Their sum is $168°$.

Calculate the size, in degrees, of the smaller of the two angles.

Two of the angles of a pentagon are $3x°$ and $11x°$ respectively. Their sum is $168°$.

Calculate the size, in degrees, of the larger of the two angles.

Two of the angles of a pentagon are $3x°$ and $11x°$ respectively. Their sum is $168°$.

Given that the remaining three angles are in the ratio $3 : 4 : 5$, calculate the size, in degrees, of the largest of these angles.

In the diagram $D\hat{B}C = 90°$, $A\hat{D}B = B\hat{D}C$, $AD = 15$ cm, $DB = 8$ cm and $DC = 10$ cm.

Calculate $BC$, in centimetres.

In the diagram $D\hat{B}C = 90°$, $A\hat{D}B = B\hat{D}C$, $AD = 15$ cm, $DB = 8$ cm and $DC = 10$ cm.

Find $\cos B\hat{D}C$.

In the diagram $D\hat{B}C = 90°$, $A\hat{D}B = B\hat{D}C$, $AD = 15$ cm, $DB = 8$ cm and $DC = 10$ cm.

Calculate $AB^2$, in square centimetres.

The matrix $\begin{pmatrix} 30 & 0 \\ 0 & \frac{15x}{4} \end{pmatrix}$ represents an enlargement with the origin as centre.

Find the value of $x$.

The matrix $\begin{pmatrix} y^2 & 2 \\ 18 & 1 \end{pmatrix}$ is singular.

Calculate the two possible values of $y$.

A bus left Bulawayo for Kwekwe with 60 passengers. It passes through Gweru (its only stop) where it picked up 27 passengers and dropped off $n$ passengers.

Write down, in terms of $n$, the number of passengers in the bus as it left Gweru.

A bus left Bulawayo for Kwekwe with 60 passengers. It passes through Gweru (its only stop) where it picked up 27 passengers and dropped off $n$ passengers.

Given that it arrived in Kwekwe with $2n$ passengers, find the value of $n$.

A bus left Bulawayo for Kwekwe with 60 passengers. It passes through Gweru (its only stop) where it picked up 27 passengers and dropped off 29 passengers.

Did the bus gain or lose passengers in Gweru?

A cyclist starts a 30 km journey at 09 00. She maintains an average speed of 20 km/h for the first three-quarters of an hour and then rests. Subsequently she continues her journey at an average speed of 25 km/h, arriving at her destination at 11 00.

Calculate the distance, in kilometres, covered in the first three-quarters of an hour.

A cyclist starts a 30 km journey at 09 00. She maintains an average speed of 20 km/h for the first three-quarters of an hour and then rests. Subsequently she continues her journey at an average speed of 25 km/h, arriving at her destination at 11 00.

Calculate, in hours, the time taken to cover the last part of the journey.

A cyclist starts a 30 km journey at 09 00. She maintains an average speed of 20 km/h for the first three-quarters of an hour and then rests. Subsequently she continues her journey at an average speed of 25 km/h, arriving at her destination at 11 00.

Calculate, in minutes, the duration of her rest.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Write down $\log_{10} 50$ correct to 4 decimal places.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Evaluate $\log_{10} 5$, giving your answer correct to 4 decimal places.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Evaluate $\log_{10} 25$, giving your answer correct to 4 decimal places.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Evaluate $\log_{10} 2$, giving your answer correct to 3 decimal places.

In this question take $\pi$ to be 3,14.

The diagram shows the right angled triangle $ABC$. The sector $AQRS$ is drawn inside it such that $BRC$ is a tangent to the sector at $R$. Given that $AB = 15$ cm, $AC = 20$ cm and $BC = 25$ cm, calculate the area, in square centimetres, of the triangle $ABC$.

In this question take $\pi$ to be 3,14.

The diagram shows the right angled triangle $ABC$. The sector $AQRS$ is drawn inside it such that $BRC$ is a tangent to the sector at $R$. Given that $AB = 15$ cm, $AC = 20$ cm and $BC = 25$ cm, calculate the radius, $AR$, in centimetres, of the sector $AQRS$.

In this question take $\pi$ to be 3,14.

The diagram shows the right angled triangle $ABC$. The sector $AQRS$ is drawn inside it such that $BRC$ is a tangent to the sector at $R$. Given that $AB = 15$ cm, $AC = 20$ cm and $BC = 25$ cm, calculate the area, in square centimetres, of the shaded region.

$ABCD$ is a rhombus whose diagonals meet at $O$.

State the number of lines of symmetry of the rhombus.

$ABCD$ is a rhombus whose diagonals meet at $O$.

State the order of rotational symmetry of the rhombus.

$ABCD$ is a rhombus whose diagonals meet at $O$.

State the size, in degrees, of $A\hat{O}B$.

A solid rectangular block measuring 6 m $\times$ 5 m $\times$ 2 m is made up of metal whose density is 7 850 kg/m$^3$.

Find the mass of the block in tonnes.

The cost of 5 rulers is \$11,25. The cost of 3 rulers and a pen is \$9,35.

Calculate the cost, in dollars, of a ruler.

The cost of 5 rulers is \$11,25. The cost of 3 rulers and a pen is \$9,35.

Calculate the cost, in dollars, of a pen.

The minimum temperatures recorded in degrees Celsius on six consecutive days were as follows: 6, 3, -2, 6, -1, 0.

Write down the lowest temperature recorded, in °C.

The minimum temperatures recorded in degrees Celsius on six consecutive days were as follows: 6, 3, -2, 6, -1, 0.

Write down the modal temperature, in °C.

The minimum temperatures recorded in degrees Celsius on six consecutive days were as follows: 6, 3, -2, 6, -1, 0.

Calculate the median temperature, in °C.

Solve the simultaneous equations $3x + 2y = -14$ and $3x - 5y = 56$.

Give the value of $x$.

Solve the simultaneous equations $3x + 2y = -14$ and $3x - 5y = 56$.

Give the value of $y$.

The exchange rate on a certain day was 3,8 dollars for 1 rand.

Calculate the equivalent of 150 rands in dollars.

The exchange rate on a certain day was 3,8 dollars for 1 rand.

Calculate the equivalent of 304 dollars in rands.

In the diagram, $Q$ is due north of $R$. $PQR$ is an isosceles triangle with $PQ = PR$ and $Q\hat{P}R = 36°$.

Calculate, giving the answer in three figure notation, the bearing of $Q$ from $P$.

In the diagram, $Q$ is due north of $R$. $PQR$ is an isosceles triangle with $PQ = PR$ and $Q\hat{P}R = 36°$.

Calculate, giving the answer in three figure notation, the bearing of $P$ from $R$.

In the diagram, $Q$ is due north of $R$. $PQR$ is an isosceles triangle with $PQ = PR$ and $Q\hat{P}R = 36°$.

Calculate reflex $Q\hat{P}R$, in degrees.

The scale on a map is such that 6 cm on the map represents 1,5 km on the ground.

Calculate the length, in kilometres, of a road which measures 42 cm on the map.

The scale on a map is such that 6 cm on the map represents 1,5 km on the ground.

Calculate the area on the map, in square centimetres, that represents a lake of area 8 km$^2$.

The diagram shows points $P(4, 8)$, $Q(9, 3)$ and $S(12, 10)$.

Write down $\overrightarrow{PQ}$ in column vector form.

The diagram shows points $P(4, 8)$, $Q(9, 3)$ and $S(12, 10)$.

Write down the coordinates of the point $R$ such that $PQRS$ is a parallelogram.

The diagram shows points $P(4, 8)$, $Q(9, 3)$ and $S(12, 10)$.

Write down the coordinates of the point $T$, the image of $S$ under a clockwise rotation of $90°$ about $P$.

Measured correct to the nearest centimetre, the sides of a kite are 15 cm and 12 cm.

Find the smallest possible perimeter, in centimetres, of the kite.

Two of the angles of a pentagon are $3x°$ and $11x°$ respectively. Their sum is $168°$.

Calculate the size, in degrees, of the smaller of the two angles.

Two of the angles of a pentagon are $3x°$ and $11x°$ respectively. Their sum is $168°$.

Calculate the size, in degrees, of the larger of the two angles.

Two of the angles of a pentagon are $3x°$ and $11x°$ respectively, with sum $168°$, and the remaining three angles are in the ratio $3 : 4 : 5$.

Calculate the size, in degrees, of the largest of these three angles.

In the diagram $D\hat{B}C = 90°$, $A\hat{D}B = B\hat{D}C$, $AD = 15$ cm, $DB = 8$ cm and $DC = 10$ cm.

Calculate $BC$, in centimetres.

In the diagram $D\hat{B}C = 90°$, $A\hat{D}B = B\hat{D}C$, $AD = 15$ cm, $DB = 8$ cm and $DC = 10$ cm.

Find $\cos B\hat{D}C$.

In the diagram $D\hat{B}C = 90°$, $A\hat{D}B = B\hat{D}C$, $AD = 15$ cm, $DB = 8$ cm and $DC = 10$ cm.

Calculate $AB^2$, in square centimetres.

The matrix $\begin{pmatrix} 30 & 0 \\ 0 & \frac{15x}{4} \end{pmatrix}$ represents an enlargement with the origin as centre.

Find the value of $x$.

The matrix $\begin{pmatrix} y^2 & 2 \\ 18 & 1 \end{pmatrix}$ is singular.

Calculate the two possible values of $y$.

A bus left Bulawayo for Kwekwe with 60 passengers. It passes through Gweru (its only stop) where it picked up 27 passengers and dropped off $n$ passengers.

Write down, in terms of $n$, the number of passengers in the bus as it left Gweru.

A bus left Bulawayo for Kwekwe with 60 passengers. It passes through Gweru (its only stop) where it picked up 27 passengers and dropped off 29 passengers.

Did the bus gain or lose passengers in Gweru?

A cyclist starts a 30 km journey at 09 00. She maintains an average speed of 20 km/h for the first three-quarters of an hour and then rests. Subsequently she continues her journey at an average speed of 25 km/h, arriving at her destination at 11 00.

Calculate the distance, in kilometres, covered in the first three-quarters of an hour.

A cyclist starts a 30 km journey at 09 00. She maintains an average speed of 20 km/h for the first three-quarters of an hour (covering 15 km) and then rests. Subsequently she continues her journey at an average speed of 25 km/h to complete the remaining distance, arriving at her destination at 11 00.

Calculate, in hours, the time taken to cover the last part of the journey.

A cyclist starts a 30 km journey at 09 00, covering the first three-quarters of an hour (15 km) at 20 km/h before resting, then covering the remaining 15 km at 25 km/h (taking 0,6 hours), arriving at her destination at 11 00.

Calculate, in minutes, the duration of her rest.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Write down $\log_{10} 50$ correct to 4 decimal places.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Evaluate $\log_{10} 5$, giving your answer correct to 4 decimal places.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Evaluate $\log_{10} 25$, giving your answer correct to 4 decimal places.

It is given that $\log_{10} 50 = 1,69897$ correct to five decimal places.

Evaluate $\log_{10} 2$, giving your answer correct to 3 decimal places.

In this question take $\pi$ to be 3,14.

The diagram shows the right angled triangle $ABC$. Given that $AB = 15$ cm, $AC = 20$ cm and $BC = 25$ cm, calculate the area, in square centimetres, of the triangle $ABC$.

In this question take $\pi$ to be 3,14.

The diagram shows the right angled triangle $ABC$. The sector $AQRS$ is drawn inside it, centred at $A$, such that $BRC$ is a tangent to the sector at $R$ on $BC$. Given that $AB = 15$ cm, $AC = 20$ cm and $BC = 25$ cm, calculate the radius, $AR$, in centimetres, of the sector $AQRS$.

In this question take $\pi$ to be 3,14.

The right angled triangle $ABC$ has $AB = 15$ cm, $AC = 20$ cm and $BC = 25$ cm (area 150 cm2), with the right angle at $A$. The sector $AQRS$, centred at $A$ with radius 12 cm, is tangent to $BC$ at $R$.

Calculate the area, in square centimetres, of the shaded region (the triangle minus the sector).