ZIMSEC O Level Mathematics Paper 1 November 2001

Question 101

[1 marks]Number

Evaluate, giving your answer as a common fraction in its lowest terms:

\frac{3}{4} + \frac{1}{5}

Answer this when you sit the paper.

Question 102

[1 marks]Number

Evaluate, giving your answer as a common fraction in its lowest terms:

\frac{5}{8} \times \frac{22}{45}

Answer this when you sit the paper.

Question 103

[1 marks]Number

Evaluate, giving your answer as a common fraction in its lowest terms:

\frac{1}{3} \div \frac{11}{24}

Answer this when you sit the paper.

Question 201

[1 marks]Fractions, Decimals & Percentages

Find 15% of $270.

Answer this when you sit the paper.

Question 202

[2 marks]Change of Units

Express 93 m as a decimal fraction of 3 km.

Answer this when you sit the paper.

Question 301

[1 marks]Number

Calculate, in decimal form, the exact value of

0,02 \times 0,6

Answer this when you sit the paper.

Question 302

[1 marks]Number

Calculate, in decimal form, the exact value of

\sqrt{0,000004}

Answer this when you sit the paper.

Question 303

[1 marks]Directed numbers

Calculate, in decimal form, the exact value of

5,6 - 7,3

Answer this when you sit the paper.

Question 401

[1 marks]Laws of Indices

Evaluate

32^{\frac{3}{5}}

Answer this when you sit the paper.

Question 402

[1 marks]Laws of Indices

Evaluate

3^4 \times 3^0

Answer this when you sit the paper.

Question 403

[1 marks]Laws of Indices

Given that

5^x = 125

, find the value of

x

Answer this when you sit the paper.

Question 501

[1 marks]Algebra

x = m + n

and

y = m - n

, express

3x + 2y

in terms of

m

and

n

Answer this when you sit the paper.

Question 502

[2 marks]Algebra

Factorise completely

5r^2 - 5rt + qr - qt

Answer this when you sit the paper.

Question 601

[1 marks]Circle Geometry

A

B

C

D

and

E

are points on a circle. Given that

AB = BC = CD

D\hat{A}E = 24°

and

A\hat{E}B = 17°

, find

E\hat{C}D

Answer this when you sit the paper.

Question 602

[1 marks]Circle Geometry

A

B

C

D

and

E

are points on a circle. Given that

AB = BC = CD

D\hat{A}E = 24°

and

A\hat{E}B = 17°

, find

B\hat{E}D

Answer this when you sit the paper.

Question 603

[1 marks]Circle Geometry

A

B

C

D

and

E

are points on a circle. Given that

AB = BC = CD

D\hat{A}E = 24°

and

A\hat{E}B = 17°

, find

B\hat{A}E

Answer this when you sit the paper.

Question 701

[1 marks]Approximations & Estimations

Express 0,0148 correct to one significant figure.

Answer this when you sit the paper.

Question 702

[2 marks]Approximations & Estimations

The sides of a rectangle are 15 cm and 7 cm measured correct to the nearest centimetre. Find the smallest possible area of the rectangle, in square centimetres.

Answer this when you sit the paper.

Question 801

[1 marks]Inequalities

Solve the inequality

4 + 3x < 25

Answer this when you sit the paper.

Question 802

[1 marks]Algebra

Expand

x^2y(x^4 - xy^3)

Answer this when you sit the paper.

Question 803

[1 marks]Ordinary & Standard Form

Express 37 100 in standard form.

Answer this when you sit the paper.

Question 901

[1 marks]Number Bases

Evaluate

341_5 - 23_5

, giving your answer in base 5.

Answer this when you sit the paper.

Question 902

[1 marks]Time

Jabulani completed a track event in 16,45 minutes. Express this time in minutes and seconds.

Answer this when you sit the paper.

Question 903

[1 marks]Time

Jabulani completed a track event in 16 minutes 27 seconds. If Farai took 1 minute 56 seconds longer than Jabulani, calculate the time he took to complete the event.

Answer this when you sit the paper.

Question 1001

[1 marks]Ratios, Rates & Proportions

A bus has 80 passengers consisting of adults and school children. Given that the ratio of the adults to school children is 2 : 3, calculate the number of adults on the bus.

Answer this when you sit the paper.

Question 1002

[2 marks]Ratios, Rates & Proportions

A bus has 80 passengers consisting of adults and school children, in the ratio 2 : 3. Adult passengers pay $15 while school children pay half the fare. Calculate the total amount paid by the passengers.

Answer this when you sit the paper.

Question 1101

[1 marks]Sets

There are 25 children in a class. Of these, 9 are in the debating club and 13 are in the history club.

\xi

= {children in the class},

D

= {children in the debating club},

H

= {children in the history club} and

n(D \cap H) = 5

. Find the number of children in the debating club only.

Answer this when you sit the paper.

Question 1102

[1 marks]Sets

There are 25 children in a class. Of these, 9 are in the debating club and 13 are in the history club.

\xi

= {children in the class},

D

= {children in the debating club},

H

= {children in the history club} and

n(D \cap H) = 5

. Find

n(D \cup H)

Answer this when you sit the paper.

Question 1103

[1 marks]Sets

There are 25 children in a class.

D

= {children in the debating club},

H

= {children in the history club}. Express in set notation the children who are in neither the debating club nor the history club.

Answer this when you sit the paper.

Question 1201

[3 marks]Algebra

It is given that

C = a + KN^2

. Find the two possible values of

N

given that

C = 102

a = 27

and

K = 3

Answer this when you sit the paper.

Question 1301

[1 marks]Consumer Arithmetic

An incomplete water bill for a household shows: previous reading (14 May) 5992,4, present reading (27 June) 6034,6, rate 350 cents/unit. Find the value of

x

, the consumption in units.

Answer this when you sit the paper.

Question 1302

[1 marks]Consumer Arithmetic

A household's water consumption was 42,2 units at a rate of 350 cents/unit. Find the value of

y

, the cost of the water in dollars.

Answer this when you sit the paper.

Question 1303

[1 marks]Consumer Arithmetic

A household's water bill has a water charge of $147,70 and a fixed charge of $50,00. Find the value of

z

, the total amount due.

Answer this when you sit the paper.

Question 1401

[1 marks]Statistics & Probability

In a survey, the adults in a literacy class were each asked their shoe size. The bar chart of results shows: size 5 - 6 adults, size 6 - 9 adults, size 7 - 3 adults, size 8 - 2 adults, size 9 - 1 adult. State the mode of the distribution.

Answer this when you sit the paper.

Question 1402

[1 marks]Statistics & Probability

Answer this when you sit the paper.

Question 1403

[1 marks]Statistics & Probability

Answer this when you sit the paper.

Question 1501

[1 marks]Polygons, Symmetry & Circles

In the diagram,

AB

and

BC

are adjacent sides of a regular

n

-sided polygon, and

AB

and

BD

are adjacent sides of a square. The side

AB

is produced to

E

. Given that

A\hat{B}C = 15x°

and

C\hat{B}E = 3x°

, calculate the exterior angle of the

n

-sided polygon, in degrees.

Answer this when you sit the paper.

Question 1502

[1 marks]Polygons, Symmetry & Circles

In the diagram,

AB

and

BC

are adjacent sides of a regular

n

-sided polygon, and

AB

and

BD

are adjacent sides of a square. The side

AB

is produced to

E

. Given that

A\hat{B}C = 15x°

and

C\hat{B}E = 3x°

, calculate the value of

n

Answer this when you sit the paper.

Question 1503

[1 marks]Polygons, Symmetry & Circles

In the diagram,

AB

and

BC

are adjacent sides of a regular

n

-sided polygon, and

AB

and

BD

are adjacent sides of a square. The side

AB

is produced to

E

. Given that

A\hat{B}C = 15x°

and

C\hat{B}E = 3x°

, calculate reflex

C\hat{B}D

, in degrees.

Answer this when you sit the paper.

Question 1601

[1 marks]Functional Notation

Given that

f(x) = x(x - 6)

and

f(1) = k

, find the value of

k

Answer this when you sit the paper.

Question 1602

[1 marks]Logarithms

\log 3 = m

and

\log 8 = n

, express

\log 9

in terms of

m

Answer this when you sit the paper.

Question 1603

[1 marks]Logarithms

\log 3 = m

and

\log 8 = n

, express

\log 2\frac{2}{3}

in terms of

m

and

n

Answer this when you sit the paper.

Question 1701

[1 marks]Algebra

A rod consists of two parts,

x

metres and

y

centimetres long, where

x

and

y

are whole numbers. Write down, in terms of

x

and

y

, an expression for the length of the rod in centimetres.

Answer this when you sit the paper.

Question 1702

[1 marks]Algebra

A rod consists of two parts,

x

metres and

y

centimetres long (both whole numbers). If the length of the rod is 244 cm, state the value of

x

Answer this when you sit the paper.

Question 1703

[1 marks]Algebra

A rod consists of two parts,

x

metres and

y

centimetres long (both whole numbers). If the length of the rod is 244 cm, state the value of

y

Answer this when you sit the paper.

Question 1801

[3 marks]Trigonometry, Bearing & Distances

The diagram shows triangle

ABC

with

AB = 4x

cm,

BC = 6

cm and

A\hat{B}C = 30°

. Given that the area of the triangle is 15 cm

^2

, find the value of

x

. [sin 30° = 0,5; cos 30° = 0,87; tan 30° = 0,58]

Answer this when you sit the paper.

Question 1901

[1 marks]Functional Graphs

The unshaded region A in the diagram is defined by four inequalities, three of which are

y \ge 1

x + 3y \le 12

and

y \le x

. Write down the fourth inequality.

Answer this when you sit the paper.

Question 1902

[2 marks]Functional Graphs

The unshaded region A in the diagram is defined by the inequalities

y \ge 1

x + 3y \le 12

y \le x

and

x + y \le 8

. Find the least value of

3x + 4y

, given that

x

and

y

satisfy the inequalities.

Answer this when you sit the paper.

Question 2001

[2 marks]Statistics & Probability

The table below gives the changes in the number of jobs in three industries for the period January 1991 to January 1992 in a certain town: Food -91, Retail -152, Electronics +186. Calculate the mean change in the number of jobs for the three industries.

Answer this when you sit the paper.

Question 2002

[1 marks]Statistics & Probability

The change in the number of jobs in the food industry from January 1991 to January 1992 was -91. Given that there were 150 jobs as at January 1991 in the food industry, calculate the number of jobs as at January 1992.

Answer this when you sit the paper.

Question 2003

[1 marks]Statistics & Probability

The change in the number of jobs in the retail industry from January 1991 to January 1992 was -152. Given that there were 286 jobs as at January 1992 in the retail industry, calculate the number of jobs as at January 1991.

Answer this when you sit the paper.

Question 2101

[1 marks]Polygons, Symmetry & Circles

ABCD

is a rhombus whose diagonals meet at

O

. State the size of

A\hat{O}B

in degrees.

Answer this when you sit the paper.

Question 2102

[2 marks]Polygons, Symmetry & Circles

ABCD

is a rhombus whose diagonals meet at

O

. Given that

BD = 10

cm and

AC = 24

cm, calculate

AD

Answer this when you sit the paper.

Question 2103

[1 marks]Circle Geometry

ABCD

is a rhombus whose diagonals meet at

O

, with

BD = 10

cm,

AC = 24

cm and

AD = 13

cm. State the radius of the circle that passes through

A

O

and

D

Answer this when you sit the paper.

Question 2201

[1 marks]Geometrical Transformation

In the diagram, rectangle

PQRS

is transformed onto rectangle

TUVW

by an enlargement, centre

O

and scale factor

1\frac{1}{2}

PQ = 6

cm and the area of rectangle

TUVW

is 117 cm

^2

. Calculate the length of

TU

Answer this when you sit the paper.

Question 2202

[2 marks]Geometrical Transformation

In the diagram, rectangle

PQRS

is transformed onto rectangle

TUVW

by an enlargement, centre

O

and scale factor

1\frac{1}{2}

PQ = 6

cm and the area of rectangle

TUVW

is 117 cm

^2

. Calculate the area of rectangle

PQRS

Answer this when you sit the paper.

Question 2203

[1 marks]Matrices

Rectangle

PQRS

is transformed onto rectangle

TUVW

by an enlargement, centre

O(0;0)

and scale factor

1\frac{1}{2}

. Write down the matrix representing the enlargement.

Answer this when you sit the paper.

Question 2301

[1 marks]Vector Geometry

It is given that

\vec{OP} = 9a + 5b

. Express

5\vec{OP}

in terms of

a

and

b

Answer this when you sit the paper.

Question 2302

[3 marks]Vector Geometry

It is given that

\vec{OP} = 9a + 5b

. Given that

\frac{3h}{4}a + (h-k)b = \vec{OP}

, find the value of

h

and the value of

k

Answer this when you sit the paper.

Question 2501

[1 marks]Functional Graphs

The diagram shows the graph of the quadratic curve

y = -x^2 + 6x - 5

. State the maximum value of

y

Answer this when you sit the paper.

Question 2502

[1 marks]Functional Graphs

The diagram shows the graph of the quadratic curve

y = -x^2 + 6x - 5

. State the equation of the line of symmetry of the curve.

Answer this when you sit the paper.

Question 2503

[1 marks]Functional Graphs

The curve

y = -x^2 + 6x - 5

cuts the

y

-axis at

P(0;-5)

. Find the coordinates of

P_1

, the image of

P

on the graph, under a reflection in the line of symmetry

x = 3

Answer this when you sit the paper.

Question 2504

[2 marks]Functional Graphs

Write down the equation whose roots are at the intersection of the graphs

y = -x + 5

and

y = -x^2 + 6x - 5

Answer this when you sit the paper.

Question 2601

[1 marks]Trigonometry, Bearing & Distances

In the diagram,

AB

is parallel to

DC

AD = 3,3

cm,

DC = 6

cm and

BC = 10

cm.

A\hat{B}C = 16°

and

D\hat{A}C = 90°

. Find

\sin A\hat{C}D

leaving the answer as a proper fraction.

Answer this when you sit the paper.

Question 2602

[1 marks]Trigonometry, Bearing & Distances

In the diagram,

AB

is parallel to

DC

AD = 3,3

cm,

DC = 6

cm and

BC = 10

cm.

A\hat{B}C = 16°

and

D\hat{A}C = 90°

. Name an angle which is equal to

A\hat{C}D

Answer this when you sit the paper.

Question 2603

[3 marks]Trigonometry, Bearing & Distances

In the diagram,

AB

is parallel to

DC

AD = 3,3

cm,

DC = 6

cm and

BC = 10

cm.

A\hat{B}C = 16°

and

D\hat{A}C = 90°

. Calculate

AC

. [sin16° = 0,28; cos16° = 0,96; tan16° = 0,29]

Answer this when you sit the paper.

Question 2701

[3 marks]Measures & Mensuration

In this question take

\pi

to be

\frac{22}{7}

. A solid sphere of radius

10\frac{1}{2}

cm is made of a metal alloy. Given that 1 cm

^3

of the alloy has a mass of 5 g, find the mass of the sphere in kilograms. [Volume of sphere

= \frac{4}{3}\pi r^3

]

Answer this when you sit the paper.

Question 2702

[3 marks]Measures & Mensuration

A solid sphere of radius

10\frac{1}{2}

cm and mass 24,255 kg is melted and used, without waste, to make a length of wire. Given that the wire is a circular cylinder of radius 0,07 cm, find its length in metres. (Take

\pi = \frac{22}{7}

Answer this when you sit the paper.

Mathematics Paper 1 November 2001

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 302

Question 303

Question 401

Question 402

Question 403

Question 501

Question 502

Question 601

Question 602

Question 603

Question 701

Question 702

Question 801

Question 802

Question 803

Question 901

Question 902

Question 903

Question 1001

Question 1002

Question 1101

Question 1102

Question 1103

Question 1201

Question 1301

Question 1302

Question 1303

Question 1401

Question 1402

Question 1403

Question 1501

Question 1502

Question 1503

Question 1601

Question 1602

Question 1603

Question 1701

Question 1702

Question 1703

Question 1801

Question 1901

Question 1902

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2203

Question 2301

Question 2302

Question 2501

Question 2502

Question 2503

Question 2504

Question 2601

Question 2602

Question 2603

Question 2701

Question 2702

More sittings of this paper

The answers, and why they are the answers

Sit this paper online