ZIMSEC O Level Mathematics Paper 2 November 2014

Question 101

[2 marks]Number, L.C.M, Number Bases and Time

Simplify

3,27 \times 0,59

, giving the answer correct to three significant figures.

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Question 102

[3 marks]Number, L.C.M, Number Bases and Time

Find the Lowest Common Multiple (L.C.M) of 72 and 96.

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Question 103

[3 marks]Number, L.C.M, Number Bases and Time

Express

10111_2

as a number in base 5.

A $103_5$
B $23_5$
C $34_5$
D $43_5$

Question 104

[2 marks]Number, L.C.M, Number Bases and Time

A train that is scheduled to arrive in Bulawayo at 0027 is delayed by 3 hours 47 minutes. Find the time, on the 24 hour clock, at which it arrives in Bulawayo.

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Question 201

[3 marks]Equations, Factorisation and Algebraic Fractions

Solve the equation

\dfrac{2}{x} - \dfrac{1}{4} = \dfrac{3}{5x}

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Question 202

[2 marks]Equations, Factorisation and Algebraic Fractions

Factorise completely

7x^3 - 28x

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Question 203

[3 marks]Equations, Factorisation and Algebraic Fractions

Factorise completely

3y^2 - 5y + 2

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Question 204

[3 marks]Equations, Factorisation and Algebraic Fractions

Express

\dfrac{x+2}{2x-3} - \dfrac{1}{x}

as a single fraction in its simplest form.

A $\frac{x+1}{x^2-3x}$
B $\frac{x^2+3}{2x^2-3x}$
C $\frac{x^2-3}{2x^2-3x}$
D $\frac{x^2+4x-3}{2x^2-3x}$

Question 301

[3 marks]Approximations and Sets

A rectangle measures 8 cm by 6 cm to the nearest centimetre. Calculate the least possible value of the area of the rectangle, in square centimetres.

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Question 302

[2 marks]Approximations and Sets

The universal set is

\xi = \{x : 8 < x \le 16,\ x \text{ is an integer}\}

and

A = \{x : x \text{ is a square number}\}

. List all the elements of

A

A $\{9; 12; 16\}$
B $\{9; 16\}$
C $\{10; 12; 14; 16\}$
D $\{4; 9; 16\}$

Question 303

[2 marks]Approximations and Sets

The universal set is

\xi = \{x : 8 < x \le 16,\ x \text{ is an integer}\}

and

B = \{x : x \text{ is an even number}\}

. Find

n(B)

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Question 304

[3 marks]Approximations and Sets

The universal set is

\xi = \{x : 8 < x \le 16,\ x \text{ is an integer}\}

A = \{x : x \text{ is a square number}\}

and

B = \{x : x \text{ is an even number}\}

. Find the number of elements of

\xi

that belong to neither

A

nor

B

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Question 401

[2 marks]Similarity and Variation

In the diagram,

\triangle LMN

is right-angled at L and LP is an altitude drawn to NM. Which pair of triangles is similar to

\triangle LMN

A $\triangle LPM$ and $\triangle PMN$
B $\triangle NPL$ and $\triangle NLM$
C $\triangle NPL$ and $\triangle LPM$
D $\triangle NPL$ and $\triangle NPM$

Question 402

[3 marks]Similarity and Variation

In the diagram,

\triangle LMN

is right-angled at L and LP is an altitude. PN = 9 cm and LM = 6 cm. Find PM, in centimetres.

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Question 403

[2 marks]Similarity and Variation

The annual premium,

P

dollars, for a funeral insurance scheme varies jointly as the square root of the age,

Y

years, and the number of dependants,

D

, of the applicant. A 25 year old applicant with 6 dependants pays $150,00 a year. Find the constant of variation.

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Question 404

[3 marks]Similarity and Variation

The annual premium,

P

dollars, for a funeral insurance scheme varies jointly as the square root of the age,

Y

years, and the number of dependants,

D

, of the applicant. A 25 year old applicant with 6 dependants pays $150,00 a year. Calculate the monthly premium, in dollars, for a 49 year old applicant with 4 dependants.

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Question 501

[3 marks]Consumer Arithmetic

Mrs Shoko erects a durawall around her rectangular stand measuring 20 m by 11 m. Three metres are to be left for a gate. Find the perimeter of the durawall, in metres.

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Question 502

[2 marks]Consumer Arithmetic

A durawall 59 m long is to be built. A contractor charges $12 per metre on a fix-and-supply basis. Calculate the total cost, in dollars, of engaging the contractor.

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Question 503

[3 marks]Consumer Arithmetic

To build a durawall Mrs Shoko buys 5 000 bricks at $80,00 for every 1 000, ten 50 kg bags of cement at $10 per bag, 5 bundles of brick force at $5 per bundle and 2 loads of pit sand at $30 per load. She also engages a builder who charges $100 for the job. Calculate her total cost, in dollars.

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Question 504

[2 marks]Consumer Arithmetic

Mrs Shoko can erect her durawall either by engaging a contractor, at a total cost of $708,00, or by buying materials and paying a builder, at a total cost of $685,00. She uses the cheaper of the two. Calculate the amount, in dollars, that she saves.

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Question 601

[2 marks]Constructions and Loci

A triangular field PQR has PQ = 30 m,

P\hat{Q}R = 60^\circ

and

R\hat{P}Q = 45^\circ

. Calculate the size, in degrees, of

Q\hat{R}P

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Question 602

[3 marks]Constructions and Loci

A triangular field PQR has PQ = 30 m,

P\hat{Q}R = 60^\circ

and

R\hat{P}Q = 45^\circ

. Calculate the length of QR, in metres, correct to three significant figures.

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Question 603

[3 marks]Constructions and Loci

A triangular field PQR has PQ = 30 m,

P\hat{Q}R = 60^\circ

and

R\hat{P}Q = 45^\circ

. Calculate the length of PR, in metres, correct to three significant figures.

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Question 604

[2 marks]Constructions and Loci

A triangular field PQR is to be drawn to a scale of 1 cm to represent 3 m. The side PQ measures 30 m on the ground. Find the length, in centimetres, that PQ must be drawn.

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Question 701

[2 marks]Measures and Mensuration

A farmer has a square orchard of side 10 m. He extends it by increasing the length of one side by

x

metres and the other by

2x

metres, as in the diagram. Which expression gives the area, in square metres, of the extension alone?

A $2x^2 + 30x$
B $2x^2 + 30x + 100$
C $2x^2 + 20x$
D $3x^2 + 30x$

Question 702

[3 marks]Measures and Mensuration

Solve the equation

2x^2 + 30x - 87,5 = 0

A $x = 2,5$ or $x = 17,5$
B $x = -2,5$ or $x = 17,5$
C $x = 3,5$ or $x = -12,5$
D $x = 2,5$ or $x = -17,5$

Question 703

[2 marks]Measures and Mensuration

A square orchard of side 10 m is extended by increasing one side by

x

metres and the other by

2x

metres. Given that

x = 2,5

, write down the actual length, in metres, of the longer side of the extended orchard.

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Question 704

[3 marks]Measures and Mensuration

A square orchard of side 10 m is extended by increasing one side by

x

metres and the other by

2x

metres, where

x = 2,5

. Calculate the total area, in square metres, of the extended orchard.

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Question 801

[3 marks]Geometrical Transformation

Describe fully the single transformation represented by the matrix

\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}

AA rotation through $180^\circ$ about the origin
BA reflection in the $x$ -axis
CA rotation through $90^\circ$ anticlockwise about the origin
DA reflection in the line $y = x$

Question 802

[3 marks]Geometrical Transformation

Triangle PQR has vertices P(1; 1), Q(3; 4) and R(4; 0). It is mapped onto triangle

P_1Q_1R_1

by the transformation whose matrix is

\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}

. Find the coordinates of

Q_1

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Question 803

[3 marks]Geometrical Transformation

Triangle PQR has vertices P(1; 1), Q(3; 4) and R(4; 0). It is mapped onto triangle

P_2Q_2R_2

by the translation

\begin{pmatrix} 5 \\ -2 \end{pmatrix}

followed by the transformation whose matrix is

\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}

. Find the coordinates of

P_2

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Question 804

[2 marks]Geometrical Transformation

Triangle PQR has vertices P(1; 1), Q(3; 4) and R(4; 0). Calculate its area, in square units.

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Question 901

[2 marks]Statistics and Probability

In one week a University library lent out 30 Geography books, 45 Science books, 25 Maths books, 20 Shona books and 60 Theory of Education books. Find the total number of books borrowed in that week.

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Question 902

[2 marks]Statistics and Probability

In one week a University library lent out 30 Geography books, 45 Science books, 25 Maths books, 20 Shona books and 60 Theory of Education books. Express the number of Theory of Education books as a fraction, in its lowest terms, of all the books borrowed.

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Question 903

[3 marks]Statistics and Probability

In one week a University library lent out 30 Geography books, 45 Science books, 25 Maths books, 20 Shona books and 60 Theory of Education books. These five figures are to be shown as sectors of a circle. Calculate the angle, in degrees, of the sector representing Theory of Education.

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Question 904

[3 marks]Statistics and Probability

A University library lent out 180 books in one week: 30 Geography, 45 Science, 25 Maths, 20 Shona and 60 Theory of Education. Two students each borrowed one of these books, and the book taken by the first student was no longer available to the second. Calculate the probability that the first student borrowed a Science book and the second a Maths book. Give the answer as a fraction in its lowest terms.

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Question 1001

[2 marks]Travel Graphs

The velocity,

v

m/s, of a moving body at time

t

seconds is given by

v = t^2 - 3t + 5

. In a list of values of

v

, the entry at

t = 0

m

and the entry at

t = 4

n

. Find the value of

m

and the value of

n

A $m = 3$ and $n = 11$
B $m = 5$ and $n = 9$
C $m = 0$ and $n = 9$
D $m = 5$ and $n = 7$

Question 1002

[3 marks]Travel Graphs

The velocity,

v

m/s, of a moving body at time

t

seconds is given by

v = t^2 - 3t + 5

, for

0 \le t \le 7

. Find the values of

t

at which

v = 4

, each correct to one decimal place.

A $t = 0,6$ and $t = 2,4$
B $t = 1,5$ and $t = 3,5$
C $t = 0,4$ and $t = 2,6$
D $t = 1,0$ and $t = 2,0$

Question 1003

[2 marks]Travel Graphs

The velocity,

v

m/s, of a moving body at time

t

seconds is given by

v = t^2 - 3t + 5

. Find the acceleration, in m/s squared, when

t = 3

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Question 1004

[3 marks]Travel Graphs

The velocity,

v

m/s, of a moving body at time

t

seconds is given by

v = t^2 - 3t + 5

. Estimate the distance, in metres, travelled by the body from

t = 4

t = 6

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Question 1101

[2 marks]Polygons, Bearings and Trigonometry

A regular polygon has an interior angle that is twice the exterior angle. Find the number of sides of the polygon.

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Question 1102

[2 marks]Polygons, Bearings and Trigonometry

A regular polygon has an interior angle that is twice the exterior angle. Find the sum, in degrees, of the interior angles of the polygon.

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Question 1103

[3 marks]Polygons, Bearings and Trigonometry

In the diagram, A, B, C and D lie on level ground and ABC is a straight road running west to east. AD = BD = 9 km and

A\hat{B}D = 40^\circ

. Calculate the bearing of A from D, in degrees.

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Question 1104

[3 marks]Polygons, Bearings and Trigonometry

In the diagram, A, B, C and D lie on level ground and ABC is a straight road. BD = 9 km,

A\hat{B}D = 40^\circ

and BC = 6 km. Calculate the distance CD, in kilometres, correct to three significant figures.

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Question 1105

[2 marks]Polygons, Bearings and Trigonometry

In the diagram, A, B, C and D lie on level ground and ABC is a straight road. BD = 9 km,

A\hat{B}D = 40^\circ

and BC = 6 km. Calculate the area of

\triangle

BCD, in square kilometres, correct to three significant figures.

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Question 1201

[2 marks]Vector Geometry

In the diagram, ABC is a triangle with

\overrightarrow{AB} = \mathbf{q}

and

\overrightarrow{AC} = \mathbf{p}

, and M is the mid-point of AB. Express

\overrightarrow{CM}

in terms of

\mathbf{p}

and

\mathbf{q}

A $\mathbf{p} - \frac{1}{2}\mathbf{q}$
B $\frac{1}{2}\mathbf{q} + \mathbf{p}$
C $\frac{1}{2}\mathbf{q} - \mathbf{p}$
D $\frac{1}{2}(\mathbf{p} + \mathbf{q})$

Question 1202

[3 marks]Vector Geometry

In the diagram, ABC is a triangle with

\overrightarrow{AB} = \mathbf{q}

and

\overrightarrow{AC} = \mathbf{p}

, and X lies on BC with BX : XC = 4 : 1. Express

\overrightarrow{AX}

in terms of

\mathbf{p}

and

\mathbf{q}

A $\frac{4}{5}\mathbf{p} + \frac{1}{5}\mathbf{q}$
B $\frac{4}{5}\mathbf{p} - \frac{1}{5}\mathbf{q}$
C $\frac{1}{5}\mathbf{p} + \frac{1}{5}\mathbf{q}$
D $\frac{1}{5}\mathbf{p} + \frac{4}{5}\mathbf{q}$

Question 1203

[3 marks]Vector Geometry

In the diagram, ABC is a triangle with

\overrightarrow{AB} = \mathbf{q}

and

\overrightarrow{AC} = \mathbf{p}

, M is the mid-point of AB and X lies on BC with BX : XC = 4 : 1. CM and AX cross at Y, where

\overrightarrow{CY} = k\,\overrightarrow{CM}

and

\overrightarrow{AY} = h\,\overrightarrow{AX}

. Find the value of

h

, as a fraction.

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Question 1204

[2 marks]Vector Geometry

In the diagram, ABC is a triangle with

\overrightarrow{AB} = \mathbf{q}

and

\overrightarrow{AC} = \mathbf{p}

, M is the mid-point of AB and X lies on BC with BX : XC = 4 : 1. CM and AX cross at Y, where

\overrightarrow{CY} = k\,\overrightarrow{CM}

and

\overrightarrow{AY} = h\,\overrightarrow{AX}

. Given that

h = \frac{5}{6}

, find the value of

k

, as a fraction.

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Question 1205

[2 marks]Vector Geometry

In the diagram, ABC is a triangle with

\overrightarrow{AB} = \mathbf{q}

and

\overrightarrow{AC} = \mathbf{p}

, and X lies on BC with BX : XC = 4 : 1, so that

\overrightarrow{AX} = \frac{4}{5}\mathbf{p} + \frac{1}{5}\mathbf{q}

. Given that

\overrightarrow{AY} = \frac{5}{6}\overrightarrow{AX}

, express

\overrightarrow{AY}

in terms of

\mathbf{p}

and

\mathbf{q}

A $\frac{1}{6}\mathbf{p} + \frac{2}{3}\mathbf{q}$
B $\frac{4}{5}\mathbf{p} + \frac{1}{5}\mathbf{q}$
C $\frac{5}{6}\mathbf{p} + \frac{1}{6}\mathbf{q}$
D $\frac{2}{3}\mathbf{p} + \frac{1}{6}\mathbf{q}$

Mathematics Paper 2 November 2014

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The questions

Question 101

Question 102

Question 103

Question 104

Question 201

Question 202

Question 203

Question 204

Question 301

Question 302

Question 303

Question 304

Question 401

Question 402

Question 403

Question 404

Question 501

Question 502

Question 503

Question 504

Question 601

Question 602

Question 603

Question 604

Question 701

Question 702

Question 703

Question 704

Question 801

Question 802

Question 803

Question 804

Question 901

Question 902

Question 903

Question 904

Question 1001

Question 1002

Question 1003

Question 1004

Question 1101

Question 1102

Question 1103

Question 1104

Question 1105

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

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