ZIMSEC O Level Mathematics Paper 2 June 2011

Question 101

[2 marks]Fractions, Decimals and Percentages

Simplify

\left(3\tfrac{1}{2} - 1\tfrac{3}{5}\right) + 1\tfrac{2}{3}

, giving your answer as a mixed number.

Answer this when you sit the paper.

Question 102

[2 marks]Fractions, Decimals and Percentages

Find the exact value of

10,03 \times 0,17

Answer this when you sit the paper.

Question 103

[2 marks]Fractions, Decimals and Percentages

Three farmers share 120 hectares of land in the ratio

3 : 4 : 5

. Calculate, in hectares, the area of the largest piece of land.

Answer this when you sit the paper.

Question 104

[2 marks]Fractions, Decimals and Percentages

Find the Highest Common Factor of

27x^2yz

72xy^3z^2

and

108xyz^3

A $9x^2y^3z^3$
B $216xyz$
C $3x^2y^3z^3$
D $9xyz$

Question 201

[2 marks]Algebraic Fractions

It is given that

r = 2q - 5

and

q = 3p + 2

. Express

r

in terms of

p

, in its simplest form.

Answer this when you sit the paper.

Question 202

[2 marks]Algebraic Fractions

Express

\dfrac{x}{3} + \dfrac{x - 4}{5}

as a single fraction in its simplest form.

A $\dfrac{5x - 12}{15}$
B $\dfrac{8x - 12}{15}$
C $\dfrac{2x - 4}{8}$
D $\dfrac{8x + 12}{15}$

Question 203

[3 marks]Algebraic Fractions

Solve the equation

\dfrac{x}{3} + \dfrac{x - 4}{5} = 4

Answer this when you sit the paper.

Question 204

[2 marks]Algebraic Fractions

Express 150 g as a percentage of 3 kg.

Answer this when you sit the paper.

Question 301

[2 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle, and AC and BD meet at F. Given that

A\hat{C}D = 33^\circ

, calculate

A\hat{B}D

, in degrees.

Answer this when you sit the paper.

Question 302

[3 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle, and CD is produced to E. Given that

A\hat{C}D = 33^\circ

and

A\hat{D}E = 87^\circ

, calculate

C\hat{B}D

, in degrees.

Answer this when you sit the paper.

Question 303

[3 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle with

BC = CD

, and CD is produced to E. Given that

A\hat{C}D = 33^\circ

and

A\hat{D}E = 87^\circ

, calculate

A\hat{D}B

, in degrees.

Answer this when you sit the paper.

Question 304

[2 marks]Circle Geometry

A sector POQ of a circle has centre O, with

P\hat{O}Q = 37^\circ

and

PO = 8

cm. PT is perpendicular to QO, with T lying on QO. Calculate PT, in centimetres, correct to three significant figures.

Answer this when you sit the paper.

Question 305

[3 marks]Circle Geometry

A sector POQ of a circle has centre O, with

P\hat{O}Q = 37^\circ

and

PO = 8

cm. Taking

\pi

to be 3,142, calculate the area, in square centimetres, of the segment cut off by the chord PQ, correct to three significant figures.

Answer this when you sit the paper.

Question 401

[2 marks]Factorisation and Sets

Factorise completely

3np - 6nq + ap - 2aq

A $(3n + a)(p + 2q)$
B $(n + 3a)(3p - 2q)$
C $(3n + a)(p - 2q)$
D $(3n - a)(p + 2q)$

Question 402

[2 marks]Factorisation and Sets

Factorise completely

12 - 4g - g^2

Answer this when you sit the paper.

Question 403

[2 marks]Factorisation and Sets

In a survey of 72 girls, every girl watched at least one of the TV programmes Teen Scene or Fashion Show. Fifty girls watched Teen Scene and 62 girls watched Fashion Show. Find the number of girls who watched both programmes.

Answer this when you sit the paper.

Question 404

[2 marks]Factorisation and Sets

Answer this when you sit the paper.

Question 501

[2 marks]Number Bases and Logarithms

Convert

112_3

to a number in base 5.

Answer this when you sit the paper.

Question 502

[2 marks]Number Bases and Logarithms

Evaluate

1101_2 + 1011_2

, giving your answer in base 2.

Answer this when you sit the paper.

Question 503

[3 marks]Number Bases and Logarithms

Express

2\log_5(3x + 2) - \log_5 2

as a single logarithm.

A $\left(\log_5\dfrac{3x + 2}{2}\right)^2$
B $\log_5\left(\dfrac{6x + 4}{2}\right)$
C $\log_5\left(\dfrac{(3x + 2)^2}{4}\right)$
D $\log_5\left(\dfrac{(3x + 2)^2}{2}\right)$

Question 504

[3 marks]Number Bases and Logarithms

Solve the equation

3x^2 + 4x - 2 = 0

and state its positive root, correct to two decimal places.

Answer this when you sit the paper.

Question 505

[2 marks]Number Bases and Logarithms

For the equation

3x^2 + 4x - 2 = 0

, find the value of

b^2 - 4ac

Answer this when you sit the paper.

Question 601

[2 marks]Constructions and Loci

Shinga is 16 km from Tugwi. On a drawing made to a scale of 1 cm to represent 2 km, find the length, in centimetres, of the line joining Tugwi to Shinga.

Answer this when you sit the paper.

Question 602

[2 marks]Constructions and Loci

Hlangu is 15 km North-East of Shinga. State the bearing of Hlangu from Shinga, given as a three-figure bearing.

A $045^\circ$
B $135^\circ$
C $225^\circ$
D $315^\circ$

Question 603

[2 marks]Constructions and Loci

On a drawing made to a scale of 1 cm to represent 2 km, the locus of points 8 km from Shinga is a circle centred on Shinga. Find the radius, in centimetres, of that circle.

Answer this when you sit the paper.

Question 604

[2 marks]Constructions and Loci

Boterekwa is equidistant from Tugwi and from Hlangu. Name the locus of all points that are equidistant from Tugwi and Hlangu.

AThe circle drawn with the line joining Tugwi and Hlangu as its diameter
BThe bisector of the angle between the line to Tugwi and the line to Hlangu
CThe arc of a circle centred on the midpoint of Tugwi and Hlangu
DThe perpendicular bisector of the line joining Tugwi and Hlangu

Question 605

[3 marks]Constructions and Loci

Shinga is 16 km from Tugwi on a bearing of

150^\circ

, and Hlangu is 15 km North-East of Shinga. Boterekwa is 8 km from Shinga and equidistant from Tugwi and Hlangu. Taking the nearer of the two possible positions, find the distance, in kilometres to the nearest kilometre, from Boterekwa to Tugwi.

Answer this when you sit the paper.

Question 701

[3 marks]Matrices and Vector Geometry

Find the inverse of the matrix

\mathbf{A} = \begin{pmatrix} 3 & -4 \\ 1 & -2 \end{pmatrix}

A $\begin{pmatrix} 1 & 2 \\ 0,5 & 1,5 \end{pmatrix}$
B $\begin{pmatrix} 1 & -2 \\ 0,5 & -1,5 \end{pmatrix}$
C $\begin{pmatrix} -1 & 2 \\ -0,5 & 1,5 \end{pmatrix}$
D $\begin{pmatrix} -3 & 4 \\ -1 & 2 \end{pmatrix}$

Question 702

[3 marks]Matrices and Vector Geometry

Solve the simultaneous equations

3x - 4y = -3

and

x - 2y = -2

, and state the value of

y

Answer this when you sit the paper.

Question 703

[2 marks]Matrices and Vector Geometry

OABC is a trapezium in which OC is parallel to AB, with

\overrightarrow{OA} = x

and

\overrightarrow{OC} = y

. The diagonals OB and AC meet at D, where

AD : DC = 3 : 2

. Express

\overrightarrow{AD}

in terms of

x

and

y

A $\tfrac{3}{5}(y - x)$
B $\tfrac{3}{2}(y - x)$
C $\tfrac{3}{5}(x - y)$
D $\tfrac{2}{5}(y - x)$

Question 704

[2 marks]Matrices and Vector Geometry

OABC is a trapezium in which OC is parallel to AB, with

\overrightarrow{OA} = x

and

\overrightarrow{OC} = y

. The diagonals OB and AC meet at D, where

AD : DC = 3 : 2

, and

\overrightarrow{AB} = k\overrightarrow{OC}

and

\overrightarrow{OB} = h\overrightarrow{OD}

. Find the value of

h

Answer this when you sit the paper.

Question 705

[2 marks]Matrices and Vector Geometry

OABC is a trapezium in which OC is parallel to AB, with

\overrightarrow{OA} = x

and

\overrightarrow{OC} = y

. The diagonals OB and AC meet at D, where

AD : DC = 3 : 2

, and

\overrightarrow{AB} = k\overrightarrow{OC}

and

\overrightarrow{OB} = h\overrightarrow{OD}

. Find the value of

k

Answer this when you sit the paper.

Question 801

[2 marks]Geometrical Transformation

Triangle ABC has vertices

A(2; 1)

B(4; 1)

and

C(4; 4)

. Triangle

A_1B_1C_1

is the reflection of triangle ABC in the line

y = -2

. Write down the coordinates of

C_1

Answer this when you sit the paper.

Question 802

[3 marks]Geometrical Transformation

Triangle ABC has vertices

A(2; 1)

B(4; 1)

and

C(4; 4)

, and triangle

A_2B_2C_2

has vertices

A_2(6; 4)

B_2(10; 4)

and

C_2(10; 10)

. Describe fully the single transformation that maps triangle ABC onto triangle

A_2B_2C_2

AAn enlargement with centre $(-2; -2)$ and scale factor 2
BAn enlargement with centre $(0; 0)$ and scale factor 2
CAn enlargement with centre $(2; 1)$ and scale factor 3
DAn enlargement with centre $(-2; -2)$ and scale factor 3

Question 803

[2 marks]Geometrical Transformation

Triangle ABC has vertices

A(2; 1)

B(4; 1)

and

C(4; 4)

. It is rotated through

90^\circ

anticlockwise about

(0; 0)

onto triangle

A_3B_3C_3

. Write down the coordinates of

A_3

Answer this when you sit the paper.

Question 804

[2 marks]Geometrical Transformation

Write down the matrix that represents a rotation through

90^\circ

anticlockwise about the origin.

A $\begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix}$
B $\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$
C $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$
D $\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$

Question 805

[3 marks]Geometrical Transformation

Triangle ABC has vertices

A(2; 1)

B(4; 1)

and

C(4; 4)

. Triangle

A_1B_1C_1

is the reflection of triangle ABC in the line

y = -2

. Find the area, in square units, of triangle

A_1B_1C_1

Answer this when you sit the paper.

Question 901

[2 marks]Statistics and Probability

In a Mathematics examination the grades A, B, C, D, E and U were obtained by 10, 25, 40, 24, 21 and 30 candidates respectively. Calculate the number of candidates who wrote the examination.

Answer this when you sit the paper.

Question 902

[1 marks]Statistics and Probability

In a Mathematics examination the grades A, B, C, D, E and U were obtained by 10, 25, 40, 24, 21 and 30 candidates respectively. State the modal grade.

AGrade A
BGrade B
CGrade C
DGrade U

Question 903

[3 marks]Statistics and Probability

In a Mathematics examination the grades A, B, C, D, E and U were obtained by 10, 25, 40, 24, 21 and 30 candidates respectively. Given that the passing grades are A, B and C, find the probability that two candidates chosen at random both passed the examination.

Answer this when you sit the paper.

Question 904

[2 marks]Statistics and Probability

In a Mathematics examination the grades A, B, C, D, E and U were obtained by 10, 25, 40, 24, 21 and 30 candidates respectively. If a pie-chart is drawn for this information, calculate the angle, in degrees, of the sector that represents grade C.

Answer this when you sit the paper.

Question 905

[2 marks]Statistics and Probability

In a Mathematics examination the grades A, B, C, D, E and U were obtained by 10, 25, 40, 24, 21 and 30 candidates respectively. Calculate the percentage of the candidates who obtained grade U.

Answer this when you sit the paper.

Question 906

[2 marks]Statistics and Probability

In a Mathematics examination the grades A, B, C, D, E and U were obtained by 10, 25, 40, 24, 21 and 30 candidates respectively, and the passing grades are A, B and C. Find the probability that one candidate chosen at random failed the examination.

Answer this when you sit the paper.

Question 1001

[2 marks]Variation, Inequalities and Linear Programming

The length,

l

, of a rectangle of constant area varies inversely as

b

, the width of the rectangle. State the relationship between

l

b

and a constant

k

A $l = \dfrac{k}{b}$
B $l = \dfrac{b}{k}$
C $l = k + b$
D $l = kb$

Question 1002

[3 marks]Variation, Inequalities and Linear Programming

The length,

l

, of a rectangle of constant area varies inversely as

b

, its width. Given that

l = 8,5

cm when

b = 6

cm, find

b

, in centimetres, when

l = 10,2

cm.

Answer this when you sit the paper.

Question 1003

[2 marks]Variation, Inequalities and Linear Programming

Find the coordinates of the point where the line

x + 2y = 8

crosses the line

y = -2

Answer this when you sit the paper.

Question 1004

[3 marks]Variation, Inequalities and Linear Programming

A region is defined by

x \ge 3

y \ge -2

and

x + 2y \le 8

. Find the maximum value of

3x - 2y

over that region.

Answer this when you sit the paper.

Question 1005

[2 marks]Variation, Inequalities and Linear Programming

A region is defined by

x \ge 3

y \ge -2

and

x + 2y \le 8

. Find the coordinates of the corner of that region which lies on both

x = 3

and

x + 2y = 8

Answer this when you sit the paper.

Question 1101

[2 marks]Consumer Arithmetic

A set with 1 element has 2 subsets, a set with 2 elements has 4 subsets and a set with 3 elements has 8 subsets. Find the number of subsets of a set with 5 elements.

Answer this when you sit the paper.

Question 1102

[2 marks]Consumer Arithmetic

The number of subsets of a set with

m

elements is

2^m

. A certain set has 128 subsets. Find the number of elements in that set.

Answer this when you sit the paper.

Question 1103

[2 marks]Consumer Arithmetic

For a set of

n

elements the number of subsets is

r

, where a set of 1 element has 2 subsets, a set of 2 elements has 4 and a set of 3 elements has 8. Express

r

in terms of

n

A $r = 2^{n - 1}$
B $r = 2^n$
C $r = 2n$
D $r = n^2$

Question 1104

[3 marks]Consumer Arithmetic

Mbudzi Investments borrowed 6 000 dollars from a bank. At the end of the first month the bank charged interest of 80 dollars on that balance of 6 000 dollars. Find the rate of simple interest per annum, as a percentage.

Answer this when you sit the paper.

Question 1105

[3 marks]Consumer Arithmetic

A loan is charged interest at the end of each month at

1\tfrac{1}{3}\%

of the balance standing at that time. Find the interest, in dollars correct to the nearest cent, charged on a balance of 5 878,40 dollars.

Answer this when you sit the paper.

Question 1201

[2 marks]Travel Graphs

The velocity of a particle moving along a straight line is given by

v = 15 + 7t - 2t^2

, where

v

is in m/s and

t

is in seconds. Find the value of

v

when

t = 1

Answer this when you sit the paper.

Question 1202

[2 marks]Travel Graphs

The velocity of a particle moving along a straight line is given by

v = 15 + 7t - 2t^2

, where

v

is in m/s and

t

is in seconds. Find the value of

v

when

t = 4

Answer this when you sit the paper.

Question 1203

[2 marks]Travel Graphs

The velocity of a particle moving along a straight line is given by

v = 15 + 7t - 2t^2

, where

v

is in m/s and

t

is in seconds. Find the value of

t

, in seconds, at which

v

is greatest.

Answer this when you sit the paper.

Question 1204

[3 marks]Travel Graphs

The velocity of a particle moving along a straight line is given by

v = 15 + 7t - 2t^2

, where

v

is in m/s and

t

is in seconds. Find the maximum value of

v

, in m/s, correct to three significant figures.

Answer this when you sit the paper.

Question 1205

[3 marks]Travel Graphs

The velocity of a particle moving along a straight line is given by

v = 15 + 7t - 2t^2

, where

v

is in m/s and

t

is in seconds. Find the acceleration of the particle, in metres per second per second, when

t = 3

Answer this when you sit the paper.

Mathematics Paper 2 June 2011

Sit this paper online

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 305

Question 401

Question 402

Question 403

Question 404

Question 501

Question 502

Question 503

Question 504

Question 505

Question 601

Question 602

Question 603

Question 604

Question 605

Question 701

Question 702

Question 703

Question 704

Question 705

Question 801

Question 802

Question 803

Question 804

Question 805

Question 901

Question 902

Question 903

Question 904

Question 905

Question 906

Question 1001

Question 1002

Question 1003

Question 1004

Question 1005

Question 1101

Question 1102

Question 1103

Question 1104

Question 1105

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

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