ZIMSEC O Level Mathematics Paper 2 June 2020

Question 101

[2 marks]Fractions, Standard Form and Number Bases

The difference between two fractions is

3\frac{2}{3}

. The smaller fraction is

2\frac{1}{4}

. Find the other fraction, giving the answer as a mixed number.

Answer this when you sit the paper.

Question 102

[2 marks]Fractions, Standard Form and Number Bases

The population of a certain country is 24,9 million. Express this population in standard form.

Answer this when you sit the paper.

Question 103

[2 marks]Fractions, Standard Form and Number Bases

Increase $40,00 in the ratio 8:5.

Answer this when you sit the paper.

Question 104

[1 marks]Fractions, Standard Form and Number Bases

Evaluate

\left(7\sqrt{5}\right)^2

Answer this when you sit the paper.

Question 105

[3 marks]Fractions, Standard Form and Number Bases

Simplify

11011_2 + 243_5

, giving the answer in base five.

Answer this when you sit the paper.

Question 201

[2 marks]Similarity and Measures & Mensuration

Two similar cups have diameters of 6 cm and 10 cm. Write down the ratio of their volumes, in its lowest terms.

Answer this when you sit the paper.

Question 202

[2 marks]Similarity and Measures & Mensuration

Two similar cups have diameters of 6 cm and 10 cm. The volume of the smaller cup is 100 cm

^3

. Calculate the volume of the larger cup, in cm

^3

, correct to 3 significant figures.

Answer this when you sit the paper.

Question 203

[2 marks]Similarity and Measures & Mensuration

A wooden block is a prism whose cross-section is a parallelogram with base 35 cm and perpendicular height 20 cm. Calculate the surface area of the cross-section, in cm

^2

Answer this when you sit the paper.

Question 204

[2 marks]Similarity and Measures & Mensuration

A wooden block is a prism of length 1,2 m whose cross-section is a parallelogram of area 700 cm

^2

. Calculate the volume of the block, in cm

^3

Answer this when you sit the paper.

Question 205

[2 marks]Similarity and Measures & Mensuration

A wooden block has a volume of 84 000 cm

^3

. Given that 3 cm

^3

of the block weigh 2,5 g, calculate the mass of the block, in grams.

Answer this when you sit the paper.

Question 301

[2 marks]Matrices and Coordinate Geometry

Find the value of

y

for which

\begin{pmatrix} y & 4 \end{pmatrix} \begin{pmatrix} -2 \\ 3 \end{pmatrix} = \begin{pmatrix} -2 \end{pmatrix}

Answer this when you sit the paper.

Question 302

[3 marks]Matrices and Coordinate Geometry

Find the matrix

P

such that

P \begin{pmatrix} 3 & -4 \\ 2 & 0 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}

. Give each element as a decimal.

Answer this when you sit the paper.

Question 303

[2 marks]Matrices and Coordinate Geometry

The equation of a straight line is

y + 3x = -4

. Find the coordinates of the point where the line crosses the y-axis.

Answer this when you sit the paper.

Question 304

[1 marks]Matrices and Coordinate Geometry

The equation of a straight line is

y + 3x = -4

. Find the gradient of the line.

Answer this when you sit the paper.

Question 305

[2 marks]Matrices and Coordinate Geometry

Find the equation of the line parallel to the line

y + 3x = -4

and passing through the point

(3; 5)

Answer this when you sit the paper.

Question 401

[2 marks]Constructions and Loci

In triangle ABC, AB = 7 cm, BC = 8 cm and

B\hat{A}C = 45^\circ

. Calculate the size of

A\hat{B}C

, correct to the nearest degree.

Answer this when you sit the paper.

Question 402

[1 marks]Constructions and Loci

Two points B and C are 8 cm apart. Name the locus of points that are equidistant from B and C.

Answer this when you sit the paper.

Question 403

[1 marks]Constructions and Loci

C is a fixed point on level ground. Describe the locus of points that are 5 cm from C.

Answer this when you sit the paper.

Question 501

[3 marks]Quadratic Equations and Circle Geometry

Solve the equation

3x^2 - 9x - 5 = 0

, giving both answers correct to 2 decimal places.

Answer this when you sit the paper.

Question 502

[1 marks]Quadratic Equations and Circle Geometry

ABCD is a cyclic quadrilateral drawn in a circle with centre O, and the diagonal BD passes through O. Find

B\hat{C}D

Answer this when you sit the paper.

Question 503

[2 marks]Quadratic Equations and Circle Geometry

ABCD is a cyclic quadrilateral drawn in a circle with centre O, and the diagonal BD passes through O. AB is produced to M so that

M\hat{B}C = 70^\circ

, and

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

. Find

A\hat{B}D

Answer this when you sit the paper.

Question 504

[2 marks]Quadratic Equations and Circle Geometry

ABCD is a cyclic quadrilateral drawn in a circle with centre O, and the diagonal BD passes through O. AB is produced to M so that

M\hat{B}C = 70^\circ

, and

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

. Find

A\hat{D}O

Answer this when you sit the paper.

Question 505

[2 marks]Quadratic Equations and Circle Geometry

The equation

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

can be written in the form

3x^2 + bx + c = 0

. Find the value of

b

and the value of

c

Answer this when you sit the paper.

Question 601

[1 marks]Vector Geometry

In triangle ABO,

\vec{OA} = a

and

\vec{OB} = b

. The point N lies on AB such that

AN = \frac{1}{5}AB

. Express

\vec{AN}

in terms of

a

and

b

Answer this when you sit the paper.

Question 602

[2 marks]Vector Geometry

In triangle ABO,

\vec{OA} = a

and

\vec{OB} = b

. The point N lies on AB such that

AN = \frac{1}{5}AB

. Express

\vec{ON}

in terms of

a

and

b

Answer this when you sit the paper.

Question 603

[1 marks]Vector Geometry

In triangle ABO,

\vec{OA} = a

and

\vec{OB} = b

. M is the mid-point of OB. Express

\vec{AM}

in terms of

a

and

b

Answer this when you sit the paper.

Question 604

[3 marks]Vector Geometry

It is given that

\vec{OX} = (1 - h)a + \frac{1}{2}hb

and also that

\vec{OX} = k\,\vec{ON}

, where

\vec{ON} = \frac{4}{5}a + \frac{1}{5}b

. Find the value of

h

and the value of

k

Answer this when you sit the paper.

Question 605

[1 marks]Vector Geometry

In triangle ABO, X lies on AM with

\vec{AX} = \frac{1}{3}\vec{AM}

. Find the ratio of the area of triangle OAX to the area of triangle OAM.

Answer this when you sit the paper.

Question 606

[1 marks]Vector Geometry

It is given that

\vec{OX} = k\,\vec{ON}

, where

\vec{ON} = \dfrac{4}{5}a + \dfrac{1}{5}b

. Express

\vec{OX}

in terms of

a

b

and

k

Answer this when you sit the paper.

Question 701

[2 marks]Geometrical Transformation

Triangle PQR has vertices at

P(1; 3)

Q(2; 1)

and

R(4; 3)

. Triangle

P_1Q_1R_1

is the image of triangle PQR under a reflection in the line

y = -x

. Write down the coordinates of

P_1

Answer this when you sit the paper.

Question 702

[1 marks]Geometrical Transformation

Triangle PQR has vertices at

P(1; 3)

Q(2; 1)

and

R(4; 3)

. Triangle

P_1Q_1R_1

is the image of triangle PQR under a reflection in the line

y = -x

. Write down the coordinates of

R_1

Answer this when you sit the paper.

Question 703

[3 marks]Geometrical Transformation

A single transformation G maps triangle PQR, with vertices

P(1; 3)

Q(2; 1)

and

R(4; 3)

, onto triangle

P_2Q_2R_2

with vertices

P_2(1; -6)

Q_2(2; -2)

and

R_2(4; -6)

. Describe fully the transformation G.

Answer this when you sit the paper.

Question 704

[1 marks]Geometrical Transformation

The point

R(4; 3)

is mapped onto the point

R_3(-1; 2)

by a translation. Find the translation vector.

Answer this when you sit the paper.

Question 705

[2 marks]Geometrical Transformation

Under a translation with vector

\begin{pmatrix} -5 \\ -1 \end{pmatrix}

, the points

P(1; 3)

and

Q(2; 1)

map onto

P_3

and

Q_3

. Write down the coordinates of

P_3

and

Q_3

Answer this when you sit the paper.

Question 801

[1 marks]Functional Graphs

In a table of values for the function

y = x^3 - 3x^2

, the value of

y

when

x = -1

is written as

m

. Find the value of

m

Answer this when you sit the paper.

Question 802

[2 marks]Functional Graphs

Find the gradient of the curve

y = x^3 - 3x^2

at the point where

x = 3

Answer this when you sit the paper.

Question 803

[1 marks]Functional Graphs

Write down the range of values of

x

for which the curve

y = x^3 - 3x^2

has a negative gradient.

Answer this when you sit the paper.

Question 804

[2 marks]Functional Graphs

Use the graph of

y = x^3 - 3x^2

to solve the equation

x^3 - 3x^2 = 2

, for positive values of

x

. Give the answer correct to 1 decimal place.

Answer this when you sit the paper.

Question 805

[2 marks]Functional Graphs

The graph of

y = x^3 - 3x^2

is drawn for

-2 \le x \le 4

. Use the graph to estimate the area, in square units, of the region bounded by the curve, the

y

-axis and the line

y = -12

Answer this when you sit the paper.

Question 901

[2 marks]Factorisation, Change of Subject and Sets

Factorise completely

x^2 - 4

Answer this when you sit the paper.

Question 902

[2 marks]Factorisation, Change of Subject and Sets

Factorise completely

x^2 - 5x + 6

Answer this when you sit the paper.

Question 903

[1 marks]Factorisation, Change of Subject and Sets

Find the Highest Common Factor (H.C.F.) of

x^2 - 4

and

x^2 - 5x + 6

Answer this when you sit the paper.

Question 904

[2 marks]Factorisation, Change of Subject and Sets

It is given that

S = \dfrac{a}{1 - r}

. Find the value of

S

when

a = 81

and

r = \dfrac{1}{3}

Answer this when you sit the paper.

Question 905

[3 marks]Factorisation, Change of Subject and Sets

It is given that

S = \dfrac{a}{1 - r}

. Make

r

the subject of the formula.

Answer this when you sit the paper.

Question 906

[2 marks]Factorisation, Change of Subject and Sets

From a group of 30 people at a party, 17 people ate beef, 16 people ate pork,

x

people ate both beef and pork and 6 people ate neither beef nor pork. Calculate

x

Answer this when you sit the paper.

Question 1001

[2 marks]Trigonometry

In the diagram KLNG is a trapezium in which LMN is a straight line and

K\hat{L}M = M\hat{N}G = 90^\circ

. MG = 5 cm and

N\hat{M}G = 35^\circ

. Calculate the length of NG, in cm, correct to 3 significant figures.

Answer this when you sit the paper.

Question 1002

[1 marks]Trigonometry

In the diagram KLNG is a trapezium in which LMN is a straight line.

L\hat{M}K = 60^\circ

and

N\hat{M}G = 35^\circ

. Find the size of

K\hat{M}G

Answer this when you sit the paper.

Question 1003

[2 marks]Trigonometry

In triangle KMG, MK = 7 cm, MG = 5 cm and

K\hat{M}G = 85^\circ

. Calculate the area of triangle KMG, in cm

^2

, correct to 3 significant figures.

Answer this when you sit the paper.

Question 1004

[3 marks]Trigonometry

In triangle KMG, MK = 7 cm, MG = 5 cm and

K\hat{M}G = 85^\circ

. Calculate the length of KG, in cm, correct to 3 significant figures.

Answer this when you sit the paper.

Question 1005

[3 marks]Trigonometry

In triangle KMG, MG = 5 cm, KG = 8,24 cm and

K\hat{M}G = 85^\circ

. Calculate the size of

M\hat{K}G

, correct to 1 decimal place.

Answer this when you sit the paper.

Question 1101

[2 marks]Inequalities and Linear Programming

A group of youths makes chairs and tables for sale. Let

x

be the number of chairs and

y

the number of tables. The group wishes to produce at least 5 chairs and not less than 5 tables. Write down two inequalities, one in

x

and the other in

y

, that satisfy these conditions.

Answer this when you sit the paper.

Question 1102

[1 marks]Inequalities and Linear Programming

A group of youths has 48 hours to make chairs and tables. It takes 4 hours to make a chair and 3 hours to make a table. Taking

x

as the number of chairs and

y

as the number of tables, write down an inequality in

x

and

y

that satisfies this condition.

Answer this when you sit the paper.

Question 1103

[1 marks]Inequalities and Linear Programming

A group of youths hired a compressor for 14 hours to paint chairs and tables. It takes 1 hour to paint a chair and 1 hour to paint a table. Taking

x

as the number of chairs and

y

as the number of tables, form an inequality in

x

and

y

that satisfies this condition.

Answer this when you sit the paper.

Question 1104

[2 marks]Inequalities and Linear Programming

The number of chairs

x

and the number of tables

y

made by a group satisfy

x \ge 5

y \ge 5

4x + 3y \le 48

and

x + y \le 14

. The profit on a chair is $10 and the profit on a table is $20. Find the greatest possible profit, in dollars.

Answer this when you sit the paper.

Question 1201

[1 marks]Statistics and Probability

The heights,

h

cm, of 200 children are grouped. The class

75 < h \le 80

has a frequency of 45 and a frequency density of

p

. Find the value of

p

Answer this when you sit the paper.

Question 1202

[1 marks]Statistics and Probability

The heights,

h

cm, of 200 children are grouped. The class

80 < h \le 100

has a frequency of 40 and a frequency density of

q

. Find the value of

q

Answer this when you sit the paper.

Question 1203

[3 marks]Statistics and Probability

The heights,

h

cm, of a group of 200 children are:

50 < h \le 60

, 24 children;

60 < h \le 70

, 38 children;

70 < h \le 75

, 53 children;

75 < h \le 80

, 45 children;

80 < h \le 100

, 40 children. Calculate an estimate of the mean height, in cm.

Answer this when you sit the paper.

Question 1204

[2 marks]Statistics and Probability

In a group of 200 children, 45 have heights in the class

75 < h \le 80

cm and 40 have heights in the class

80 < h \le 100

cm. Two children are chosen at random from the group. Find the probability that each has a height which is greater than 75 cm. Give the answer as a fraction in its lowest terms.

Answer this when you sit the paper.

Mathematics Paper 2 June 2020

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 104

Question 105

Question 201

Question 202

Question 203

Question 204

Question 205

Question 301

Question 302

Question 303

Question 304

Question 305

Question 401

Question 402

Question 403

Question 501

Question 502

Question 503

Question 504

Question 505

Question 601

Question 602

Question 603

Question 604

Question 605

Question 606

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 1201

Question 1202

Question 1203

Question 1204

More sittings of this paper

The answers, and why they are the answers

Sit this paper online