ZIMSEC O Level Mathematics Paper 2 November 2022

Question 101

[1 marks]Circle Geometry

A, B, C and D lie on a circle centre O, AC passes through O, TC is a tangent at C and

B\hat{C}T = 80^\circ

. Find

A\hat{C}B

, in degrees.

Answer this when you sit the paper.

Question 102

[1 marks]Circle Geometry

A, B, C and D lie on a circle, TC is a tangent at C and

B\hat{C}T = 80^\circ

. Find

B\hat{D}C

, in degrees.

Answer this when you sit the paper.

Question 103

[2 marks]Circle Geometry

AC and BD intersect at P inside a circle, with

C\hat{B}D = 32^\circ

and

A\hat{C}B = 10^\circ

. Find

C\hat{P}D

, in degrees.

Answer this when you sit the paper.

Question 104

[3 marks]Circle Geometry

A, B, C and D lie on a circle centre O with AC as diameter, and

C\hat{B}D = 32^\circ

. Find

A\hat{O}D

, in degrees.

Answer this when you sit the paper.

Question 201

[2 marks]Quadratic Equations

Factorise

(m - n)(4m + 2n) - (m - n)^2

Answer this when you sit the paper.

Question 202

[2 marks]Quadratic Equations

The average mass of 11 players is 81 kg. When one player is removed the average becomes 80,1 kg. Calculate the mass of the removed player, in kilograms.

Answer this when you sit the paper.

Question 203

[2 marks]Quadratic Equations

Maria spends 40% of her pocket money on shoes, then 30% of what is left on a dictionary. Find the percentage of her pocket money that remains.

Answer this when you sit the paper.

Question 204

[3 marks]Quadratic Equations

Solve the equation

\frac{4 - x}{x} = \frac{x}{2}

Answer this when you sit the paper.

Question 301

[2 marks]Variation

The total surface area of a cone is

A = \pi r^2 + \pi r l

. Make

l

the subject of the formula.

Answer this when you sit the paper.

Question 302

[2 marks]Variation

For a cone,

A = \pi r^2 + \pi r l

. Find

l

when

A = 121,44

^2

r = 4,2

cm and

\pi = \frac{22}{7}

Answer this when you sit the paper.

Question 303

[1 marks]Variation

The time

T

minutes taken for a meeting is partly constant and partly varies as the square of

N

, the number of members present. Express

T

in terms of

N

and the constants

h

and

k

Answer this when you sit the paper.

Question 304

[3 marks]Variation

For a meeting,

T = h + kN^2

. With 4 members present the meeting lasts 30 minutes and with 6 members it lasts 45 minutes. Find the values of

h

and

k

Answer this when you sit the paper.

Question 305

[2 marks]Variation

For a meeting,

T = 18 + \frac{3}{4}N^2

minutes. Find the time the meeting will take if 7 members are present.

Answer this when you sit the paper.

Question 401

[3 marks]Fractions, Decimals and Percentages

Simplify

1\frac{7}{8} - \left(1\frac{1}{2}\right)^2

Answer this when you sit the paper.

Question 402

[2 marks]Fractions, Decimals and Percentages

Remove the brackets and simplify

(2x - y)(3x + 2y)

Answer this when you sit the paper.

Question 403

[2 marks]Fractions, Decimals and Percentages

Express

0,8125

as a fraction in its lowest terms.

Answer this when you sit the paper.

Question 404

[1 marks]Fractions, Decimals and Percentages

Express 5832 as a product of its prime factors, in index form.

Answer this when you sit the paper.

Question 405

[1 marks]Fractions, Decimals and Percentages

Given that

5832 = 2^3 \times 3^6

, find the cube root of 5832.

Answer this when you sit the paper.

Question 406

[3 marks]Fractions, Decimals and Percentages

Express

\frac{2}{x - 4} + \frac{2}{x^2 - 9x + 20}

as a single fraction in its simplest form.

Answer this when you sit the paper.

Question 501

[2 marks]Matrices

Given

A = \begin{pmatrix} 3 & 9 \\ 1 & 4 \end{pmatrix}

and

B = \begin{pmatrix} 5 & 1 \\ -4 & 2 \end{pmatrix}

, find

AB

, giving the four entries in order.

Answer this when you sit the paper.

Question 502

[3 marks]Matrices

Find the inverse of

B = \begin{pmatrix} 5 & 1 \\ -4 & 2 \end{pmatrix}

Answer this when you sit the paper.

Question 503

[3 marks]Matrices

Solve the inequality

x - 3 < 2x + 1 \leq 5 - x

, giving the answer in the form

a < x \leq b

Answer this when you sit the paper.

Question 504

[2 marks]Matrices

ABCD is a trapezium with AB parallel to DC,

AB = 8

cm,

AD = 15

cm perpendicular to both parallel sides, and area 180 cm

^2

. Calculate the length of DC, in centimetres.

Answer this when you sit the paper.

Question 505

[3 marks]Matrices

In trapezium ABCD of area 180 cm

^2

, AB is parallel to DC,

AB = 8

cm,

AD = 15

cm, and the diagonals meet at X with

BX : XD = 3 : 5

. Calculate the area of triangle BXC, in square centimetres.

Answer this when you sit the paper.

Question 601

[1 marks]Constructions and Loci

Triangle ABC is constructed with

AB = 10

cm,

A\hat{B}C = 30^\circ

and

B\hat{A}C = 120^\circ

. Measure and write down the length of BC, in centimetres.

Answer this when you sit the paper.

Question 602

[2 marks]Constructions and Loci

In triangle ABC,

A\hat{B}C = 30^\circ

and

B\hat{A}C = 120^\circ

. Find

A\hat{C}B

, in degrees.

Answer this when you sit the paper.

Question 603

[2 marks]Constructions and Loci

What is the locus of the points that are 6 cm from a fixed point A?

AAn arc of radius 6 cm centred on the midpoint of AB
BA circle of radius 6 cm with centre A
CA pair of lines 6 cm on either side of A
DThe perpendicular bisector of a 6 cm line from A

Question 701

[3 marks]Statistics and Probability

The times of 50 athletes are

5 < t \leq 8

(3 athletes),

8 < t \leq 10

(5),

10 < t \leq 12

(14),

12 < t \leq 14

(16),

14 < t \leq 16

(7),

16 < t \leq 18

(4) and

18 < t \leq 20

(1). Calculate an estimate of the mean time, in minutes.

Answer this when you sit the paper.

Question 702

[2 marks]Statistics and Probability

A cumulative frequency table for 50 athletes reads 0 at

t \leq 5

, 3 at

t \leq 8

, 8 at

t \leq 10

, 22 at

t \leq 12

m

t \leq 14

, 45 at

t \leq 16

n

t \leq 18

and 50 at

t \leq 20

. The class frequencies for

12 < t \leq 14

and

16 < t \leq 18

are 16 and 4. Find

m

and

n

Answer this when you sit the paper.

Question 703

[2 marks]Statistics and Probability

A cumulative frequency curve for the times of 50 athletes passes through (12; 22) and (14; 38). Estimate the median time, in minutes.

Answer this when you sit the paper.

Question 704

[1 marks]Statistics and Probability

A cumulative frequency curve for the times of 50 athletes passes through (10; 8) and (8; 3). Estimate the number of athletes who completed the race in 9 minutes and under.

Answer this when you sit the paper.

Question 801

[3 marks]Geometrical Transformation

Triangle P has vertices at (2; 1), (3; 3) and (1; 5). It is translated through the vector

\begin{pmatrix} -6 \\ -7 \end{pmatrix}

onto triangle Q. Write down the coordinates of the vertices of Q.

Answer this when you sit the paper.

Question 802

[3 marks]Geometrical Transformation

Triangle P has vertices at (2; 1), (3; 3) and (1; 5). A one way stretch of factor

-2

with the

y

-axis invariant maps it onto triangle S. Calculate the coordinates of the vertices of S.

Answer this when you sit the paper.

Question 803

[1 marks]Geometrical Transformation

A one way stretch has factor

-2

with the

y

-axis invariant. What does it do to the point

(x; y)

AIt maps it to $(-2x;\ y)$
BIt maps it to $(x;\ -2y)$
CIt maps it to $(-2x;\ -2y)$
DIt maps it to $(y;\ -2x)$

Question 901

[2 marks]Functional Graphs

The function is

y = 6x - x^2 - x^3

. Find the values of

y

when

x = -2

and when

x = 3

Answer this when you sit the paper.

Question 902

[2 marks]Functional Graphs

The graph of

y = 6x - x^2 - x^3

passes through

(-2; -8)

. Find the gradient of the curve at that point.

Answer this when you sit the paper.

Question 903

[3 marks]Functional Graphs

Use the graphs of

y = 6x - x^2 - x^3

and

y = 2 - 2x

to solve the equation

6x - x^2 - x^3 = 2 - 2x

, giving the three roots to 1 decimal place.

Answer this when you sit the paper.

Question 1001

[3 marks]Trigonometry

Find the vectors

\mathbf{a}

and

\mathbf{b}

such that

\mathbf{a} + \mathbf{b} = \begin{pmatrix} -2 \\ 6 \end{pmatrix}

and

2\mathbf{a} - \mathbf{b} = \begin{pmatrix} 5 \\ 0 \end{pmatrix}

Answer this when you sit the paper.

Question 1002

[1 marks]Trigonometry

Sloping ground AC is inclined to the horizontal at

15^\circ

. Find the gradient of the slope AC, correct to 2 decimal places.

Answer this when you sit the paper.

Question 1003

[2 marks]Trigonometry

BP is a post standing on sloping ground AC, with A and C on opposite sides of P along the slope, and

B\hat{P}C = 75^\circ

. Calculate

A\hat{P}B

, in degrees.

Answer this when you sit the paper.

Question 1004

[3 marks]Trigonometry

In triangle APB,

AP = 7

m, the post

BP = 10

m and

A\hat{P}B = 105^\circ

. Calculate the length of AB, in metres, correct to 1 decimal place.

Answer this when you sit the paper.

Question 1101

[2 marks]Measures and Mensuration

Of 55 teachers, 31 have cars, 27 have bicycles,

x

have both and 6 have neither. Find the value of

x

Answer this when you sit the paper.

Question 1102

[3 marks]Measures and Mensuration

ABCDEF is a regular hexagon of side 5 cm. Calculate the length of BD, in centimetres, correct to 2 decimal places.

Answer this when you sit the paper.

Question 1103

[3 marks]Measures and Mensuration

ABCDEF is a regular hexagon of side 5 cm. Calculate its area, in square centimetres, correct to 1 decimal place.

Answer this when you sit the paper.

Question 1104

[2 marks]Measures and Mensuration

A hexagonal prism has a regular hexagonal base of area

64,95

^2

and height 12 cm. Calculate its volume, in cubic centimetres, to the nearest whole number.

Answer this when you sit the paper.

Question 1201

[3 marks]Measures and Mensuration

Solve the equation

3x^2 - 5x - 10 = 0

, giving the answers correct to 2 decimal places.

Answer this when you sit the paper.

Question 1202

[2 marks]Measures and Mensuration

A semicircular coupling has inner radius

3,3

cm. Taking

\pi

to be

\frac{22}{7}

, calculate the length of the semicircular arc, in centimetres, correct to 1 decimal place.

Answer this when you sit the paper.

Question 1203

[3 marks]Measures and Mensuration

A semicircular coupling is a half ring of inner radius

3,3

cm and outer radius

3,5

cm, and is 4 cm long. Taking

\pi

to be

\frac{22}{7}

, calculate the volume of metal used, in cubic centimetres, correct to 2 decimal places.

Answer this when you sit the paper.

Question 1204

[2 marks]Measures and Mensuration

A coupling contains

8,549

^3

of metal of density

7,92

g/cm

^3

. Calculate the mass of the metal used, in grams, correct to 1 decimal place.

Answer this when you sit the paper.

Mathematics Paper 2 November 2022

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 405

Question 406

Question 501

Question 502

Question 503

Question 504

Question 505

Question 601

Question 602

Question 603

Question 701

Question 702

Question 703

Question 704

Question 801

Question 802

Question 803

Question 901

Question 902

Question 903

Question 1001

Question 1002

Question 1003

Question 1004

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