ZIMSEC O Level Mathematics Paper 2 November 2020

Question 101

[2 marks]Rational, Irrational Numbers & Surds

Evaluate

20 - 20 \div 5 + 3 \times 2

Answer this when you sit the paper.

Question 102

[2 marks]Rational, Irrational Numbers & Surds

Simplify

(\sqrt{10}-\sqrt5)^2

, leaving the answer in surd form.

Answer this when you sit the paper.

Question 103

[2 marks]Rational, Irrational Numbers & Surds

Find the Lowest Common Multiple (LCM) of 15, 20 and 25.

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Question 104

[2 marks]Rational, Irrational Numbers & Surds

Express 252 as a product of its prime factors, in index form.

Answer this when you sit the paper.

Question 105

[1 marks]Rational, Irrational Numbers & Surds

252 has prime factorisation

2^2\times3^2\times7

. Find the smallest number by which 252 must be multiplied to make the product a perfect square.

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Question 201

[1 marks]Number bases, standard form

The distance from city A to city D is 33 260 km. Write this distance in standard form (km).

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Question 202

[2 marks]Number bases, standard form

In a distance table between four cities A, B, C and D, the distance from B to D is 18 740 km and the distance from B to C is 8 970 km. Calculate the distance between C and D (in km).

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Question 203

[1 marks]Number bases, standard form

A three-digit number in base

n

is written as

147_n

. Write down the least possible value of

n

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Question 204

[2 marks]Number bases, standard form

Convert the base equation

147_n = 324_6

into a single quadratic equation in

n

, in the form

n^2+bn+c=0

Answer this when you sit the paper.

Question 205

[2 marks]Number bases, standard form

Given that

147_n = 324_6

simplifies to

n^2+4n-117=0

, find the value of

n

(rejecting any value that could not be a base).

Answer this when you sit the paper.

Question 301

[1 marks]Angles, polygons, similar solids, bounds

Write down the number of degrees in 4 complete revolutions.

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Question 302

[3 marks]Angles, polygons, similar solids, bounds

Find the number of sides of a polygon whose interior angles add up to

1440°

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Question 303

[3 marks]Angles, polygons, similar solids, bounds

Two similar containers have capacities 1 728 litres and 5 832 litres. The surface area of the bigger container is 153 cm

^2

. Find the surface area of the smaller container (in cm

^2

Answer this when you sit the paper.

Question 304

[2 marks]Angles, polygons, similar solids, bounds

Triangle ABC has sides AB = 6,5 cm, BC = 7,8 cm and AC = 9,1 cm, each measured to the nearest mm. Express the length of side AB as a range, in the form ..........

\le

AB < ..........

A6,5 ≤ AB < 6,6
B6,45 ≤ AB < 6,55
C6,4 ≤ AB < 6,6
D6,45 ≤ AB ≤ 6,55

Question 305

[2 marks]Angles, polygons, similar solids, bounds

Triangle ABC has sides AB = 6,5 cm, BC = 7,8 cm and AC = 9,1 cm, each measured to the nearest mm. Using the lower bound of each side, calculate the least possible perimeter of the triangle (in cm).

Answer this when you sit the paper.

Question 401

[2 marks]Matrices, Venn diagrams

Matrix

A = \begin{pmatrix} 2 & x \\ 4 & 3 \end{pmatrix}

. Simplify

A^2

, leaving the answer in terms of

x

A[[4+4x, 5x], [20, 4x+9]]
B[[4+4x, -x], [20, 4x+9]]
C[[4+4x, 0], [0, 4x+9]]
D[[4+4x, 20], [5x, 4x+9]]

Question 402

[2 marks]Matrices, Venn diagrams

Matrix

A = \begin{pmatrix} 2 & x \\ 4 & 3 \end{pmatrix}

and matrix

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

. Simplify

AB

, leaving the answer in terms of

x

Answer this when you sit the paper.

Question 403

[2 marks]Matrices, Venn diagrams

Matrix

A = \begin{pmatrix} 2 & x \\ 4 & 3 \end{pmatrix}

is singular. Find the value of

x

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Question 404

[2 marks]Matrices, Venn diagrams

39 pupils wanted to visit Great Zimbabwe (Z), 31 wanted Birchenough Bridge (B), 30 wanted Matopo (M), 10 wanted all three, 6 wanted none, 19 wanted both Z and B, 15 wanted both Z and M, 17 wanted both B and M. On the Venn diagram the Z-only region is 15, the Z∩B-only region is 9, the B∩M-only region is 7 and the M-only region is 8. Find the number in the B-only region.

Answer this when you sit the paper.

Question 405

[2 marks]Matrices, Venn diagrams

Answer this when you sit the paper.

Question 406

[1 marks]Matrices, Venn diagrams

A Venn diagram for Grade 3 learners' choice of trip has: Z-only = 15, B-only = 5, M-only = 8, Z∩B-only = 9, Z∩M-only = 5, B∩M-only = 7, all three = 10, none = 6. Write down the total number of Grade 3 learners.

Answer this when you sit the paper.

Question 501

[1 marks]Constructions & Loci

Triangle PQR is constructed accurately with

QR=7,5

cm, angle

PQR=90°

and angle

QRP=30°

, using ruler and compasses. Measure and write down the length of PR (in cm).

Answer this when you sit the paper.

Question 601

[3 marks]Simple interest, VAT, variation

Mrs Chuhwa invested a certain amount of money with a bank that offered 4,5% p.a. simple interest. After 8 months her money amounted to $504,70 before any bank charges were deducted. Calculate the amount of money that Mrs Chuhwa had initially invested.

Answer this when you sit the paper.

Question 602

[2 marks]Simple interest, VAT, variation

Mrs Bande bought a set of sofas for $368 cash, including 15% VAT. Calculate the price of the sofas excluding VAT.

Answer this when you sit the paper.

Question 603

[3 marks]Simple interest, VAT, variation

Mrs Bande paid $368 cash (including VAT) for a set of sofas. Mr Ndlovu bought a similar set on laybye terms, paying a deposit of $150 plus three equal monthly instalments of $87 (including VAT). Calculate the difference between the total amounts paid by the two customers.

Answer this when you sit the paper.

Question 604

[1 marks]Simple interest, VAT, variation

The average expenditure

E

of a family over a period of time is partly constant and partly varies as the number

n

of people in the family. Write down a relationship between

E

and

n

using constants

h

and

k

Answer this when you sit the paper.

Question 605

[2 marks]Simple interest, VAT, variation

The expenditure

E

of a family follows

E=h+kn

, where

n

is the number of people. For a family of 5,

E=\$55

; for a family of 3,

E=\$45

. Find the value of

k

Answer this when you sit the paper.

Question 606

[1 marks]Simple interest, VAT, variation

The expenditure

E

of a family follows

E=h+kn

, with

k=5

. For a family of 3,

E=\$45

. Find the value of

h

Answer this when you sit the paper.

Question 701

[2 marks]Algebra, quadratic equations, mensuration

A rectangle with a width of

(x+2)

cm has a perimeter of

(8x+2)

cm. Find an expression, in terms of

x

, for the length of the rectangle.

Answer this when you sit the paper.

Question 702

[3 marks]Algebra, quadratic equations, mensuration

A rectangle has length

(3x-1)

cm and width

(x+2)

cm. Solve

3x^2+5x-18=0

using the quadratic formula, giving both roots correct to three significant figures.

Answer this when you sit the paper.

Question 703

[2 marks]Algebra, quadratic equations, mensuration

One root of

3x^2+5x-18=0

is negative. Give this root correct to three significant figures.

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Question 704

[2 marks]Algebra, quadratic equations, mensuration

A rectangle has length

(3x-1)

cm and width

(x+2)

cm, giving a perimeter of

(8x+2)

cm, where

x

is the positive root of

3x^2+5x-18=0

x=1,75

. Find the perimeter of the rectangle (in cm).

Answer this when you sit the paper.

Question 801

[1 marks]Functional Graphs

A particle's height

h

metres above the ground after

t

seconds is

h=10+25t-5t^2

. A table of values gives

h=10

t=0

h=30

t=1

h=m

t=2

h=40

t=3

h=30

t=4

h=10

t=5

and

h=-20

t=6

. Find the value of

m

Answer this when you sit the paper.

Question 802

[1 marks]Functional Graphs

For a particle with height

h=10+25t-5t^2

metres,

h=10

m at

t=0

s and

h=-20

m at

t=6

s. Write down the distance between the initial and final positions of the particle (in metres).

Answer this when you sit the paper.

Question 803

[2 marks]Functional Graphs

A particle's height is

h=10+25t-5t^2

metres after

t

seconds. Find the greatest height reached by the particle (in metres).

Answer this when you sit the paper.

Question 804

[2 marks]Functional Graphs

A particle's height is

h=10+25t-5t^2

metres after

t

seconds. Estimate the velocity of the particle when

t=5

(in m/s).

Answer this when you sit the paper.

Question 805

[1 marks]Functional Graphs

A particle's height is

h=10+25t-5t^2

metres after

t

seconds. There are two times when the particle is 21 m above the ground; find the later of the two times, correct to 3 significant figures (in seconds).

Answer this when you sit the paper.

Question 901

[2 marks]Mensuration (prism), sine and cosine rule

Sector OAB is the cross-section of a prism, with radius 6 cm and angle

A\hat{O}B=80°

. Taking

\pi=3,142

, calculate the length of arc AB (in cm).

Answer this when you sit the paper.

Question 902

[3 marks]Mensuration (prism), sine and cosine rule

A prism has cross-section sector OAB, radius 6 cm, angle

A\hat{O}B=80°

, and the prism is 50 cm long. Taking

\pi=3,142

, calculate the total surface area of the prism, correct to 3 significant figures (in cm

^2

Answer this when you sit the paper.

Question 903

[3 marks]Mensuration (prism), sine and cosine rule

In triangle ABC, AB = 7 cm, AC = 9 cm and

\sin B\hat{A}C=\frac23

, where angle

B\hat{A}C

is acute. Find

\cos B\hat{A}C

, correct to 3 significant figures.

Answer this when you sit the paper.

Question 904

[2 marks]Mensuration (prism), sine and cosine rule

In triangle ABC, AB = 7 cm, AC = 9 cm and

\cos B\hat{A}C=0,745

. Using the cosine rule, calculate

BC^2

, correct to 3 significant figures (in cm

^2

Answer this when you sit the paper.

Question 905

[2 marks]Mensuration (prism), sine and cosine rule

In triangle ABC,

BC^2\approx36,1

^2

. Find the length of BC, correct to 3 significant figures (in cm).

Answer this when you sit the paper.

Question 1001

[1 marks]Statistics & Probability

The heights of 30 Moringa seedlings are grouped as: 5 in

10<h\le20

, 6 in

20<h\le25

, 10 in

25<h\le35

, 9 in

35<h\le40

(h in cm). Write down the modal class.

Answer this when you sit the paper.

Question 1002

[2 marks]Statistics & Probability

The heights of 30 Moringa seedlings are grouped as: 5 in

10<h\le20

, 6 in

20<h\le25

, 10 in

25<h\le35

, 9 in

35<h\le40

(h in cm). Calculate the frequency density of the class

10<h\le20

Answer this when you sit the paper.

Question 1003

[1 marks]Statistics & Probability

The heights of 30 Moringa seedlings are grouped as: 5 in

10<h\le20

, 6 in

20<h\le25

, 10 in

25<h\le35

, 9 in

35<h\le40

(h in cm). Calculate the frequency density of the class

35<h\le40

Answer this when you sit the paper.

Question 1004

[2 marks]Statistics & Probability

Of 30 Moringa seedlings, 9 have height in the class

35<h\le40

cm. Calculate the angle that would represent this class on a pie chart.

Answer this when you sit the paper.

Question 1005

[3 marks]Statistics & Probability

The heights of 30 Moringa seedlings are grouped as: 5 in

10<h\le20

, 6 in

20<h\le25

, 10 in

25<h\le35

, 9 in

35<h\le40

(h in cm). Calculate an estimate of the mean height of the seedlings (in cm), using class mid-points.

Answer this when you sit the paper.

Question 1006

[3 marks]Statistics & Probability

Of 30 Moringa seedlings, 5 are at most 20 cm tall and 9 are more than 35 cm tall. If 2 seedlings are picked at random without replacement, find the probability that one is at most 20 cm tall and the other is more than 35 cm tall.

Answer this when you sit the paper.

Question 1101

[2 marks]Geometrical Transformation

Triangle ABC has vertices

A(2;-2)

B(4;2)

C(6;2)

. Triangle

A_1B_1C_1

has vertices

A_1(-2;2)

B_1(0;6)

C_1(2;6)

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

A_1B_1C_1

ARotation of 180° about (0;2)
BTranslation by vector (4;-4)
CTranslation by vector (-4;4)
DReflection in the line x=-1

Question 1201

[1 marks]Vector Geometry

In a star diagram, a regular hexagon ABCDEF (centre X) is surrounded by 6 equilateral triangles AOB, BPC, CQD, DRE, ESF and FTA.

\vec{OA}=\mathbf{a}

and

\vec{OB}=\mathbf{b}

. Write down

\vec{OS}

in terms of

\mathbf{a}

and/or

\mathbf{b}

, in simplest form.

Answer this when you sit the paper.

Question 1202

[1 marks]Vector Geometry

In the same star diagram (regular hexagon ABCDEF surrounded by 6 equilateral triangles,

\vec{OA}=\mathbf{a}

\vec{OB}=\mathbf{b}

), write down

\vec{AB}

in terms of

\mathbf{a}

and/or

\mathbf{b}

, in simplest form.

Answer this when you sit the paper.

Question 1203

[2 marks]Vector Geometry

In the same star diagram (regular hexagon ABCDEF surrounded by 6 equilateral triangles,

\vec{OA}=\mathbf{a}

\vec{OB}=\mathbf{b}

), write down

\vec{OR}

in terms of

\mathbf{a}

and/or

\mathbf{b}

, in simplest form.

Answer this when you sit the paper.

Question 1204

[2 marks]Vector Geometry

In the same star diagram (regular hexagon ABCDEF surrounded by 6 equilateral triangles,

\vec{OA}=\mathbf{a}

\vec{OB}=\mathbf{b}

), write down

\vec{CF}

in terms of

\mathbf{a}

and/or

\mathbf{b}

, in simplest form.

Answer this when you sit the paper.

Question 1205

[2 marks]Vector Geometry

In a star diagram, triangle OAB is equilateral with

OA=OB=AB=5

cm, and

\mathbf{a}=\vec{OA}

\mathbf{b}=\vec{OB}

. Find

|\mathbf{a}-\mathbf{b}|

(in cm).

Answer this when you sit the paper.

Question 1206

[2 marks]Vector Geometry

In a star diagram, OA = 5 cm, and OQ and OS are each three times the length of OA. Triangle OQS is equilateral. Find the perimeter of triangle OQS (in cm).

Answer this when you sit the paper.

Question 1207

[2 marks]Vector Geometry

Triangle OAB is equilateral with side 5 cm. Calculate the area of triangle OAB, correct to 3 significant figures (in cm

^2

Answer this when you sit the paper.

Mathematics Paper 2 November 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 404

Question 405

Question 406

Question 501

Question 601

Question 602

Question 603

Question 604

Question 605

Question 606

Question 701

Question 702

Question 703

Question 704

Question 801

Question 802

Question 803

Question 804

Question 805

Question 901

Question 902

Question 903

Question 904

Question 905

Question 1001

Question 1002

Question 1003

Question 1004

Question 1005

Question 1006

Question 1101

Question 1201

Question 1202

Question 1203

Question 1204

Question 1205

Question 1206

Question 1207

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The answers, and why they are the answers

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