ZIMSEC O Level Mathematics Paper 1 November 2018

Question 101

[1 marks]Laws of Indices

Simplify

\frac{2^3}{5^2}

, giving the answer as a fraction.

Answer this when you sit the paper.

Question 102

[1 marks]Fractions, Decimals & Percentages

Express

\frac{6}{25}

as a decimal fraction.

Answer this when you sit the paper.

Question 103

[1 marks]Ordinary and Standard Form

Express 0,125 in standard form.

Answer this when you sit the paper.

Question 201

[1 marks]Prime Numbers, Sequences & Types of Numbers

The following is a list of real numbers:

\frac{3}{7}

; 11;

\sqrt{\frac{3}{2}}

; 121;

-19

;

\pi

;

\sqrt{64}

. Choose from the list a square number.

Answer this when you sit the paper.

Question 202

[2 marks]Prime Numbers, Sequences & Types of Numbers

The following is a list of real numbers:

\frac{3}{7}

; 11;

\sqrt{\frac{3}{2}}

; 121;

-19

;

\pi

;

\sqrt{64}

. Choose from the list the irrational numbers.

Answer this when you sit the paper.

Question 301

[1 marks]Number Bases

Express

4 \times 5^3 + 3 \times 5^2 + 2

as a number in base 5.

Answer this when you sit the paper.

Question 303

[1 marks]Number Bases

Evaluate

512_7 - 435_7

, giving the answer in base 7.

Answer this when you sit the paper.

Question 401

[1 marks]Time

Express 00 45 in 12 hour notation.

Answer this when you sit the paper.

Question 402

[1 marks]Time

Gortha's local time is 3 hours 45 minutes ahead of Harare's local time. Find the time in Harare when the time in Gortha is 21 23.

Answer this when you sit the paper.

Question 403

[1 marks]Change of Units

Convert

5\ \text{km}^2

to hectares.

Answer this when you sit the paper.

Question 501

[1 marks]Ordinary and Standard Form

Express

6,07 \times 10^4

in ordinary form.

Answer this when you sit the paper.

Question 502

[2 marks]Ordinary and Standard Form

Evaluate

2,53 \times 10^1 + 6,1 \times 10^{-1}

, giving the answer in standard form.

Answer this when you sit the paper.

Question 601

[1 marks]Polygons, Symmetry and Circles

In the diagram AQ and BS are parallel lines such that PQ = PR,

A\hat{P}R = 84^\circ

and

R\hat{Q}S = 90^\circ

. Find

P\hat{R}Q

Answer this when you sit the paper.

Question 602

[1 marks]Polygons, Symmetry and Circles

In the diagram AQ and BS are parallel lines such that PQ = PR,

A\hat{P}R = 84^\circ

and

R\hat{Q}S = 90^\circ

. Find

Q\hat{R}B

Answer this when you sit the paper.

Question 603

[1 marks]Polygons, Symmetry and Circles

In the diagram AQ and BS are parallel lines such that PQ = PR,

A\hat{P}R = 84^\circ

and

R\hat{Q}S = 90^\circ

. Find

Q\hat{S}R

Answer this when you sit the paper.

Question 701

[4 marks]Simultaneous Equations

Solve the simultaneous equations

2x + 3y = 11

and

3x - 5y = -12

Answer this when you sit the paper.

Question 801

[2 marks]Variation

The wave length,

w

, is inversely proportional to its frequency,

f

. When

f = 90

w = 675

. Find an equation connecting

f

and

w

Answer this when you sit the paper.

Question 802

[1 marks]Variation

The wave length,

w

, is inversely proportional to its frequency,

f

. When

f = 90

w = 675

. Find the value of

f

when

w = 500

Answer this when you sit the paper.

Question 901

[1 marks]Approximations and Estimations

Write 45,3981 correct to 4 significant figures.

Answer this when you sit the paper.

Question 902

[2 marks]Approximations and Estimations

A student spends 8 seconds, correct to the nearest second, to solve a problem. Find the limits between which this time lies in the form

a \le t < b

where

a

and

b

are constants and

t

is the time.

Answer this when you sit the paper.

Question 1001

[1 marks]Factorisation, H.C.F and L.C.M

Factorise

3x^2 - 15x

completely.

Answer this when you sit the paper.

Question 1002

[2 marks]Factorisation, H.C.F and L.C.M

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

8kl^2m

28k^2l^3m

and

36l^2mn

Answer this when you sit the paper.

Question 1101

[1 marks]Co-ordinate Geometry

The points A(6; 2) and B(8; 5) lie on a straight line. Find the gradient of the line AB.

Answer this when you sit the paper.

Question 1102

[2 marks]Co-ordinate Geometry

The points A(6; 2) and B(8; 5) lie on a straight line. Find the equation of the line AB, giving the answer in the form

y = mx + c

Answer this when you sit the paper.

Question 1201

[3 marks]Algebraic Fractions

Simplify

\frac{2a + 6}{a - 3} \div \frac{a + 3}{a^2 - 2a - 3}

Answer this when you sit the paper.

Question 1302

[2 marks]Fractions, Decimals & Percentages

In 2016 a farmer harvested 45 tonnes of maize. This was 20% more than what he had harvested in 2015. Find the number of tonnes of maize the farmer harvested in 2015.

Answer this when you sit the paper.

Question 1401

[2 marks]Inequalities

Solve the inequality

4 - 5x < 2x + 8

Answer this when you sit the paper.

Question 1402

[1 marks]Inequalities

Write down the smallest integer that satisfies the inequality

4 - 5x < 2x + 8

Answer this when you sit the paper.

Question 1501

[1 marks]Logarithms

\log a = 3

and

\log b = 7

, calculate

\log ab

Answer this when you sit the paper.

Question 1502

[1 marks]Logarithms

\log a = 3

and

\log b = 7

, calculate

\log \frac{1}{b}

Answer this when you sit the paper.

Question 1503

[2 marks]Logarithms

\log a = 3

and

\log b = 7

, calculate

\log \sqrt[3]{a}

Answer this when you sit the paper.

Question 1601

[2 marks]Functional Notation

If a function

f(x) = (x + 4)(2x - 1)

, find

f(3)

Answer this when you sit the paper.

Question 1602

[2 marks]Algebra

Solve the equation

\frac{3m}{4} - \frac{m}{3} = 2\frac{1}{2}

Answer this when you sit the paper.

Question 1701

[1 marks]Vector Geometry

It is given that vector

p = \begin{pmatrix} 0 \\ -3 \end{pmatrix}

and vector

q = \begin{pmatrix} x \\ 1 \end{pmatrix}

. Find

p - q

in terms of

x

in its simplest form.

Answer this when you sit the paper.

Question 1702

[3 marks]Vector Geometry

It is given that vector

p = \begin{pmatrix} 0 \\ -3 \end{pmatrix}

and vector

q = \begin{pmatrix} x \\ 1 \end{pmatrix}

. Find the possible values of

x

given that

|p - q| = 5

Answer this when you sit the paper.

Question 1801

[1 marks]Polygons, Symmetry and Circles

State the special name given to a regular polygon with 4 sides.

Answer this when you sit the paper.

Question 1802

[3 marks]Polygons, Symmetry and Circles

The angles of a hexagon are

115^\circ

89^\circ

x^\circ

x^\circ

x^\circ

and

x^\circ

. Find the value of

x

Answer this when you sit the paper.

Question 1901

[2 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ABC is right angled at B, BCD is a straight line, AC = 12 cm and

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

. [

\sin 45^\circ = \frac{\sqrt{2}}{2}

\cos 45^\circ = \frac{\sqrt{2}}{2}

] Using as much of the information given above as is necessary, calculate BC, leaving the answer in surd form.

Answer this when you sit the paper.

Question 1902

[1 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ABC is right angled at B, BCD is a straight line, AC = 12 cm and

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

. [

\sin 45^\circ = \frac{\sqrt{2}}{2}

\cos 45^\circ = \frac{\sqrt{2}}{2}

] Using as much of the information given above as is necessary, calculate

\sin A\hat{C}D

, leaving the answer in surd form.

Answer this when you sit the paper.

Question 1903

[2 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ABC is right angled at B, BCD is a straight line, AC = 12 cm and

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

. Using as much of the information given above as is necessary, calculate

\tan A\hat{C}D

Answer this when you sit the paper.

Question 2001

[1 marks]Statistics

The table shows the heights,

h

, of 50 trees in a school orchard. Write down the interval which contains the modal height.

Answer this when you sit the paper.

Question 2002

[1 marks]Statistics

The table shows the heights,

h

, of 50 trees in a school orchard. Write down the interval which contains the median height.

Answer this when you sit the paper.

Question 2003

[3 marks]Statistics

The table shows the heights,

h

, of 50 trees in a school orchard. Calculate an estimate of the mean height of the trees.

Answer this when you sit the paper.

Question 2101

[2 marks]Probability

The probability that Themba will score in a match is

\frac{1}{3}

. The probability that Allan will score in the same match is

\frac{3}{4}

. Calculate the probability that in the same match both score.

Answer this when you sit the paper.

Question 2102

[2 marks]Probability

The probability that Themba will score in a match is

\frac{1}{3}

. The probability that Allan will score in the same match is

\frac{3}{4}

. Calculate the probability that in the same match neither of them scores.

Answer this when you sit the paper.

Question 2103

[2 marks]Probability

The probability that Themba will score in a match is

\frac{1}{3}

. The probability that Allan will score in the same match is

\frac{3}{4}

. Calculate the probability that in the same match only one of them scores.

Answer this when you sit the paper.

Question 2202

[2 marks]Travel Graphs

The graph shows the motion of an athlete running on level ground at a constant speed of 12 m/s for 5 seconds. The athlete then retards uniformly to rest after a further 3 seconds. Calculate the total distance covered in the 8 seconds.

Answer this when you sit the paper.

Question 2203

[2 marks]Travel Graphs

Answer this when you sit the paper.

Question 2301

[1 marks]Circle Geometry

In the diagram points A, B and C are on the circumference of circle centre O, OB = 7 cm and

A\hat{O}B = 60^\circ

. In this question take

\pi

to be

\frac{22}{7}

. Calculate

A\hat{C}B

Answer this when you sit the paper.

Question 2302

[1 marks]Circle Geometry

In the diagram points A, B and C are on the circumference of circle centre O, OB = 7 cm and

A\hat{O}B = 60^\circ

. In this question take

\pi

to be

\frac{22}{7}

. Calculate

O\hat{A}B

Answer this when you sit the paper.

Question 2303

[2 marks]Circle Geometry

In the diagram points A, B and C are on the circumference of circle centre O, OB = 7 cm and

A\hat{O}B = 60^\circ

. In this question take

\pi

to be

\frac{22}{7}

. Calculate the length of minor arc AB.

Answer this when you sit the paper.

Question 2304

[2 marks]Circle Geometry

In the diagram points A, B and C are on the circumference of circle centre O, OB = 7 cm and

A\hat{O}B = 60^\circ

. In this question take

\pi

to be

\frac{22}{7}

. Calculate the area of the minor sector AOB.

Answer this when you sit the paper.

Question 2401

[2 marks]Sets

It is given that the universal set,

\xi

, has subsets P, S and M such that

\xi = \{1; 2; 3; 4; 5; 6; 7; 8; 9\}

, P = {prime numbers}, S = {perfect square numbers} and M = {multiples of 3}. List all elements of set P.

Answer this when you sit the paper.

Question 2402

[1 marks]Sets

It is given that the universal set,

\xi

, has subsets P, S and M such that

\xi = \{1; 2; 3; 4; 5; 6; 7; 8; 9\}

, P = {prime numbers}, S = {perfect square numbers} and M = {multiples of 3}. Write down

n(P \cap S \cap M)

Answer this when you sit the paper.

Question 2501

[3 marks]Geometrical Transformation

The graph shows triangles X and Y. Triangle Y is an image of triangle X under a certain single transformation. Describe fully the single transformation which maps triangle X onto triangle Y.

Answer this when you sit the paper.

Question 2502

[2 marks]Geometrical Transformation

Triangle Z is the image of triangle X under an Enlargement of scale factor 2 and centre (0; 0). State the matrix that represents the enlargement.

Answer this when you sit the paper.

Mathematics Paper 1 November 2018

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 303

Question 401

Question 402

Question 403

Question 501

Question 502

Question 601

Question 602

Question 603

Question 701

Question 801

Question 802

Question 901

Question 902

Question 1001

Question 1002

Question 1101

Question 1102

Question 1201

Question 1302

Question 1401

Question 1402

Question 1501

Question 1502

Question 1503

Question 1601

Question 1602

Question 1701

Question 1702

Question 1801

Question 1802

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2103

Question 2202

Question 2203

Question 2301

Question 2302

Question 2303

Question 2304

Question 2401

Question 2402

Question 2501

Question 2502

More sittings of this paper

The answers, and why they are the answers

Sit this paper online