ZIMSEC O Level Mathematics Paper 1 June 2020

Question 101

[1 marks]Ordinary and Standard Form

Express 208,9 in standard form.

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Question 102

[1 marks]Approximations and Estimations

Express 208,9 correct to 3 significant figures.

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Question 103

[1 marks]Approximations and Estimations

Express 208,9 correct to the nearest hundred.

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Question 201

[1 marks]Laws of Indices

Evaluate

-10^{0}

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Question 202

[2 marks]Laws of Indices

Evaluate

\left(\dfrac{4}{9}\right)^{\frac{3}{2}}

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Question 301

[1 marks]Sets

The Venn diagram shows three sets A, B and C with their respective elements. List all elements of

A \cap B

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Question 302

[1 marks]Sets

The Venn diagram shows three sets A, B and C with their respective elements. List all elements of

(A \cup B)' \cap C

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Question 303

[1 marks]Sets

The Venn diagram shows three sets A, B and C with their respective elements. Find

n(A \cup C)

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Question 401

[2 marks]Inequalities

Solve the inequality

2 - y < 3y - 10

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Question 402

[1 marks]Inequalities

The perfect square,

y

, satisfies both

2 - y < 3y - 10

and

y \le 9

. Find the possible values of

y

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Question 501

[3 marks]Simultaneous Equations

Solve the simultaneous equations:

2x + y = 4

x - y = -2

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Question 601

[1 marks]Number Bases

Convert

301_4

to a number in base 10.

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Question 602

[1 marks]Number Bases

Evaluate

1101_2 + 111_2

, giving the answer in base 2.

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Question 603

[1 marks]Number Bases

Evaluate

131_5 - 42_5

, giving the answer in base 5.

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Question 701

[3 marks]Statistics

The mean of 3 numbers is 7. Two of the numbers are 4 and

-5

. Find the third number.

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Question 801

[1 marks]Substitution

Given that

m = \dfrac{1}{2}

and

n = -2

, evaluate

m - n

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Question 802

[2 marks]Substitution

Given that

m = \dfrac{1}{2}

and

n = -2

, evaluate

\dfrac{mn}{m + n}

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Question 901

[3 marks]Algebraic Fractions

Express

\dfrac{2}{2 - 3n} - \dfrac{1}{n}

as a single fraction in its simplest terms.

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Question 1001

[3 marks]Matrices

The matrix

\begin{pmatrix} (x+2) & 4 \\ 6 & x \end{pmatrix}

is singular. Find the possible values of

x

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Question 1101

[3 marks]Functional Notation

Given that

f(x) = \dfrac{k + x}{3x - 2}

and that

f\left(-\dfrac{1}{3}\right) = \dfrac{1}{6}

, find the value of

k

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Question 1201

[1 marks]Vectors

It is given that

\mathbf{p} = \begin{pmatrix} 5 \\ 4 \end{pmatrix}

\mathbf{q} = \begin{pmatrix} -3 \\ 2 \end{pmatrix}

and

\mathbf{r} = \begin{pmatrix} x \\ y \end{pmatrix}

. Find

|\mathbf{p}|

, leaving the answer in surd form.

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Question 1202

[2 marks]Vectors

It is given that

\mathbf{p} = \begin{pmatrix} 5 \\ 4 \end{pmatrix}

\mathbf{q} = \begin{pmatrix} -3 \\ 2 \end{pmatrix}

and

\mathbf{r} = \begin{pmatrix} x \\ y \end{pmatrix}

. Find the value of

x

and the value of

y

\mathbf{p} - \mathbf{q} = 2\mathbf{r}

Answer this when you sit the paper.

Question 1301

[1 marks]Consumer Arithmetic

A salesman's total monthly salary consists of a basic salary of $200 and a 2% commission on his monthly sales. In one month his total salary was $560. Calculate his commission for that month.

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Question 1302

[2 marks]Consumer Arithmetic

A salesman's total monthly salary consists of a basic salary of $200 and a 2% commission on his monthly sales. In one month his total salary was $560. Calculate the sales he made for that month.

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Question 1401

[2 marks]Trigonometry, Bearing & Distances

It is given that

\sin y = \dfrac{5}{13}

and that

y

is an acute angle. Find, as a common fraction,

\cos(180^\circ - y^\circ)

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Question 1402

[1 marks]Trigonometry, Bearing & Distances

It is given that

\sin y = \dfrac{5}{13}

and that

y

is an acute angle. Find, as a common fraction,

\tan y^\circ

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Question 1501

[1 marks]Statistics

The table shows grades obtained by 150 candidates in a Mathematics test.

Grade	A	B	C	D	E	U
Frequency	5	25	30	29	21	40

Find the median grade.

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Question 1502

[2 marks]Probability

The table shows grades obtained by 150 candidates in a Mathematics test.

Grade	A	B	C	D	E	U
Frequency	5	25	30	29	21	40

Calculate the probability that two candidates chosen at random from the 150 obtained grade A or B.

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Question 1601

[1 marks]Geometrical Transformation

Point R(

-3

;

-2

) is mapped onto point

R_1

by a transformation represented by the matrix

\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}

. Find the coordinates of

R_1

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Question 1602

[2 marks]Geometrical Transformation

In the diagram triangle P is the image of triangle Q under a certain transformation. Describe fully the single transformation that maps triangle P onto triangle Q.

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Question 1701

[2 marks]Variation

It is given that

g \propto \dfrac{m}{r}

and

g = 1

when

m = 2

and

r = 3

. Find the formula connecting

g

m

and

r

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Question 1702

[1 marks]Variation

It is given that

g \propto \dfrac{m}{r}

and

g = 1

when

m = 2

and

r = 3

. Find the numerical value of

g

when

m = 10

and

r = 3

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Question 1801

[1 marks]Circle Geometry

In the diagram A, B, C and D are points on the circumference of a circle centre O. PD is a tangent to the circle at D,

A\hat{D}B = 28^\circ

and

C\hat{B}D = 47^\circ

. Calculate

B\hat{A}D

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Question 1802

[1 marks]Circle Geometry

In the diagram A, B, C and D are points on the circumference of a circle centre O. PD is a tangent to the circle at D,

A\hat{D}B = 28^\circ

and

C\hat{B}D = 47^\circ

. Calculate

C\hat{D}P

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Question 1803

[1 marks]Circle Geometry

In the diagram A, B, C and D are points on the circumference of a circle centre O. PD is a tangent to the circle at D,

A\hat{D}B = 28^\circ

and

C\hat{B}D = 47^\circ

. Calculate

C\hat{A}B

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Question 1804

[1 marks]Circle Geometry

In the diagram A, B, C and D are points on the circumference of a circle centre O. PD is a tangent to the circle at D,

A\hat{D}B = 28^\circ

and

C\hat{B}D = 47^\circ

. Calculate

B\hat{C}D

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Question 1901

[2 marks]Algebraic Expressions

Simplify

4b - 3(4 - 2b)

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Question 1902

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

Factorise completely

x - y - xy + x^2

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Question 2001

[1 marks]Polygons, Symmetry and Circles

Name the regular polygon which has rotational symmetry of order 5.

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Question 2002

[3 marks]Polygons, Symmetry and Circles

The sum of the interior angles of a hexagon is

720^\circ

. Three of its interior angles are

140^\circ

120^\circ

and

160^\circ

. The remaining angles are in the ratio

2 : 3 : 5

. Calculate the size of the largest of the remaining angles.

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Question 2101

[2 marks]Logarithms

It is given that

\log x = 6

and

\log y = -2

. Evaluate

\log(xy)

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Question 2102

[2 marks]Logarithms

It is given that

\log x = 6

and

\log y = -2

. Evaluate

\log\left(\dfrac{1}{\sqrt{x}}\right)

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Question 2201

[2 marks]Scales & Simple Map Problems

On a certain map, a length of 2 cm represents a distance of 5 km. Express the scale of the map giving the answer in the form

1 : n

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Question 2202

[2 marks]Scales & Simple Map Problems

On a certain map, a length of 2 cm represents a distance of 5 km. Calculate the area on the map in

\text{cm}^2

which represents an actual area of

4\ \text{km}^2

Answer this when you sit the paper.

Question 2301

[1 marks]Similarity and Congruency

In the diagram AODF and BOCE are straight lines intersecting at O. AB is parallel to CD and EF, AB = CD = 6 cm, OD = 4 cm and DF = 8 cm. Name the triangle which is congruent to triangle AOB.

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Question 2302

[2 marks]Similarity and Congruency

In the diagram AODF and BOCE are straight lines intersecting at O. AB is parallel to CD and EF, AB = CD = 6 cm, OD = 4 cm and DF = 8 cm. Name two triangles which are similar to triangle AOB.

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Question 2303

[2 marks]Similarity and Congruency

In the diagram AODF and BOCE are straight lines intersecting at O. AB is parallel to CD and EF, AB = CD = 6 cm, OD = 4 cm and DF = 8 cm. Calculate the length EF.

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Question 2401

[2 marks]Co-ordinate Geometry

A straight line has gradient

-1

and passes through the point

(3; 0)

. Find the equation of the line in the form

y = mx + c

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Question 2402

[3 marks]Quadratic Equations

The solutions of a quadratic equation are

x = -1

and

x = 3

. Write down the quadratic equation in the form

ax^2 + bx + c = 0

where

a

b

and

c

are integers.

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Question 2501

[2 marks]Trigonometry, Bearing & Distances

The diagram shows triangle XYZ with XY = 6 cm, XZ = 10 cm and

Y\hat{X}Z = 30^\circ

. Use as much of the information given below as is necessary. [

\sin 30^\circ = 0,50

\cos 30^\circ = 0,87

\tan 30^\circ = 0,58

] Calculate the area of the triangle XYZ.

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Question 2502

[3 marks]Trigonometry, Bearing & Distances

The diagram shows triangle XYZ with XY = 6 cm, XZ = 10 cm and

Y\hat{X}Z = 30^\circ

. Use as much of the information given below as is necessary. [

\sin 30^\circ = 0,50

\cos 30^\circ = 0,87

\tan 30^\circ = 0,58

] Calculate the length of YZ leaving the answer in surd form.

Answer this when you sit the paper.

Question 2601

[2 marks]Travel Graphs

The diagram is a speed-time graph of an object which decelerates uniformly from a speed of 50 m/s to a speed of 30 m/s in 20 seconds. It further decelerates uniformly for 10 seconds until it comes to rest. Find the speed when

t = 5

seconds.

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Question 2602

[2 marks]Travel Graphs

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Question 2603

[2 marks]Travel Graphs

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Question 2701

[3 marks]Measures and Mensuration

The diagram shows the cross-section of a concrete drinking trough which is 3 m long. AB = 2,2 m, BC = AG = 1 m and CD = FG = 0,4 m. DF, the diameter of the drinking trough, is 1,4 m. Take

\pi

to be

\dfrac{22}{7}

. Calculate the perimeter of the cross-section.

Answer this when you sit the paper.

Question 2702

[3 marks]Measures and Mensuration

The diagram shows the cross-section of a concrete drinking trough which is 3 m long. AB = 2,2 m, BC = AG = 1 m and CD = FG = 0,4 m. DF, the diameter of the drinking trough, is 1,4 m. Take

\pi

to be

\dfrac{22}{7}

. Calculate the area of the cross-section.

Answer this when you sit the paper.

Question 2703

[2 marks]Measures and Mensuration

The diagram shows the cross-section of a concrete drinking trough which is 3 m long. AB = 2,2 m, BC = AG = 1 m and CD = FG = 0,4 m. DF, the diameter of the drinking trough, is 1,4 m. Take

\pi

to be

\dfrac{22}{7}

. Calculate the volume of the concrete used to make the drinking trough.

Answer this when you sit the paper.

Mathematics Paper 1 June 2020

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 302

Question 303

Question 401

Question 402

Question 501

Question 601

Question 602

Question 603

Question 701

Question 801

Question 802

Question 901

Question 1001

Question 1101

Question 1201

Question 1202

Question 1301

Question 1302

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1602

Question 1701

Question 1702

Question 1801

Question 1802

Question 1803

Question 1804

Question 1901

Question 1902

Question 2001

Question 2002

Question 2101

Question 2102

Question 2201

Question 2202

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2501

Question 2502

Question 2601

Question 2602

Question 2603

Question 2701

Question 2702

Question 2703

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