ZIMSEC O Level Mathematics Paper 1 June 2011

Question 101

[3 marks]Fractions, Decimals & Percentages

Simplify

\dfrac{\frac{2}{3} + \frac{3}{4}}{1\frac{1}{6}}

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Question 201

[1 marks]Ratios, Rates & Proportions

Express the ratio 20 minutes :

1\frac{1}{3}

hours, in its simplest form.

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Question 202

[2 marks]Ratios, Rates & Proportions

Two partners, A and B, shared their profits from a business in the ratio

5 : 3

. If B received \$4 800 000, calculate A's share.

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Question 301

[1 marks]Polygons, Symmetry & Circles

In the diagram, PQRS is a parallelogram,

P\hat{S}Q = 85^\circ

S\hat{R}Q = 60^\circ

and SQT is a straight line. Find

P\hat{Q}R

Answer this when you sit the paper.

Question 302

[1 marks]Polygons, Symmetry & Circles

In the diagram, PQRS is a parallelogram,

P\hat{S}Q = 85^\circ

S\hat{R}Q = 60^\circ

and SQT is a straight line. Find

R\hat{S}Q

Answer this when you sit the paper.

Question 303

[1 marks]Polygons, Symmetry & Circles

In the diagram, PQRS is a parallelogram,

P\hat{S}Q = 85^\circ

S\hat{R}Q = 60^\circ

and SQT is a straight line. Find

R\hat{Q}T

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Question 401

[2 marks]Trigonometry, Bearing & Distances

The bearing of village P from village Q is 109°. Find the three figure bearing of Q from P.

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Question 402

[1 marks]Trigonometry, Bearing & Distances

The bearing of village P from village Q is 109°. Find the compass bearing of Q from P.

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Question 501

[2 marks]Inequalities & Linear Programming

Solve

x - 3 \le 3x + 10

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Question 502

[1 marks]Inequalities & Linear Programming

Given that

x

is an integer, write down the least value of

x

for which

x - 3 \le 3x + 10

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Question 601

[3 marks]Change of Subject of Formula

Make

u

the subject of the formula

T = \dfrac{mu^2}{K} - 5mg

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Question 701

[1 marks]Number Bases

Express

5^2 + 3 \times 5 + 4

as a number in base 5.

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Question 702

[2 marks]Number Bases

Express

5^2 + 3 \times 5 + 4

as a number in base 8.

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Question 801

[1 marks]Polygons, Symmetry & Circles

State the order of rotational symmetry of a parallelogram.

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Question 802

[2 marks]Polygons, Symmetry & Circles

The triangle XYZ has XY = 5 cm and YZ = 6 cm. Given that the triangle XYZ has only one line of symmetry, write down the two possible lengths of XZ.

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Question 901

[3 marks]Approximations & Estimations

A rectangle measures 10,2 cm by 7,1 cm, correct to one decimal place. Find the minimum possible perimeter of the rectangle.

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Question 1001

[1 marks]Variation

A car uses

l

litres of petrol for every

d

kilometres travelled. State the type of variation between

l

and

d

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Question 1002

[2 marks]Variation

A car uses

l

litres of petrol for every

d

kilometres travelled, so

l

varies directly as

d

. Given that the car uses 5 litres to cover 60 kilometres, find the equation connecting

l

and

d

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Question 1101

[1 marks]Laws of Indices

Evaluate

3m^{-5} \times 2m^{5}

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Question 1102

[2 marks]Laws of Indices

Evaluate

\left(\dfrac{4}{9}\right)^{-\frac{1}{2}}

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Question 1201

[1 marks]Polygons, Symmetry & Circles

In the diagram, ABCD and PBCQ are intersecting circles. DCQ and ABP are straight lines. Given that

A\hat{D}C = 95^\circ

, calculate

A\hat{B}C

Answer this when you sit the paper.

Question 1202

[1 marks]Polygons, Symmetry & Circles

In the diagram, ABCD and PBCQ are intersecting circles. DCQ and ABP are straight lines. Given that

A\hat{D}C = 95^\circ

, calculate

P\hat{Q}C

Answer this when you sit the paper.

Question 1203

[1 marks]Polygons, Symmetry & Circles

In the diagram, ABCD and PBCQ are intersecting circles. DCQ and ABP are straight lines. Given that

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

, find an expression for

B\hat{P}Q

in terms of

x

Answer this when you sit the paper.

Question 1301

[1 marks]Sets

In the Venn diagram, R, S, T and

\xi

are sets with their elements as shown. The region inside R only holds 5, the region common to R and S only holds 7, the region common to all three sets holds 4, the region common to R and T only holds 8, the region common to S and T only holds 6, the region inside T only holds 1, 2 and 9, and 11 and 12 lie inside the universal set but outside all three sets. Nothing lies inside S alone. Use the Venn diagram to find

R' \cap S

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Question 1302

[1 marks]Sets

In the Venn diagram, R, S, T and

\xi

(R \cap S) \cup (R \cap T)

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Question 1303

[1 marks]Sets

In the Venn diagram, R, S, T and

\xi

n(R \cup S \cup T)'

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Question 1401

[3 marks]Logarithms

Express

\log_{10} x + 2\log_{10} y = 1

as an equation in index form.

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Question 1501

[1 marks]Vector Geometry

It is given that

\mathbf{p} = \begin{pmatrix} 6 \\ -8 \end{pmatrix}

and

\mathbf{q} = \begin{pmatrix} 3 \\ 5 \end{pmatrix}

. Express

\mathbf{p} - 3\mathbf{q}

as a column vector.

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Question 1502

[2 marks]Vector Geometry

It is given that

\mathbf{p} = \begin{pmatrix} 6 \\ -8 \end{pmatrix}

\mathbf{q} = \begin{pmatrix} 3 \\ 5 \end{pmatrix}

and

\mathbf{r} = \begin{pmatrix} m \\ n \end{pmatrix}

. Given that

\mathbf{p} + \mathbf{q} = 3\mathbf{r}

, find the value of

m

and the value of

n

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Question 1601

[1 marks]Fractions, Decimals & Percentages

Convert the fraction

\dfrac{3}{8}

to a percentage.

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Question 1602

[1 marks]Fractions, Decimals & Percentages

Convert 9% to a decimal fraction.

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Question 1603

[2 marks]Rational, Irrational Numbers & Surds

Simplify the expression

\sqrt{3} + \sqrt{12}

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Question 1701

[1 marks]Travel Graphs

In the diagram, O, A, B and C are four points on the velocity-time graph of an object. The object speeds up from rest at O to 40 m/s at A after 8 seconds, holds 40 m/s from A to B until 16 seconds, then slows to rest at C after 20 seconds. Describe the motion of the object from O to A.

AIt moves at a constant velocity of 40 m/s.
BIt accelerates uniformly from rest.
CIt is at rest.
DIt decelerates uniformly to rest.

Question 1702

[1 marks]Travel Graphs

AIt accelerates uniformly.
BIt decelerates uniformly.
CIt moves at a constant velocity of 40 m/s.
DIt is at rest.

Question 1703

[2 marks]Travel Graphs

Answer this when you sit the paper.

Question 1801

[1 marks]Statistics & Probability

The following entries show the number of bicycles sold per day in nine days.

6; 10; 12; 9; 14; 10; 15; 10; 12

Find the mode.

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Question 1802

[1 marks]Statistics & Probability

The following entries show the number of bicycles sold per day in nine days.

6; 10; 12; 9; 14; 10; 15; 10; 12

Find the median.

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Question 1803

[2 marks]Statistics & Probability

The following entries show the number of bicycles sold per day in nine days.

6; 10; 12; 9; 14; 10; 15; 10; 12

Find the next entry if the new mean on the tenth day is 12.

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Question 1901

[2 marks]Algebraic Expressions

Expand and simplify

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

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Question 1902

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

Factorise completely

20x^2 - 5y^2

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Question 2001

[1 marks]Similarity & Congruency

In the diagram,

D\hat{A}B = A\hat{B}C

, AD = BC and AC and BD intersect at P. Name the triangle that is congruent to triangle ABC.

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Question 2002

[1 marks]Similarity & Congruency

In the diagram,

D\hat{A}B = A\hat{B}C

, AD = BC and AC and BD intersect at P. Triangle ABC is congruent to triangle BAD. State the case for congruency.

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Question 2003

[2 marks]Similarity & Congruency

The sides of a triangle X are 9 cm, 7 cm and 6 cm. The shortest side of a triangle Y, which is similar to triangle X, is 3 cm. Write down the ratio, area of X : area of Y.

Answer this when you sit the paper.

Question 2101

[1 marks]Co-ordinate Geometry

In the diagram, PQ and MN are two straight lines which intersect at T. PQ passes through the origin and through the point

(-3;\ -3)

, and MN cuts the

y

-axis at

(0;\ 4)

and the

x

-axis at

(2;\ 0)

. Find the equation of the line PQ.

Answer this when you sit the paper.

Question 2102

[2 marks]Co-ordinate Geometry

In the diagram, PQ and MN are two straight lines which intersect at T. PQ passes through the origin and through the point

(-3;\ -3)

, and MN cuts the

y

-axis at

(0;\ 4)

and the

x

-axis at

(2;\ 0)

. Find the equation of the line MN.

Answer this when you sit the paper.

Question 2103

[2 marks]Co-ordinate Geometry

In the diagram, PQ and MN are two straight lines which intersect at T. PQ passes through the origin and through the point

(-3;\ -3)

, and MN cuts the

y

-axis at

(0;\ 4)

and the

x

-axis at

(2;\ 0)

. Calculate the coordinates of the point T.

Answer this when you sit the paper.

Question 2201

[2 marks]Consumer Arithmetic

The following is an extract from Mrs Green's telephone Bill for the period 01/03/06 to 31/03/06.

\$
Rental ............................ 2 000
177 units at $X$ cents/unit ........ 7 965
Sub-Total ......................... 9 965
VAT at 15% ............................ $Y$
Amount due ............................ $Z$

Calculate $X$ .

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Question 2202

[2 marks]Consumer Arithmetic

The following is an extract from Mrs Green's telephone Bill for the period 01/03/06 to 31/03/06.

Calculate $Y$ .

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Question 2203

[1 marks]Consumer Arithmetic

The following is an extract from Mrs Green's telephone Bill for the period 01/03/06 to 31/03/06.

Calculate $Z$ .

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Question 2401

[1 marks]Algebraic Fractions

Solve the equation

\dfrac{2}{x + 2} = \dfrac{1}{3}

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Question 2402

[2 marks]Functional Notation

Given that

f(x) = x^2 + x

, find

f(3)

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Question 2403

[2 marks]Functional Notation

Given that

f(x) = x^2 + x

, find the values of

x

for which

f(x) = 0

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Question 2501

[1 marks]Statistics & Probability

When a biased coin is tossed, the probability of getting a head is 0,6. For this coin, find the probability of getting a tail if it is tossed once.

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Question 2502

[2 marks]Statistics & Probability

When a biased coin is tossed, the probability of getting a head is 0,6. For this coin, find the probability of getting at least one head if it is tossed twice.

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Question 2503

[2 marks]Statistics & Probability

When a biased coin is tossed, the probability of getting a head is 0,6. For this coin, find the expected number of heads if it is tossed 50 times.

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Question 2601

[1 marks]Functional Graphs

In the diagram, the curve

y = x^2

and the line

y = 8 - 2x

intersect at A and at B, A being the point of intersection on the left and B the point of intersection on the right. Write down the gradient of the line

y = 8 - 2x

Answer this when you sit the paper.

Question 2602

[1 marks]Functional Graphs

In the diagram, the curve

y = x^2

and the line

y = 8 - 2x

intersect at A and at B, A being the point of intersection on the left and B the point of intersection on the right. Write down the equation of the line passing through the origin and parallel to the line

y = 8 - 2x

Answer this when you sit the paper.

Question 2603

[1 marks]Functional Graphs

In the diagram, the curve

y = x^2

and the line

y = 8 - 2x

intersect at A and at B, A being the point of intersection on the left and B the point of intersection on the right. Write down the

x

-coordinate of A.

Answer this when you sit the paper.

Question 2604

[1 marks]Functional Graphs

In the diagram, the curve

y = x^2

and the line

y = 8 - 2x

intersect at A and at B, A being the point of intersection on the left and B the point of intersection on the right. Write down the

x

-coordinate of B.

Answer this when you sit the paper.

Question 2605

[1 marks]Quadratic Equations

The curve

y = x^2

and the line

y = 8 - 2x

meet at points whose

x

-coordinates are

-4

and

2

. Write down an equation in

x

whose roots are

-4

and

2

Answer this when you sit the paper.

Question 2701

[2 marks]Measures & Mensuration

In this question take

\pi

to be 3,14. A spherical ball is 20 centimetres in diameter. Calculate the surface area of the ball, in

\text{cm}^2

. [Surface area

= 4\pi r^2

]

Answer this when you sit the paper.

Question 2702

[3 marks]Measures & Mensuration

In this question take

\pi

to be 3,14. A spherical ball is 20 centimetres in diameter. Calculate the volume of the ball, correct to the nearest whole number, in

\text{cm}^3

. [Volume

= \frac{4}{3}\pi r^3

]

Answer this when you sit the paper.

Mathematics Paper 1 June 2011

Sit this paper online

The questions

Question 101

Question 201

Question 202

Question 301

Question 302

Question 303

Question 401

Question 402

Question 501

Question 502

Question 601

Question 701

Question 702

Question 801

Question 802

Question 901

Question 1001

Question 1002

Question 1101

Question 1102

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1303

Question 1401

Question 1501

Question 1502

Question 1601

Question 1602

Question 1603

Question 1701

Question 1702

Question 1703

Question 1801

Question 1802

Question 1803

Question 1901

Question 1902

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2203

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2503

Question 2601

Question 2602

Question 2603

Question 2604

Question 2605

Question 2701

Question 2702

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