ZIMSEC O Level Mathematics Paper 1 November 2014 resit

Question 101

[1 marks]Ordinary and Standard Form

Express

0,07649

in standard form. [1]

Answer this when you sit the paper.

Question 102

[1 marks]Approximations and Estimations

Express

0,07649

correct to 2 significant figures. [1]

Answer this when you sit the paper.

Question 103

[1 marks]Approximations and Estimations

Express

0,07649

correct to the nearest hundredth. [1]

Answer this when you sit the paper.

Question 201

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

Write down the next term in the sequence

-2; 1; 6; 13; 22; \ldots

[1]

Answer this when you sit the paper.

Question 202

[1 marks]Approximations and Estimations

Given the expression

\dfrac{(3,65 + 5,49) \times 9,84}{5,16 \times (12,1 - 8,52)}

, rewrite the expression, giving each number correct to the nearest whole number. [1]

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Question 203

[1 marks]Approximations and Estimations

Estimate the value of

\dfrac{(3,65 + 5,49) \times 9,84}{5,16 \times (12,1 - 8,52)}

correct to the nearest whole number, by first giving each number correct to the nearest whole number. [1]

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Question 301

[1 marks]Circle Geometry

In the diagram, TA and TB are tangents to the circle, centre O, at A and B respectively. C is a point on the major arc ACB and D is a point on the minor arc ADB such that TDO is a straight line and

A\hat{T}O = 36°

. Name the two congruent triangles. [1]

Answer this when you sit the paper.

Question 302

[1 marks]Circle Geometry

In the diagram, TA and TB are tangents to the circle, centre O, at A and B respectively. C is a point on the major arc ACB and D is a point on the minor arc ADB such that TDO is a straight line and

A\hat{T}O = 36°

. Calculate

A\hat{O}D

. [1]

Answer this when you sit the paper.

Question 303

[1 marks]Circle Geometry

In the diagram, TA and TB are tangents to the circle, centre O, at A and B respectively. C is a point on the major arc ACB and D is a point on the minor arc ADB such that TDO is a straight line and

A\hat{T}O = 36°

. Calculate

A\hat{O}B

. [1]

Answer this when you sit the paper.

Question 401

[2 marks]Geometrical Transformation

The grid shows triangle ABC and triangle EBD. Triangle ABC is mapped onto triangle EBD by a combination of two transformations. Name the two transformations. [1] [1]

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Question 402

[1 marks]Geometrical Transformation

The grid shows triangle ABC and triangle EBD. Triangle ABC is mapped onto triangle EBD by a combination of two transformations. Write down the ratio AB : BE in its simplest form. [1]

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Question 501

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

Write down the smallest prime number. [1]

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Question 502

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

Express

5\ 292

as a product of its prime factors in index form. [2]

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Question 601

[1 marks]Ordinary and Standard Form

The population of town A is

4,5 \times 10^4

and that of town B is

3,9 \times 10^4

. Calculate the difference between the two populations. [1]

Answer this when you sit the paper.

Question 602

[2 marks]Ordinary and Standard Form

The population of town A is

4,5 \times 10^4

. This is 125 % greater than what it was forty years ago. Calculate the population of town A forty years ago. Give the answer in standard form. [2]

Answer this when you sit the paper.

Question 701

[1 marks]Laws of Indices

32 = 2^m

, find the value of m. [1]

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Question 702

[2 marks]Laws of Indices

Simplify

\left(\dfrac{1}{27}\right)^{\frac{2}{3}}

. [2]

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Question 801

[1 marks]Trigonometry, Bearing & Distances

In the diagram, the bearing of B from A is

060°

and the bearing of C from B is

100°

. Find the bearing of B from C. [1]

Answer this when you sit the paper.

Question 802

[2 marks]Polygons

In the diagram, the bearing of B from A is

060°

and the bearing of C from B is

100°

. If AB and BC are adjacent sides of a regular polygon, find the number of sides of the polygon. [2]

Answer this when you sit the paper.

Question 901

[2 marks]Variation

It is given that w is inversely proportional to f and when

f = 20

w = 150

. Find an equation connecting f and w. [2]

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Question 902

[1 marks]Variation

It is given that w is inversely proportional to f and when

f = 20

w = 150

. Find the value of f when

w = 60

. [1]

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Question 1001

[3 marks]Algebraic Fractions

Express

\dfrac{6x + 5}{7} - \dfrac{4x - 6}{21}

as a single fraction in its simplest form [3]

Answer this when you sit the paper.

Question 1101

[3 marks]Logarithms

\log(2x + 21) - \log 5x = 0

, find the value of x. [3]

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Question 1201

[3 marks]Approximations and Estimations

The dimensions of a rectangle, correct to the nearest centimetre, are 9 cm by 7 cm. Calculate the minimum possible area of the rectangle. [3]

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Question 1301

[1 marks]Number Bases

Convert

372_8

to a number in base 10. [1]

Answer this when you sit the paper.

Question 1302

[1 marks]Polygons, Symmetry and Circles

A quadrilateral has a rotational symmetry of order 1 and one line of symmetry. State the name of the quadrilateral. [1]

Answer this when you sit the paper.

Question 1303

[2 marks]Scales & Simple Map Problems

A lake has a surface area of

36

^2

. On a map, drawn to scale, the lake has an area of

9

^2

. Calculate the scale used in drawing the map giving the answer in the form

1 : n

. [2]

Answer this when you sit the paper.

Question 1401

[2 marks]Vector Geometry

In the diagram,

\overrightarrow{AB} = \begin{pmatrix} 14 \\ 6 \end{pmatrix}

and

\overrightarrow{AC} = \begin{pmatrix} 12 \\ 8 \end{pmatrix}

. M and N are the mid-points of AB and AC respectively. Find

\overrightarrow{MN}

. [2]

Answer this when you sit the paper.

Question 1402

[1 marks]Vector Geometry

In the diagram,

\overrightarrow{AB} = \begin{pmatrix} 14 \\ 6 \end{pmatrix}

and

\overrightarrow{AC} = \begin{pmatrix} 12 \\ 8 \end{pmatrix}

. M and N are the mid-points of AB and AC respectively. Find

\overrightarrow{BC}

. [1]

Answer this when you sit the paper.

Question 1403

[1 marks]Vector Geometry

In the diagram,

\overrightarrow{AB} = \begin{pmatrix} 14 \\ 6 \end{pmatrix}

and

\overrightarrow{AC} = \begin{pmatrix} 12 \\ 8 \end{pmatrix}

. M and N are the mid-points of AB and AC respectively. MN is parallel to BC. Write down the value of the scalar k for which

\overrightarrow{MN} = k\,\overrightarrow{BC}

. [1]

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Question 1501

[1 marks]Travel Graphs

The diagram shows the velocity-time graphs of two cars. Car A and car B start moving from the same point at the same time. Find the acceleration of car A. [1]

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Question 1502

[1 marks]Travel Graphs

The diagram shows the velocity-time graphs of two cars. Car A and car B start moving from the same point at the same time. Find the time the two cars have equal velocities. [1]

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Question 1503

[1 marks]Travel Graphs

The diagram shows the velocity-time graphs of two cars. Car A and car B start moving from the same point at the same time. Find the distance covered by car A in the 8 seconds. [1]

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Question 1504

[1 marks]Travel Graphs

The diagram shows the velocity-time graphs of two cars. Car A and car B start moving from the same point at the same time. Find the average velocity of car A during the 8 seconds. [1]

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Question 1601

[2 marks]Change of Subject of Formula

The equation of a straight line is given as

5x + 4y - 30 = 0

. Make y the subject of the equation. [2]

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Question 1602

[1 marks]Co-ordinate Geometry

The equation of a straight line is given as

5x + 4y - 30 = 0

. Write down the gradient of the straight line. [1]

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Question 1603

[1 marks]Co-ordinate Geometry

The equation of a straight line is given as

5x + 4y - 30 = 0

. Write down the coordinates of the point where the line crosses the x-axis. [1]

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Question 1701

[1 marks]Change of Units

Below is a list of some of the units used in measuring quantities: hour; hectare; kilometre, kilogramme, degree. Write down the unit of area from the given list. [1]

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Question 1702

[3 marks]Measures and Mensuration

Find the capacity, in litres, of a cylindrical tank of height 3,5 m and diameter 4 m.

\left[\text{Take } \pi \text{ to be } \frac{22}{7}\right]

. [3]

Answer this when you sit the paper.

Question 1801

[2 marks]Functional Notation

Given that

f(x) = x^2 - 5x - 12

, find

f(-2)

. [2]

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Question 1802

[2 marks]Functional Notation

Given that

f(x) = x^2 - 5x - 12

, find the values of x for which

f(x) = 12

. [2]

Answer this when you sit the paper.

Question 1901

[4 marks]Inequalities and Linear Programming

On the Cartesian plane the three inequalities

y > -6

x \geq 2

and

x + y \leq 0

define a triangular region. Write down the coordinates of the vertex of that region which is furthest to the right. [4]

Answer this when you sit the paper.

Question 2001

[1 marks]Sets

It is given that

n(\xi) = 14

n(P) = 7

n(P \cap Q) = 2

and

n(P \cup Q) = 11

. Find

n(Q)

. [1]

Answer this when you sit the paper.

Question 2002

[1 marks]Sets

It is given that

n(\xi) = 14

n(P) = 7

n(P \cap Q) = 2

and

n(P \cup Q) = 11

. Find

n(Q \cup P')

. [1]

Answer this when you sit the paper.

Question 2101

[1 marks]Matrices

It is given that

C = \begin{pmatrix} 4 & 3 & -2 \\ -1 & -2 & 0 \end{pmatrix}

. Write down the order of matrix C. [1]

Answer this when you sit the paper.

Question 2102

[2 marks]Matrices

It is given that

A = \begin{pmatrix} 2 & 3 \\ -4 & -1 \end{pmatrix}

and

D = \begin{pmatrix} 7 \\ -3 \end{pmatrix}

. Express AD as a single matrix. [2]

Answer this when you sit the paper.

Question 2103

[2 marks]Matrices

It is given that

B = \begin{pmatrix} x+1 & 2 \\ 2x-3 & 3 \end{pmatrix}

. Find x such that B has no inverse. [2]

Answer this when you sit the paper.

Question 2201

[1 marks]Probability

A bag has green, red and blue balls. The balls are identical except for colour. Anna picks a ball at random and puts it back. The table shows the probabilities that Anna picks any of the balls.

$\begin{array}{|l|c|c|c|}\hline \text{colour} & \text{green} & \text{red} & \text{blue} \\ \hline \text{probability} & 0,55 & 0,25 & x \\ \hline \end{array}$

Find x. [1]

Answer this when you sit the paper.

Question 2202

[2 marks]Probability

A bag has green, red and blue balls. The balls are identical except for colour. Anna picks a ball at random and puts it back. The table shows the probabilities that Anna picks any of the balls.

$\begin{array}{|l|c|c|c|}\hline \text{colour} & \text{green} & \text{red} & \text{blue} \\ \hline \text{probability} & 0,55 & 0,25 & x \\ \hline \end{array}$

If there are 20 red balls in the bag, find the number of the green balls in the bag. [2]

Answer this when you sit the paper.

Question 2203

[2 marks]Probability

A bag has green, red and blue balls, and the probability that Anna picks a green ball is

0,55

. She picks a ball at random and puts it back. Write down the probability that she does not pick a green ball. [2]

Answer this when you sit the paper.

Question 2301

[4 marks]Constructions and Loci

A, B and C are points on the arc of a circle, and TC is a tangent to the arc at C, as shown in the diagram. The locus of a point equidistant from A and B is constructed, and so is the perpendicular to TC at C. State what the point where these two loci meet is. [4]

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Question 2401

[1 marks]Points, Lines and Angles

Write down the special name given to two angles that add up to

180°

. [1]

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Question 2402

[2 marks]Points, Lines and Angles

The diagram shows a triangle between two parallel lines. Its upper vertex lies on the upper line, where two angles of

x°

are marked, and its lower vertex lies on the lower line, where two angles of

y°

are marked. Find the value of

x + y

. [2]

Answer this when you sit the paper.

Question 2403

[2 marks]Consumer Arithmetic

Jojo invests

\$7\ 500

at 3,5 % per year simple interest. Calculate the simple interest he earns after 4 years. [2]

Answer this when you sit the paper.

Question 2501

[2 marks]Trigonometry, Bearing & Distances

Using as much of the information given below as is necessary and leaving the answer in surd form where appropriate, find

\left(\sin 60°\right)^2 + \left(\cos 60°\right)^2

\left[\sin 60° = \frac{\sqrt{3}}{2}; \cos 60° = \frac{1}{2}; \tan 60° = \frac{\sqrt{3}}{1}\right]

[2]

Answer this when you sit the paper.

Question 2502

[2 marks]Measures and Mensuration

ABC is a triangle in which

AB = 11

cm,

BC = 16

cm and

A\hat{B}C = 60°

. Leaving the answer in surd form, find the area of triangle ABC.

\left[\sin 60° = \frac{\sqrt{3}}{2}; \cos 60° = \frac{1}{2}; \tan 60° = \frac{\sqrt{3}}{1}\right]

[2]

Answer this when you sit the paper.

Question 2503

[2 marks]Trigonometry, Bearing & Distances

ABC is a triangle in which

AB = 11

cm,

BC = 16

cm and

A\hat{B}C = 60°

, and AD is the altitude from A to BC. Find the length of BD.

\left[\sin 60° = \frac{\sqrt{3}}{2}; \cos 60° = \frac{1}{2}; \tan 60° = \frac{\sqrt{3}}{1}\right]

[2]

Answer this when you sit the paper.

Question 2601

[2 marks]Statistics

The table shows the number of passengers in each of 50 taxis leaving airport one day.

$\begin{array}{|l|c|c|c|c|}\hline \text{number of passengers in taxi} & 1 & 2 & 3 & 4 \\ \hline \text{number of taxis} & x & 20 & y & 13 \\ \hline \end{array}$

Find the value of $x + y$ in its simplest form. [2]

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Question 2602

[2 marks]Statistics

The table shows the number of passengers in each of 50 taxis leaving airport one day.

$\begin{array}{|l|c|c|c|c|}\hline \text{number of passengers in taxi} & 1 & 2 & 3 & 4 \\ \hline \text{number of taxis} & x & 20 & y & 13 \\ \hline \end{array}$

The mean number of passengers per taxi is $2,66$ . Find the value of x and the value of y by solving appropriate equations. [2]

Answer this when you sit the paper.

Mathematics Paper 1 November 2014 resit

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

Question 302

Question 303

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 701

Question 702

Question 801

Question 802

Question 901

Question 902

Question 1001

Question 1101

Question 1201

Question 1301

Question 1302

Question 1303

Question 1401

Question 1402

Question 1403

Question 1501

Question 1502

Question 1503

Question 1504

Question 1601

Question 1602

Question 1603

Question 1701

Question 1702

Question 1801

Question 1802

Question 1901

Question 2001

Question 2002

Question 2101

Question 2102

Question 2103

Question 2201

Question 2202

Question 2203

Question 2301

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2503

Question 2601

Question 2602

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