ZIMSEC O Level Mathematics Paper 1 November 2007

Question 101

[1 marks]Approximations & Estimations

Express 1548 correct to one significant figure.

Answer this when you sit the paper.

Question 102

[1 marks]Approximations & Estimations

Express 1548 correct to the nearest ten.

Answer this when you sit the paper.

Question 103

[1 marks]Approximations & Estimations

Express 0,00349 correct to 3 decimal places.

Answer this when you sit the paper.

Question 201

[1 marks]Fractions, Decimals & Percentages

Write down

\frac{13}{40}

as decimal fraction.

Answer this when you sit the paper.

Question 202

[1 marks]Ordinary & Standard Form

Write down

4\ 850 \times 10^{-1}

in standard form.

Answer this when you sit the paper.

Question 203

[1 marks]Consumer Arithmetic

John works

46\frac{1}{2}

hours per week and is paid

\$5\ 000

per hour. Find John's weekly wage, in dollars.

Answer this when you sit the paper.

Question 301

[3 marks]Simultaneous Equations

Solve the simultaneous equations

x = \frac{1}{2}y

and

3x - y = 7

. Give both values, as

x

then

y

Answer this when you sit the paper.

Question 401

[1 marks]Ratios, Rates & Proportions

Peter, John and Sekai share some money in the ratio 2 : 3 : 5 respectively. Express Peter's share as a fraction of John's share.

Answer this when you sit the paper.

Question 402

[2 marks]Ratios, Rates & Proportions

Peter, John and Sekai share some money in the ratio 2 : 3 : 5 respectively. Sekai received

\$24\ 000

. Calculate the total amount shared, in dollars.

Answer this when you sit the paper.

Question 501

[2 marks]Geometrical Transformation

In the diagram ABCD is a kite in which

AB = 5

cm,

BC = 12

cm and

A\hat{B}C = 90^\circ

. Triangle ABC is the image of triangle ADC under a single transformation. Describe fully the single transformation.

Answer this when you sit the paper.

Question 502

[1 marks]Measures & Mensuration

In the diagram ABCD is a kite in which

AB = 5

cm,

BC = 12

cm and

A\hat{B}C = 90^\circ

, and triangle ABC is the image of triangle ADC under a reflection. Calculate the area of the kite, in

\text{cm}^2

Answer this when you sit the paper.

Question 601

[1 marks]Fractions, Decimals & Percentages

Giving your answer as a common fraction in its lowest terms, find the value of

\frac{3}{16} \times 3,2

Answer this when you sit the paper.

Question 602

[2 marks]Algebraic Fractions

Find the value of

x

given that

\frac{1}{x} = \frac{5}{12} + \frac{3}{4}

Answer this when you sit the paper.

Question 701

[3 marks]Fractions, Decimals & Percentages

Simplify

\dfrac{1\frac{3}{4} + 2 \times 7}{10 \div 2 - 2}

Answer this when you sit the paper.

Question 801

[1 marks]Laws of Indices

Evaluate

25^{-1} \times 5^{2} \times 125^{\frac{1}{3}}

Answer this when you sit the paper.

Question 802

[2 marks]Laws of Indices

Solve the equation

6x^{-3} = 48

Answer this when you sit the paper.

Question 901

[1 marks]Points, Lines & Angles

In the diagram, BCD is a straight line,

A\hat{B}C = 65^\circ

and

B\hat{A}C = 75^\circ

. Calculate

A\hat{C}D

Answer this when you sit the paper.

Question 902

[1 marks]Points, Lines & Angles

In the diagram, BCD is a straight line,

A\hat{B}C = 65^\circ

and

B\hat{A}C = 75^\circ

. Calculate

A\hat{C}B

Answer this when you sit the paper.

Question 903

[1 marks]Points, Lines & Angles

In the diagram, BCD is a straight line,

A\hat{B}C = 65^\circ

and

B\hat{A}C = 75^\circ

. Calculate reflex

B\hat{A}C

Answer this when you sit the paper.

Question 1001

[1 marks]Measures & Mensuration

In the diagram EC is parallel to AB and AE is parallel to BD. The perpendicular distance between AB and EC is 6 cm and the area of parallelogram ABDE is

45\ \text{cm}^2

. Find the length of ED, in cm.

Answer this when you sit the paper.

Question 1002

[2 marks]Measures & Mensuration

In the diagram EC is parallel to AB and AE is parallel to BD. The perpendicular distance between AB and EC is 6 cm and the area of parallelogram ABDE is

45\ \text{cm}^2

. Find the area of triangle ABC, in

\text{cm}^2

Answer this when you sit the paper.

Question 1101

[1 marks]Fractions, Decimals & Percentages

Express

17\frac{1}{2}\%

as a common fraction in its lowest terms.

Answer this when you sit the paper.

Question 1102

[2 marks]Algebraic Fractions

Express

\frac{x}{2} - \frac{x-1}{2}

as a single fraction.

Answer this when you sit the paper.

Question 1201

[1 marks]Trigonometry, Bearing & Distances

A, B, C and P are four points on level ground. The bearing of C from B is

160^\circ

. P is due north of A and

A\hat{B}C = 90^\circ

. Calculate

P\hat{A}B

Answer this when you sit the paper.

Question 1202

[2 marks]Trigonometry, Bearing & Distances

A, B, C and P are four points on level ground. The bearing of C from B is

160^\circ

. P is due north of A and

A\hat{B}C = 90^\circ

. Find the three-figure bearing of B from C.

Answer this when you sit the paper.

Question 1301

[1 marks]Inequalities & Linear Programming

The diagram shows the unshaded region R, bounded by the broken line

y = 3x

, the line

x + y = 4

and the

x

-axis. The three lines meet at

O(0; 0)

(1; 3)

and

(4; 0)

. Write down the one of the 3 inequalities defining R which involves

y

and

3x

Answer this when you sit the paper.

Question 1302

[1 marks]Inequalities & Linear Programming

The diagram shows the unshaded region R, bounded by the broken line

y = 3x

, the line

x + y = 4

and the

x

-axis. The three lines meet at

O(0; 0)

(1; 3)

and

(4; 0)

. Write down the one of the 3 inequalities defining R which involves

x + y

Answer this when you sit the paper.

Question 1303

[1 marks]Inequalities & Linear Programming

The diagram shows the unshaded region R, bounded by the broken line

y = 3x

, the line

x + y = 4

and the

x

-axis. The three lines meet at

O(0; 0)

(1; 3)

and

(4; 0)

. Write down the one of the 3 inequalities defining R which involves

y

alone.

Answer this when you sit the paper.

Question 1401

[1 marks]Measures & Mensuration

The diagram shows a right-angled triangle with perpendicular sides

x

and

y

and hypotenuse

z

. Use the diagram to write down Pythagoras Theorem in terms of

x

y

and

z

Answer this when you sit the paper.

Question 1402

[2 marks]Rational, Irrational Numbers & Surds

An equilateral triangle is of side 18 cm. Calculate the length of its altitude leaving your answer in surd form, in cm.

Answer this when you sit the paper.

Question 1501

[1 marks]Statistics & Probability

The pie chart shows professionals in town A. The Teachers sector is

150^\circ

, the Doctors sector is

x^\circ

and the Lawyers sector is

2x^\circ

. Calculate the value of

x

Answer this when you sit the paper.

Question 1502

[2 marks]Statistics & Probability

The pie chart shows professionals in town A. The Teachers sector is

150^\circ

, the Doctors sector is

x^\circ

and the Lawyers sector is

2x^\circ

. Given that there are 900 teachers in the town, find the number of doctors.

Answer this when you sit the paper.

Question 1601

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

The table shows a difference pattern. The top row reads 4, 7, 12, 20,

p

; the second row reads 3, 5, 8,

n

; the third row reads 2, 3,

m

q

; and the bottom row reads 1, 1, 1. Each row is the row of differences of the row above it. Write the value of

m

Answer this when you sit the paper.

Question 1602

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

The table shows a difference pattern. The top row reads 4, 7, 12, 20,

p

; the second row reads 3, 5, 8,

n

; the third row reads 2, 3,

m

q

; and the bottom row reads 1, 1, 1. Each row is the row of differences of the row above it. Write the value of

n

Answer this when you sit the paper.

Question 1603

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

The table shows a difference pattern. The top row reads 4, 7, 12, 20,

p

; the second row reads 3, 5, 8,

n

; the third row reads 2, 3,

m

q

; and the bottom row reads 1, 1, 1. Each row is the row of differences of the row above it. Write the value of

p

Answer this when you sit the paper.

Question 1604

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

The table shows a difference pattern. The top row reads 4, 7, 12, 20,

p

; the second row reads 3, 5, 8,

n

; the third row reads 2, 3,

m

q

; and the bottom row reads 1, 1, 1. Each row is the row of differences of the row above it. Write the value of

q

Answer this when you sit the paper.

Question 1701

[2 marks]Algebraic Expressions

Factorise completely

4t^{2} - 36b^{2}

Answer this when you sit the paper.

Question 1702

[2 marks]Linear Equations

Solve the equation

p + 2 = 5 - 4(p + 2)

Answer this when you sit the paper.

Question 1801

[1 marks]Matrices

It is given that

P = \begin{pmatrix} 5 & 3 \\ -1 & 2 \end{pmatrix}

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

and

R = \begin{pmatrix} 2 \\ -1 \end{pmatrix}

. Write down the order of matrix

R

Answer this when you sit the paper.

Question 1802

[1 marks]Matrices

It is given that

P = \begin{pmatrix} 5 & 3 \\ -1 & 2 \end{pmatrix}

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

and

R = \begin{pmatrix} 2 \\ -1 \end{pmatrix}

. Find

P + Q

Answer this when you sit the paper.

Question 1803

[2 marks]Matrices

It is given that

P = \begin{pmatrix} 5 & 3 \\ -1 & 2 \end{pmatrix}

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

and

R = \begin{pmatrix} 2 \\ -1 \end{pmatrix}

. Find

QR

Answer this when you sit the paper.

Question 1901

[1 marks]Approximations & Estimations

Estimate the value of

\frac{40032}{51 \times 410}

correct to one significant figure.

Answer this when you sit the paper.

Question 1902

[1 marks]Approximations & Estimations

Given that

4 \le a \le 8

3 \le b \le 5

and

7 \le c \le 9

, find the maximum value of

c - b

Answer this when you sit the paper.

Question 1903

[2 marks]Approximations & Estimations

Given that

4 \le a \le 8

3 \le b \le 5

and

7 \le c \le 9

, find the minimum value of

\frac{c + a}{b}

Answer this when you sit the paper.

Question 2001

[1 marks]Statistics & Probability

The numbers 4; 7; 8;

k

; 10; 11; 14; 18 are in ascending order. Given that the mode is 8, find the value of

k

Answer this when you sit the paper.

Question 2002

[1 marks]Statistics & Probability

The numbers 4; 7; 8; 8; 10; 11; 14; 18 are in ascending order. Find the median.

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Question 2003

[2 marks]Statistics & Probability

The numbers 4; 7; 8; 8; 10; 11; 14; 18 are in ascending order. Find the mean.

Answer this when you sit the paper.

Question 2101

[1 marks]Inequalities & Linear Programming

Solve the inequality

10 - 2y < 4

Answer this when you sit the paper.

Question 2102

[3 marks]Quadratic Equations

Solve the equation

(2x - 3)^{2} = 49

. Give both values of

x

Answer this when you sit the paper.

Question 2201

[1 marks]Measures & Mensuration

In the diagram, ABCD is a square of side 7 cm APCB and AQCD are quadrants of circles of centres B and D respectively. The shaded part is the region common to the two quadrants. Use

\pi = 3\frac{1}{7}

. Calculate the perimeter of the shaded part, in cm.

Answer this when you sit the paper.

Question 2202

[3 marks]Measures & Mensuration

In the diagram, ABCD is a square of side 7 cm APCB and AQCD are quadrants of circles of centres B and D respectively. The shaded part is the region common to the two quadrants. Use

\pi = 3\frac{1}{7}

. Calculate the area of the shaded part, in

\text{cm}^2

Answer this when you sit the paper.

Question 2301

[1 marks]Polygons, Symmetry & Circles

A, B, C and D are points on the circumference of the circle centre O. AD is a diameter and CO is parallel to BA. It is given that

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

. Calculate

C\hat{O}D

Answer this when you sit the paper.

Question 2302

[1 marks]Polygons, Symmetry & Circles

A, B, C and D are points on the circumference of the circle centre O. AD is a diameter and CO is parallel to BA. It is given that

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

. Calculate

B\hat{A}D

Answer this when you sit the paper.

Question 2303

[1 marks]Polygons, Symmetry & Circles

A, B, C and D are points on the circumference of the circle centre O. AD is a diameter and CO is parallel to BA. It is given that

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

. Calculate

B\hat{D}C

Answer this when you sit the paper.

Question 2304

[2 marks]Polygons, Symmetry & Circles

A, B, C and D are points on the circumference of the circle centre O. AD is a diameter and CO is parallel to BA. It is given that

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

. Calculate

B\hat{O}C

Answer this when you sit the paper.

Question 2401

[1 marks]Travel Graphs

The diagram shows the velocity-time graph of a moving object. The velocity rises in a straight line from 5 m/s at

t = 0

to 15 m/s at

t = 4

s, stays at 15 m/s until

t = 10

s, then falls in a straight line to 0 at

t = 15

s. Write down the initial velocity of the object, in m/s.

Answer this when you sit the paper.

Question 2402

[1 marks]Travel Graphs

The diagram shows the velocity-time graph of a moving object. The velocity rises in a straight line from 5 m/s at

t = 0

to 15 m/s at

t = 4

s, stays at 15 m/s until

t = 10

s, then falls in a straight line to 0 at

t = 15

s. Find the duration when the acceleration of the object was zero, in seconds.

Answer this when you sit the paper.

Question 2403

[3 marks]Travel Graphs

The diagram shows the velocity-time graph of a moving object. The velocity rises in a straight line from 5 m/s at

t = 0

to 15 m/s at

t = 4

s, stays at 15 m/s until

t = 10

s, then falls in a straight line to 0 at

t = 15

s. Calculate the total distance travelled by the object, in m.

Answer this when you sit the paper.

Question 2501

[2 marks]Change of Units

Convert

2\ 500\ \text{cm}^2

\text{m}^2

Answer this when you sit the paper.

Question 2502

[1 marks]Similarity & Congruency

Two similar cylindrical mugs have their volumes in the ratio 8 : 27. Write down the ratio of their heights.

Answer this when you sit the paper.

Question 2503

[2 marks]Similarity & Congruency

Two similar cylindrical mugs have their volumes in the ratio 8 : 27, so their heights are in the ratio 2 : 3. The total surface area of the larger mug is

63\ \text{cm}^2

. Calculate the total surface area of the smaller mug, in

\text{cm}^2

Answer this when you sit the paper.

Question 2601

[1 marks]Trigonometry, Bearing & Distances

In the diagram,

A\hat{B}C = \theta

BC = 17

cm,

CD = 15

cm,

B\hat{D}C = 90^\circ

and ABD is a straight line, so

\theta

is obtuse. Calculate BD, in cm.

Answer this when you sit the paper.

Question 2602

[1 marks]Trigonometry, Bearing & Distances

In the diagram,

A\hat{B}C = \theta

BC = 17

cm,

CD = 15

cm,

B\hat{D}C = 90^\circ

and ABD is a straight line, so

\theta

is obtuse. Write down, as a common fraction, the value of

\sin\theta

Answer this when you sit the paper.

Question 2603

[2 marks]Trigonometry, Bearing & Distances

In the diagram,

A\hat{B}C = \theta

BC = 17

cm,

CD = 15

cm,

B\hat{D}C = 90^\circ

and ABD is a straight line, so

\theta

is obtuse. Write down, as a common fraction, the value of

\cos\theta

Answer this when you sit the paper.

Question 2604

[2 marks]Trigonometry, Bearing & Distances

In the diagram,

A\hat{B}C = \theta

BC = 17

cm,

CD = 15

cm,

B\hat{D}C = 90^\circ

and ABD is a straight line, so

\theta

is obtuse. Write down, as a common fraction, the value of

\tan\theta

Answer this when you sit the paper.

Question 2701

[2 marks]Trigonometry, Bearing & Distances

In the diagram, ADC is a straight line,

AD = 8

cm,

BD = 6

cm,

BC = 9

cm and

B\hat{D}C = 60^\circ

. Use

\sin 60^\circ = 0,866

\cos 60^\circ = 0,5

and

\tan 60^\circ = 1,73

as necessary. Calculate

AB^{2}

Answer this when you sit the paper.

Question 2702

[2 marks]Trigonometry, Bearing & Distances

In the diagram, ADC is a straight line,

AD = 8

cm,

BD = 6

cm,

BC = 9

cm and

B\hat{D}C = 60^\circ

. Use

\sin 60^\circ = 0,866

\cos 60^\circ = 0,5

and

\tan 60^\circ = 1,73

as necessary. Calculate

\sin B\hat{C}D

, giving your answer correct 3 to decimal places.

Answer this when you sit the paper.

Question 2703

[2 marks]Trigonometry, Bearing & Distances

In the diagram, ADC is a straight line,

AD = 8

cm,

BD = 6

cm,

BC = 9

cm and

B\hat{D}C = 60^\circ

. Use

\sin 60^\circ = 0,866

\cos 60^\circ = 0,5

and

\tan 60^\circ = 1,73

as necessary. Calculate the area of triangle ABD, in

\text{cm}^2

Answer this when you sit the paper.

Mathematics Paper 1 November 2007

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 203

Question 301

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 701

Question 801

Question 802

Question 901

Question 902

Question 903

Question 1001

Question 1002

Question 1101

Question 1102

Question 1201

Question 1202

Question 1301

Question 1302

Question 1303

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1602

Question 1603

Question 1604

Question 1701

Question 1702

Question 1801

Question 1802

Question 1803

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2201

Question 2202

Question 2301

Question 2302

Question 2303

Question 2304

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2503

Question 2601

Question 2602

Question 2603

Question 2604

Question 2701

Question 2702

Question 2703

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