ZIMSEC O Level Mathematics Paper 1 November 2011

Question 101

[1 marks]Fractions, Decimals & Percentages

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

\frac{3}{5} - \frac{5}{9}

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Question 102

[2 marks]Fractions, Decimals & Percentages

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

\dfrac{2}{3\frac{2}{5}}

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Question 201

[2 marks]Approximations & Estimations

Given

P = \dfrac{0.00274 \times 3460}{(9.88 + 23.8)^2}

, which expression rewrites this with each number correct to one significant figure?

A $\dfrac{0.003 \times 3500}{(10 + 24)^2}$
B $\dfrac{0.0027 \times 3000}{(10 + 20)^2}$
C $\dfrac{0.003 \times 3000}{(10 + 20)^2}$
D $\dfrac{0.002 \times 3000}{(9 + 20)^2}$

Question 202

[1 marks]Approximations & Estimations

Given

P = \dfrac{0.00274 \times 3460}{(9.88 + 23.8)^2}

, estimate the value of

P

correct to one significant figure.

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Question 301

[1 marks]Laws of Indices

Simplify

\left(27x^6\right)^{\frac{1}{3}}

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Question 302

[2 marks]Laws of Indices

32^{-\frac{2}{5}} = 2^p

, find

p

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Question 401

[1 marks]Ordinary & Standard Form

Evaluate

3,25 \times 10^4 \times 10^{-6}

, giving the answer in standard form.

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Question 402

[1 marks]Ordinary & Standard Form

Evaluate

3,25 \times 10^4 \times 10^{-6}

, giving the answer as a decimal fraction.

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Question 403

[1 marks]Ordinary & Standard Form

Evaluate

3,25 \times 10^4 \times 10^{-6}

, giving the answer as a common fraction in its lowest terms.

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Question 501

[1 marks]Polygons, Symmetry & Circles

State the number of lines of symmetry of an equilateral triangle.

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Question 502

[2 marks]Factorisation

Factorise completely

3x^3 - 12x

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Question 601

[3 marks]Simultaneous Equations

Solve the simultaneous equations

x - 6y = -4

and

9x + 3y = -17

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Question 701

[1 marks]Sets

A and B are sets. Write

A \cap A'

in its simplest form.

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Question 702

[1 marks]Sets

A and B are sets. Write

A \cup A'

in its simplest form.

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Question 703

[1 marks]Sets

A and B are sets. Write

(A \cap B) \cup (A \cap B')

in its simplest form.

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Question 801

[3 marks]Variation

It is given that

y

varies inversely as the square of

(x - 1)

. When

y = 2

x = 2

. Find the value of

y

when

x = 4

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Question 901

[1 marks]Matrices

If A is a non-singular matrix, simplify

\mathbf{A}\mathbf{A}^{-1}

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Question 902

[2 marks]Matrices

\mathbf{B} = \begin{pmatrix} 1 & 3 \\ 5 & 2 \end{pmatrix}\begin{pmatrix} 2 \\ 6 \end{pmatrix}

, write down the order of matrix

\mathbf{B}

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Question 1001

[1 marks]Co-ordinate Geometry

In the diagram AC is 10 units and BA is parallel to CD. BA is the line

y = 3x + 4

. Write down the value of

y

at C.

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Question 1002

[1 marks]Co-ordinate Geometry

In the diagram AC is 10 units and BA is parallel to CD. BA is the line

y = 3x + 4

. Write down the equation of the line CD.

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Question 1003

[1 marks]Co-ordinate Geometry

In the diagram AC is 10 units and BA is parallel to CD. BA is the line

y = 3x + 4

. Find the coordinates of the point D where the line CD crosses the x-axis.

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Question 1101

[1 marks]Number Bases

Evaluate

765_8 - 567_8

, giving your answer in base eight.

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Question 1102

[1 marks]Number Bases

Express

5^3 + 4

as a number in base five.

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Question 1103

[1 marks]Number Bases

Convert

13_{10}

to a number in base two.

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Question 1201

[1 marks]Approximations & Estimations

A rectangle is 9,1 cm long and 5,7 cm wide correct to one decimal place. State the least possible width of the rectangle.

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Question 1202

[2 marks]Approximations & Estimations

A rectangle is 9,1 cm long and 5,7 cm wide correct to one decimal place. Find the limits within which the perimeter of the rectangle lies, in the form

a\ \text{cm} \le \text{perimeter} < b\ \text{cm}

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Question 1301

[3 marks]Geometrical Transformation

In the diagram ABC and A¹B¹C¹ are congruent triangles and BCC¹B¹ is a straight line. Which single transformation maps triangle ABC onto triangle A¹B¹C¹?

AA reflection in the line BB¹
BA rotation through 180° about the midpoint of BB¹
CA translation along BB¹
DA rotation through 90° clockwise about C

Question 1401

[2 marks]Algebraic Expressions

Solve the equation

\frac{2y}{3} - 9 = 0

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Question 1402

[2 marks]Quadratic Equations

Solve the equation

x^2 - 5x - 6 = 0

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Question 1501

[2 marks]Similarity & Congruency

A car manufacturer makes a scale model of one of his real cars. The capacity of the fuel tank of the real car is 64 litres and that of the model car is 0.512 litres. Find the ratio of the length of the real car : the length of the model car.

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Question 1502

[2 marks]Similarity & Congruency

A car manufacturer makes a scale model of one of his real cars. The capacity of the fuel tank of the real car is 64 litres and that of the model car is 0.512 litres. The area of the front window of the model is 0.0484 m

^2

. Find the area of the front window of the real car.

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Question 1601

[1 marks]Algebraic Expressions

Given that

y = m^2 - 4n^2

, find the value of

y

when

m = 4

and

n = 2

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Question 1602

[3 marks]Change of Subject of Formula

\frac{x}{a} + \frac{y}{b} = 1

, make

x

the subject.

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Question 1701

[1 marks]Logarithms

Evaluate

\log_3 9

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Question 1702

[2 marks]Logarithms

Evaluate

\log_5\left(\frac{1}{25}\right)

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Question 1703

[1 marks]Logarithms

Evaluate

\log_{29} 1

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Question 1801

[2 marks]Scales & Simple Map Problems

On a map, a distance of 20 km is represented by a length of 40 cm. The scale of the map is

1 : n

. Calculate the value of

n

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Question 1802

[2 marks]Scales & Simple Map Problems

On a map, a distance of 20 km is represented by a length of 40 cm. The distance between two towns on the map is 70 cm. Calculate the actual distance in kilometres between the towns.

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Question 1901

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

Study the pattern below.

$3^2 - 1^2 = 8 = 4 \times 2$
$4^2 - 2^2 = 12 = 4 \times 3$
$5^2 - 3^2 = 16 = 4 \times 4$
$6^2 - p^2 = q = 4 \times 5$

Write down the value of $p$ .

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Question 1902

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

Study the pattern below.

$3^2 - 1^2 = 8 = 4 \times 2$
$4^2 - 2^2 = 12 = 4 \times 3$
$5^2 - 3^2 = 16 = 4 \times 4$
$6^2 - p^2 = q = 4 \times 5$

Write down the value of $q$ .

Answer this when you sit the paper.

Question 1903

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

Study the pattern below.

$3^2 - 1^2 = 8 = 4 \times 2$
$4^2 - 2^2 = 12 = 4 \times 3$
$5^2 - 3^2 = 16 = 4 \times 4$
$6^2 - p^2 = q = 4 \times 5$

Which is the 10th line of this pattern?

A $11^2 - 9^2 = 40 = 4 \times 10$
B $13^2 - 11^2 = 48 = 4 \times 12$
C $12^2 - 10^2 = 44 = 4 \times 11$
D $12^2 - 10^2 = 48 = 4 \times 12$

Question 2001

[5 marks]Inequalities & Linear Programming

Find the three inequalities that define the unshaded region in the diagram above.

A $y \ge -4$ , $x + y \le 4$ , $3y > 5x + 3$
B $y \ge -4$ , $x + y \le 4$ , $3y < 5x + 3$
C $y \le -4$ , $x + y \ge 4$ , $3y < 5x + 3$
D $y \ge -4$ , $x + y \le 4$ , $y < 2x + 1$

Question 2101

[1 marks]Vector Geometry

In the diagram, O is the origin and the vectors

\mathbf{a}

and

\mathbf{b}

are shown. Write down, in terms of

\mathbf{a}

and/or

\mathbf{b}

, the position vector of the point P.

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Question 2102

[1 marks]Vector Geometry

In the diagram, O is the origin and the vectors

\mathbf{a}

and

\mathbf{b}

are shown. Write down

\overrightarrow{PR}

in terms of

\mathbf{a}

and/or

\mathbf{b}

Answer this when you sit the paper.

Question 2103

[2 marks]Vector Geometry

In the diagram, O is the origin and the vectors

\mathbf{a}

and

\mathbf{b}

are shown. Write down

\overrightarrow{PR} - \overrightarrow{QR}

in terms of

\mathbf{a}

and/or

\mathbf{b}

Answer this when you sit the paper.

Question 2104

[1 marks]Vector Geometry

In the diagram, O is the origin and the vectors

\mathbf{a}

and

\mathbf{b}

are shown. If

|\mathbf{b}| = 4

, write down the value of

\left|\overrightarrow{QR}\right|

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Question 2201

[3 marks]Measures & Mensuration

In the diagram, OAB is a sector of a circle centre O and radius 12 cm and angle AOB = 50°. OCD is a sector of a circle centre O and radius 6 cm and angle COD = 30°. Calculate, in terms of

\pi

, the area of the shaded part.

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Question 2202

[3 marks]Measures & Mensuration

In the diagram, OAB is a sector of a circle centre O and radius 12 cm and angle AOB = 50°. OCD is a sector of a circle centre O and radius 6 cm and angle COD = 30°. Calculate, in terms of

\pi

, the perimeter of the shaded area AOCDOBA.

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Question 2301

[2 marks]Travel Graphs

The diagram is a velocity-time graph of a train journey between two stations. Find the maximum speed of the train in km/h.

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Question 2302

[2 marks]Travel Graphs

The diagram is a velocity-time graph of a train journey between two stations. Find the train's acceleration in the first half minute, in km/minute

^2

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Question 2303

[1 marks]Travel Graphs

The diagram is a velocity-time graph of a train journey between two stations. Find the distance the train travels at maximum speed, in kilometres.

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Question 2304

[1 marks]Travel Graphs

The diagram is a velocity-time graph of a train journey between two stations. Find the distance between the stations, in kilometres.

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Question 2401

[1 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle centre O. Write down the geometrical word which completes the following statement: "ABCD is a ...... quadrilateral".

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Question 2402

[1 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle centre O. SCT is a tangent to the circle at C and is parallel to OB.

A\hat{O}B = 130^\circ

and

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

. Find

O\hat{B}C

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Question 2403

[1 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle centre O. SCT is a tangent to the circle at C and is parallel to OB.

A\hat{O}B = 130^\circ

and

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

. Find

O\hat{B}A

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Question 2404

[1 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle centre O. SCT is a tangent to the circle at C and is parallel to OB.

A\hat{O}B = 130^\circ

and

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

. Find

A\hat{D}C

Answer this when you sit the paper.

Question 2405

[1 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle centre O. SCT is a tangent to the circle at C and is parallel to OB.

A\hat{O}B = 130^\circ

and

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

. Find

O\hat{C}T

Answer this when you sit the paper.

Question 2406

[2 marks]Circle Geometry

A, B, C and D lie on the circumference of a circle centre O. SCT is a tangent to the circle at C and is parallel to OB.

A\hat{O}B = 130^\circ

and

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

. Find the reflex angle AOC.

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Question 2501

[2 marks]Statistics & Probability

Denis must choose a bag from which he should pick a ball. The probability that he chooses Bag A is

\frac{1}{2}

. Bag A contains 5 white and 3 black balls. Bag B contains 6 white and 2 black balls. On the probability tree diagram, write down the probability that belongs on the branch from Bag B to "white ball".

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Question 2502

[2 marks]Statistics & Probability

Denis must choose a bag from which he should pick a ball. The probability that he chooses Bag A is

\frac{1}{2}

. Bag A contains 5 white and 3 black balls. Bag B contains 6 white and 2 black balls. Find the probability that Denis chooses Bag A and then a white ball.

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Question 2503

[3 marks]Statistics & Probability

Denis must choose a bag from which he should pick a ball. The probability that he chooses Bag A is

\frac{1}{2}

. Bag A contains 5 white and 3 black balls. Bag B contains 6 white and 2 black balls. Find the probability that Denis picks a white ball.

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Mathematics Paper 1 November 2011

Sit this paper online

The questions

Question 101

Question 102

Question 201

Question 202

Question 301

Question 302

Question 401

Question 402

Question 403

Question 501

Question 502

Question 601

Question 701

Question 702

Question 703

Question 801

Question 901

Question 902

Question 1001

Question 1002

Question 1003

Question 1101

Question 1102

Question 1103

Question 1201

Question 1202

Question 1301

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1602

Question 1701

Question 1702

Question 1703

Question 1801

Question 1802

Question 1901

Question 1902

Question 1903

Question 2001

Question 2101

Question 2102

Question 2103

Question 2104

Question 2201

Question 2202

Question 2301

Question 2302

Question 2303

Question 2304

Question 2401

Question 2402

Question 2403

Question 2404

Question 2405

Question 2406

Question 2501

Question 2502

Question 2503

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The answers, and why they are the answers

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