ZIMSEC O Level Mathematics Paper 1 November 2013

Question 101

[1 marks]Fractions, Decimals & Percentages

Evaluate

\frac{1}{5} + \frac{1}{6}

, giving the answer as a fraction in its lowest terms. [1]

Answer this when you sit the paper.

Question 102

[1 marks]Fractions, Decimals & Percentages

Evaluate

\frac{2}{5} \div 4

, giving the answer as a fraction in its lowest terms. [1]

Answer this when you sit the paper.

Question 103

[1 marks]Fractions, Decimals & Percentages

Evaluate

\frac{3}{4} - \frac{1}{4} \times \frac{2}{3}

, giving the answer as a fraction in its lowest terms. [1]

Answer this when you sit the paper.

Question 201

[3 marks]Ordinary and Standard Form

Evaluate

\dfrac{(0,3)^3 \times 0,02}{0,0008}

, giving your answer in standard form. [3]

Answer this when you sit the paper.

Question 301

[1 marks]Number

The temperature inside a freezer is

-8°

C. During a power cut the temperature rose by

12°

C. Find the temperature after the rise, in degrees Celsius. [1]

Answer this when you sit the paper.

Question 302

[2 marks]Number

Write down the next two terms in the following sequence:

1; \frac{1}{2}; \frac{1}{4}; \frac{1}{8}; \ldots

[2]

Answer this when you sit the paper.

Question 401

[1 marks]Change of Units

Write 3,35 minutes in minutes and seconds. [1]

Answer this when you sit the paper.

Question 402

[2 marks]Change of Units

If 1 kilometre is

\frac{5}{8}

of a mile, convert 75 miles to kilometres. [2]

Answer this when you sit the paper.

Question 501

[3 marks]Algebraic Expressions

A shopper spent

\$\frac{c}{d}

on one item and half of that amount on each of three other items. Find how much she spent altogether, in dollars, in terms of

c

and

d

. [3]

Answer this when you sit the paper.

Question 601

[1 marks]Laws of Indices

Simplify

\dfrac{(3^3)^4}{27^3}

. [1]

Answer this when you sit the paper.

Question 602

[1 marks]Laws of Indices

Simplify

\left(4x^2y^6\right)^{\frac{1}{2}}

. [1]

Answer this when you sit the paper.

Question 603

[1 marks]Laws of Indices

Simplify

x^0 + x^{-2}

. [1]

Answer this when you sit the paper.

Question 701

[1 marks]Fractions, Decimals & Percentages

Express

\frac{7}{8}

as a decimal fraction. [1]

Answer this when you sit the paper.

Question 702

[2 marks]Consumer Arithmetic

A car loses 55% of its value after four years. If it cost

\$8\ 500

when new, find its value, in dollars, after the four years. [2]

Answer this when you sit the paper.

Question 801

[1 marks]Algebraic Expressions

Simplify

5m - 2(x - 3m)

. [1]

Answer this when you sit the paper.

Question 802

[2 marks]Linear Equations

Solve the equation

\dfrac{x+5}{7} = \dfrac{3}{2}

. [2]

Answer this when you sit the paper.

Question 901

[1 marks]Change of Units

Express 200 km/h as a speed in km/min. [1]

Answer this when you sit the paper.

Question 902

[2 marks]Ratios, Rates & Proportions

Find the time taken for a racing driver to cover a 120 km race if he travels at a speed of 200 km/h, giving your answer in minutes. [2]

Answer this when you sit the paper.

Question 1001

[1 marks]Factorisation

Factorise completely

4y - 4

. [1]

Answer this when you sit the paper.

Question 1002

[2 marks]Factorisation

Factorise completely

xy^2 - 4x + 2y^2 - 8

. [2]

Answer this when you sit the paper.

Question 1101

[3 marks]Simultaneous Equations

Solve the simultaneous equations

5d - 3e = -1

and

2d + 3e = 8

, giving the values of

d

and

e

. [3]

Answer this when you sit the paper.

Question 1201

[3 marks]Quadratic Equations

Solve the equation

(x + 3)^2 = 49

. [3]

Answer this when you sit the paper.

Question 1202

[1 marks]Number

Write down the prime numbers between 20 and 30. [1]

Answer this when you sit the paper.

Question 1301

[3 marks]Algebraic Fractions

Simplify

\dfrac{x^2 + 3x + 2}{x + 2}

. [3]

Answer this when you sit the paper.

Question 1302

[1 marks]Polygons, Symmetry & Circles

Find the order of rotational symmetry of a right-angled isosceles triangle. [1]

Answer this when you sit the paper.

Question 1401

[1 marks]Sets

Given that

n(\mathbf{A}) = 10

and

n(\mathbf{B}) = 15

, find the greatest possible value of

n(\mathbf{A} \cup \mathbf{B})

. [1]

Answer this when you sit the paper.

Question 1402

[1 marks]Sets

Given that

n(\mathbf{A}) = 10

and

n(\mathbf{B}) = 15

, find the greatest possible value of

n(\mathbf{A} \cap \mathbf{B})

. [1]

Answer this when you sit the paper.

Question 1403

[2 marks]Sets

In the Venn diagram, the whole of set R is shaded, together with the part of

\mathbf{P} \cap \mathbf{Q}

that lies outside R. Use set notation to describe the shaded region in terms of sets

\mathbf{P}

\mathbf{Q}

and

\mathbf{R}

. [2]

Answer this when you sit the paper.

Question 1501

[2 marks]Matrices

Given that

\mathbf{A} = \begin{pmatrix} -2 & -1 \\ 6 & 2 \end{pmatrix}

and

\mathbf{B} = \begin{pmatrix} 0 & -1 \\ 4 & 3 \end{pmatrix}

, find

3\mathbf{A} - \mathbf{B}

. [2]

Answer this when you sit the paper.

Question 1502

[2 marks]Matrices

Given that

\mathbf{B} = \begin{pmatrix} 0 & -1 \\ 4 & 3 \end{pmatrix}

, find

\mathbf{B}^2

. [2]

Answer this when you sit the paper.

Question 1601

[1 marks]Number Bases

Write down the largest four-digit number in base eight. [1]

Answer this when you sit the paper.

Question 1602

[2 marks]Number Bases

Convert

111_8

to a number in base two. [2]

Answer this when you sit the paper.

Question 1603

[1 marks]Number Bases

Find the sum of

444_5

and

21_5

, giving your answer in base five. [1]

Answer this when you sit the paper.

Question 1701

[1 marks]Statistics

A rugby team scored the following points in 12 matches: 21; 18; 3; 12; 15; 18; 42; 18; 24; 6; 12; 3. Find the mode. [1]

Answer this when you sit the paper.

Question 1702

[2 marks]Statistics

A rugby team scored the following points in 12 matches: 21; 18; 3; 12; 15; 18; 42; 18; 24; 6; 12; 3. Find the mean. [2]

Answer this when you sit the paper.

Question 1703

[1 marks]Statistics

A rugby team scored the following points in 12 matches: 21; 18; 3; 12; 15; 18; 42; 18; 24; 6; 12; 3. In the next match, the team scored 55 points. Write down the median score for the 13 matches. [1]

Answer this when you sit the paper.

Question 1801

[2 marks]Scales & Simple Map Problems

The scale of a map is 1:10 000. Two hills are 4,5 cm apart on the map. Find the actual distance between the hills, giving your answer in kilometres. [2]

Answer this when you sit the paper.

Question 1802

[2 marks]Scales & Simple Map Problems

The scale of a map is 1:10 000. Two towns are 80 km apart. Find the distance between them on the map, giving your answer in centimetres. [2]

Answer this when you sit the paper.

Question 1901

[1 marks]Substitution

The temperature

T°

C at a height of

H

metres above sea level is given by the formula

T = 20 - \dfrac{H}{150}

. Calculate the temperature, in degrees Celsius, at 4 500 metres. [1]

Answer this when you sit the paper.

Question 1902

[2 marks]Change of Subject of Formula

The temperature

T°

C at a height of

H

metres above sea level is given by the formula

T = 20 - \dfrac{H}{150}

. Make

H

the subject of the formula. [2]

Answer this when you sit the paper.

Question 1903

[1 marks]Change of Subject of Formula

The temperature

T°

C at a height of

H

metres above sea level is given by the formula

T = 20 - \dfrac{H}{150}

. Find the height, in metres, at which the temperature is

12°

C. [1]

Answer this when you sit the paper.

Question 2001

[1 marks]Variation

The number of revolutions,

n

, of a wheel over a fixed distance varies inversely as the circumference,

C

cm, of the wheel. Write down an equation involving

n

C

and a constant

k

. [1]

Answer this when you sit the paper.

Question 2002

[3 marks]Variation

The number of revolutions,

n

, of a wheel over a fixed distance varies inversely as the circumference,

C

cm, of the wheel. If a wheel of circumference 80 cm makes 10 revolutions, find the number of revolutions made by a wheel of circumference 200 cm. [3]

Answer this when you sit the paper.

Question 2101

[2 marks]Similarity & Congruency

In the diagram, XY is parallel to QR, PY = 2 cm, YR = 3 cm and XY = 4 cm. Find the length of QR, in centimetres. [2]

Answer this when you sit the paper.

Question 2102

[2 marks]Similarity & Congruency

In the diagram, XY is parallel to QR, PY = 2 cm, YR = 3 cm and XY = 4 cm. Find the ratio

\dfrac{\text{area } \triangle PXY}{\text{area } \triangle PQR}

. [2]

Answer this when you sit the paper.

Question 2201

[1 marks]Probability

Tendai and Vimbai take a driving test. The probability that Tendai will pass is

\frac{3}{5}

and the probability that Vimbai will pass is

\frac{2}{3}

. State which one of them is more likely to pass. [1]

Answer this when you sit the paper.

Question 2202

[2 marks]Probability

Tendai and Vimbai take a driving test. The probability that Tendai will pass is

\frac{3}{5}

and the probability that Vimbai will pass is

\frac{2}{3}

. Calculate the probability that they both fail. [2]

Answer this when you sit the paper.

Question 2203

[2 marks]Probability

Tendai and Vimbai take a driving test. The probability that Tendai will pass is

\frac{3}{5}

and the probability that Vimbai will pass is

\frac{2}{3}

. Calculate the probability that only one of them will pass. [2]

Answer this when you sit the paper.

Question 2301

[1 marks]Vector Geometry

In the diagram

\overrightarrow{PQ} = \mathbf{p}

\overrightarrow{QR} = \mathbf{q}

and

\overrightarrow{RS} = \mathbf{r}

, and triangles PQT, QTR and TRS are equilateral. Express

\overrightarrow{PS}

in terms of

\mathbf{p}

\mathbf{q}

and

\mathbf{r}

. [1]

Answer this when you sit the paper.

Question 2302

[2 marks]Vector Geometry

In the diagram

\overrightarrow{QR} = \mathbf{q}

, and triangles PQT, QTR and TRS are equilateral. Express

\overrightarrow{PS}

in terms of

\mathbf{q}

only. [2]

Answer this when you sit the paper.

Question 2303

[2 marks]Vector Geometry

In the diagram

\overrightarrow{PQ} = \mathbf{p}

\overrightarrow{QR} = \mathbf{q}

and

\overrightarrow{RS} = \mathbf{r}

, and triangles PQT, QTR and TRS are equilateral, so that

\overrightarrow{PS} = 2\mathbf{q}

. Express

\mathbf{p}

in terms of

\mathbf{q}

and

\mathbf{r}

. [2]

Answer this when you sit the paper.

Question 2401

[1 marks]Co-ordinate Geometry

The graph of

y = mx + c

passes through the points A

(0; 2)

and B

(5; -3)

. Find the value of

c

. [1]

Answer this when you sit the paper.

Question 2402

[2 marks]Co-ordinate Geometry

The graph of

y = mx + c

passes through the points A

(0; 2)

and B

(5; -3)

. Find the value of

m

. [2]

Answer this when you sit the paper.

Question 2403

[2 marks]Co-ordinate Geometry

The graph of

y = mx + c

passes through the points A

(0; 2)

and B

(5; -3)

. Calculate the length of AB, leaving your answer in surd form. [2]

Answer this when you sit the paper.

Question 2501

[2 marks]Travel Graphs

The diagram is the speed-time graph of a sprinter during an athletics training session. The sprinter accelerates uniformly from rest to 10 m/s in the first 4 seconds, runs at 10 m/s until

t = 10

, accelerates to a speed V at

t = 12

, then decelerates uniformly to rest at

t = 17

. Calculate the distance, in metres, the sprinter covers during the first 10 seconds. [2]

Answer this when you sit the paper.

Question 2502

[2 marks]Travel Graphs

The diagram is the speed-time graph of a sprinter during an athletics training session. The sprinter is running at 10 m/s at

t = 10

and reaches a speed V at

t = 12

. Given that the acceleration during the time interval from

t = 10

t = 12

is 5 m/s

^2

, find the value of V, in m/s. [2]

Answer this when you sit the paper.

Question 2503

[2 marks]Travel Graphs

The diagram is the speed-time graph of a sprinter during an athletics training session. The sprinter reaches 20 m/s at

t = 12

and comes to rest at

t = 17

. Calculate the deceleration of the sprinter, in m/s

^2

, from

t = 12

to the time the sprinter stops running. [2]

Answer this when you sit the paper.

Question 2601

[2 marks]Circle Geometry

The points P, Q and R lie on the circumference of a circle, centre O. PQ = 5 cm, PR = 8 cm and

Q\hat{P}R = 80°

. Calculate the area of triangle PQR, in cm

^2

. [sin 80° = 0.985; cos 80° = 0.174; tan 80° = 5.67] [2]

Answer this when you sit the paper.

Question 2602

[2 marks]Circle Geometry

The points P, Q and R lie on the circumference of a circle, centre O. PQ = 5 cm, PR = 8 cm and

Q\hat{P}R = 80°

. Calculate the value of QR

^2

. [sin 80° = 0.985; cos 80° = 0.174; tan 80° = 5.67] [2]

Answer this when you sit the paper.

Question 2603

[2 marks]Circle Geometry

The points P, Q and R lie on the circumference of a circle, centre O. PQ = 5 cm, PR = 8 cm and

Q\hat{P}R = 80°

. Find the reflex

Q\hat{O}R

, in degrees. [2]

Answer this when you sit the paper.

Mathematics Paper 1 November 2013

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 201

Question 301

Question 302

Question 401

Question 402

Question 501

Question 601

Question 602

Question 603

Question 701

Question 702

Question 801

Question 802

Question 901

Question 902

Question 1001

Question 1002

Question 1101

Question 1201

Question 1202

Question 1301

Question 1302

Question 1401

Question 1402

Question 1403

Question 1501

Question 1502

Question 1601

Question 1602

Question 1603

Question 1701

Question 1702

Question 1703

Question 1801

Question 1802

Question 1901

Question 1902

Question 1903

Question 2001

Question 2002

Question 2101

Question 2102

Question 2201

Question 2202

Question 2203

Question 2301

Question 2302

Question 2303

Question 2401

Question 2402

Question 2403

Question 2501

Question 2502

Question 2503

Question 2601

Question 2602

Question 2603

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