ZIMSEC O Level Mathematics Paper 1 November 2015

Question 101

[1 marks]Fractions, Decimals & Percentages

Find the value of

\frac{8}{0,04}

Answer this when you sit the paper.

Question 102

[2 marks]Fractions, Decimals & Percentages

Simplify

1\frac{1}{2} - \frac{4}{7} \div \frac{2}{3}

, giving the answer as a fraction in its simplest form.

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Question 201

[1 marks]Substitution

Given that

p = -4

q = 3

and

r = -1

, evaluate

\frac{p+q}{r}

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Question 202

[2 marks]Substitution

Given that

p = -4

q = 3

and

r = -1

, evaluate

\sqrt{p^2 q - r}

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Question 301

[2 marks]Ordinary and Standard Form

In an athletics competition, under 20 boys compete in a 5 000 m race, while under 16 boys compete in a 3 000 m race. Calculate the difference in the distances they run giving the answer in standard form.

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Question 302

[1 marks]Ordinary and Standard Form

In an athletics competition, under 20 boys compete in a 5 000 m race, while under 16 boys compete in a 3 000 m race. A lap is 400 m long. Find the number of laps in the 5 000 m race.

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Question 401

[1 marks]Vector Geometry

It is given that

\overrightarrow{OP} = \begin{pmatrix} -2 \\ 7 \end{pmatrix}

and

\overrightarrow{OQ} = \begin{pmatrix} 12 \\ -5 \end{pmatrix}

where O is the origin. Express

\overrightarrow{PQ}

as a column vector.

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Question 402

[1 marks]Vector Geometry

It is given that

\overrightarrow{OP} = \begin{pmatrix} -2 \\ 7 \end{pmatrix}

and

\overrightarrow{OQ} = \begin{pmatrix} 12 \\ -5 \end{pmatrix}

where O is the origin. Find

\left|\overrightarrow{OQ}\right|

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Question 403

[1 marks]Vector Geometry

It is given that

\overrightarrow{OP} = \begin{pmatrix} -2 \\ 7 \end{pmatrix}

and

\overrightarrow{OQ} = \begin{pmatrix} 12 \\ -5 \end{pmatrix}

where O is the origin. Find the co-ordinates of M, the midpoint of PQ.

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Question 501

[1 marks]Number Bases

Express

1 \times 3^5 + 2 \times 3^3 + 3

as a number in base 3.

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Question 502

[1 marks]Number Bases

Convert

101_{10}

to a number in base 9.

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Question 503

[1 marks]Number Bases

Evaluate

203_7 - 154_7

giving the answer in base 7.

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Question 601

[3 marks]Simultaneous Equations

Solve the simultaneous equations:

2x + 3y = 28

x + 5y = 35

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Question 701

[3 marks]Equations

Solve the equation

\frac{2y+5}{3y-2} = \frac{9}{4}

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Question 801

[3 marks]Change of Subject of Formula

Make

a

the subject of the formula

\frac{1}{a} + \frac{1}{b} = 3

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Question 901

[1 marks]Ratios, Rates & Proportions

When baking scones, a baker mixes six cups of flour, one cup of sugar, two cups of water and half a cup of milk, together with other ingredients. Express the quantities of flour, sugar, water and milk as a ratio in its simplest form.

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Question 902

[2 marks]Ratios, Rates & Proportions

When baking scones, a baker mixes six cups of flour, one cup of sugar, two cups of water and half a cup of milk, together with other ingredients. Calculate the number of cups of water needed if the baker uses four cups of flour.

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Question 1001

[1 marks]Probability

The probability that Sihle will bring a calculator is

\frac{5}{6}

while the probability that Yemurai will bring a calculator is

\frac{3}{5}

. Giving the answer as a fraction in its simplest form, find the probability that Sihle will not bring a calculator for the lesson.

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Question 1002

[2 marks]Probability

The probability that Sihle will bring a calculator is

\frac{5}{6}

while the probability that Yemurai will bring a calculator is

\frac{3}{5}

. Giving the answer as a fraction in its simplest form, find the probability that only one of them will bring a calculator for the lesson.

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Question 1101

[1 marks]Polygons, Symmetry & Circles

Write down the special name given to a polygon with five sides.

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Question 1102

[1 marks]Polygons, Symmetry & Circles

State, for a regular five sided polygon, the number of lines of symmetry.

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Question 1103

[1 marks]Polygons, Symmetry & Circles

State, for a regular five sided polygon, the order of rotational symmetry.

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Question 1201

[3 marks]Inequalities

Solve the inequality

2 - x \le 2x - 1 < 11

, giving your answer in the form

a \le x < b

, where

a

and

b

are integers.

Answer this when you sit the paper.

Question 1301

[1 marks]Trigonometry, Bearing & Distances

In the diagram, A, B and C are positions of 3 boreholes where BA = BC. The borehole at C has a bearing of 116° from the borehole at B. Calculate

A\hat{C}B

Answer this when you sit the paper.

Question 1302

[2 marks]Trigonometry, Bearing & Distances

In the diagram, A, B and C are positions of 3 boreholes where BA = BC. The borehole at C has a bearing of 116° from the borehole at B. Calculate the bearing of the borehole at A from the borehole at C.

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Question 1401

[1 marks]Logarithms

\log_{10} 7 = 0,8451

, evaluate

\log_{10} 0,07

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Question 1402

[1 marks]Logarithms

\log_{10} 7 = 0,8451

, evaluate

\log_{10} 49

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Question 1403

[2 marks]Logarithms

Evaluate

\log_2\left(\frac{1}{64}\right)

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Question 1501

[1 marks]Consumer Arithmetic

The table shows part of Ms Dube's payslip for a particular month. Calculate the total deductions.

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Question 1502

[1 marks]Consumer Arithmetic

The table shows part of Ms Dube's payslip for a particular month. Calculate the net salary.

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Question 1503

[2 marks]Consumer Arithmetic

The table shows part of Ms Dube's payslip for a particular month. Express the pension contribution as a percentage of her basic salary.

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Question 1601

[2 marks]Laws of Indices

Evaluate

81^{\frac{3}{4}}

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Question 1602

[2 marks]Laws of Indices

Find

x

9^{x-1} \times 3^{3x-2} = 3

Answer this when you sit the paper.

Question 1701

[2 marks]Variation

Given that

y

is inversely proportional to

(x-1)^2

and that

y = 2

when

x = 7

, express

y

in terms of

x

Answer this when you sit the paper.

Question 1702

[2 marks]Variation

Given that

y

is inversely proportional to

(x-1)^2

and that

y = 2

when

x = 7

, calculate the values of

x

when

y = 8

Answer this when you sit the paper.

Question 1801

[1 marks]Time

A luxury coach leaves Bulawayo for Harare every morning at 7.30 am and arrives in Harare at 1.00 pm. Express the departure time as a time in the 24 hour notation.

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Question 1802

[1 marks]Time

A luxury coach leaves Bulawayo for Harare every morning at 7.30 am and arrives in Harare at 1.00 pm. Calculate the total time taken to travel from Bulawayo to Harare.

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Question 1803

[2 marks]Speed, distance and time

A luxury coach leaves Bulawayo for Harare every morning at 7.30 am and arrives in Harare at 1.00 pm. Calculate the average speed of the bus to the nearest whole number if the distance from Bulawayo to Harare is 439 km.

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Question 1901

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

Factorise completely

cg - dg - ch + dh

Answer this when you sit the paper.

Question 1902

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

Factorise completely

5d^2 - d - 4

Answer this when you sit the paper.

Question 2001

[1 marks]Statistics

The pie chart shows the distribution of an athlete's daily exercise programme. Calculate the value of

x

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Question 2002

[1 marks]Statistics

The pie chart shows the distribution of an athlete's daily exercise programme. If the athlete spent 18 minutes jogging, calculate the time the athlete spent on weight lifting.

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Question 2003

[2 marks]Statistics

The pie chart shows the distribution of an athlete's daily exercise programme. If the athlete spent 18 minutes jogging, calculate the total time spent exercising.

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Question 2101

[2 marks]Trigonometry, Bearing & Distances

In the diagram, PQR is an isosceles triangle such that PQ = PR = 7 cm and

P\hat{R}Q = 35°

. Using as much of the information given below as is necessary, calculate QR, in centimetres. [Sin 35° = 0,57; Cos 35° = 0,82; Tan 35° = 0,70; Sin 70° = 0,94; Cos 70° = 0,34; Tan 70° = 2,75]

Answer this when you sit the paper.

Question 2102

[2 marks]Trigonometry, Bearing & Distances

In the diagram, PQR is an isosceles triangle such that PQ = PR = 7 cm and

P\hat{R}Q = 35°

. Using as much of the information given below as is necessary, calculate the area of triangle PQR, in square centimetres. [Sin 35° = 0,57; Cos 35° = 0,82; Tan 35° = 0,70; Sin 70° = 0,94; Cos 70° = 0,34; Tan 70° = 2,75]

Answer this when you sit the paper.

Question 2201

[1 marks]Sets

It is given that

\xi = \{x : 31 \le x < 37

and

x

is an integer

\}

has subsets P, Q and R such that

P = \{x : x

is a multiple of

3\}

Q = \{x : x

is a factor of

99\}

and

R = \{x : x

is a prime number

\}

. List all the elements of R.

Answer this when you sit the paper.

Question 2202

[1 marks]Sets

It is given that

\xi = \{x : 31 \le x < 37

and

x

is an integer

\}

has subsets P, Q and R such that

P = \{x : x

is a multiple of

3\}

Q = \{x : x

is a factor of

99\}

and

R = \{x : x

is a prime number

\}

. Write down

n(P \cup R)'

Answer this when you sit the paper.

Question 2203

[2 marks]Sets

It is given that

\xi = \{x : 31 \le x < 37

and

x

is an integer

\}

has subsets P, Q and R such that

P = \{x : x

is a multiple of

3\}

Q = \{x : x

is a factor of

99\}

and

R = \{x : x

is a prime number

\}

. List all elements of

(P \cup Q \cup R)'

Answer this when you sit the paper.

Question 2301

[2 marks]Scales & Simple Map Problems

A map is drawn to a scale of 1 : 75 000. Calculate in km the actual distance between two towns which are 40 cm apart on the map.

Answer this when you sit the paper.

Question 2302

[2 marks]Scales & Simple Map Problems

A map is drawn to a scale of 1 : 75 000. An airport has an actual area of

22,5\ \text{km}^2

. Calculate in

\text{cm}^2

the area of the airport on the map.

Answer this when you sit the paper.

Question 2401

[2 marks]Travel Graphs

In the diagram, a moving object decelerates from a speed of 30 m/s to a speed of 18 m/s in 4 seconds and further decelerates from a speed of 18 m/s to rest in 6 seconds. Calculate the speed of the object after the first 2 seconds.

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Question 2402

[2 marks]Travel Graphs

In the diagram, a moving object decelerates from a speed of 30 m/s to a speed of 18 m/s in 4 seconds and further decelerates from a speed of 18 m/s to rest in 6 seconds. Calculate the total distance covered by the object in the 10 seconds.

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Question 2501

[3 marks]Geometrical Transformation

The diagram shows three shapes A, B and C on a Cartesian plane. Describe completely the single transformation which maps shape A onto shape B.

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Question 2502

[2 marks]Geometrical Transformation

The diagram shows three shapes A, B and C on a Cartesian plane. Shape B is mapped onto shape C by a transformation P. Describe fully the transformation P.

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Question 2601

[1 marks]Circle Geometry

In the diagram, O is the centre of the circle. TAS is a tangent to the circle at A.

B\hat{A}S = 40°

and

O\hat{B}C = 54°

. Calculate

O\hat{A}B

Answer this when you sit the paper.

Question 2602

[1 marks]Circle Geometry

In the diagram, O is the centre of the circle. TAS is a tangent to the circle at A.

B\hat{A}S = 40°

and

O\hat{B}C = 54°

. Calculate

A\hat{O}B

Answer this when you sit the paper.

Question 2603

[2 marks]Circle Geometry

In the diagram, O is the centre of the circle. TAS is a tangent to the circle at A.

B\hat{A}S = 40°

and

O\hat{B}C = 54°

. Calculate

A\hat{D}C

Answer this when you sit the paper.

Question 2604

[2 marks]Circle Geometry

In the diagram, O is the centre of the circle. TAS is a tangent to the circle at A.

B\hat{A}S = 40°

and

O\hat{B}C = 54°

. Calculate reflex

A\hat{O}C

Answer this when you sit the paper.

Question 2701

[2 marks]Matrices

F = \begin{pmatrix} 3 & x \\ -4 & -6 \end{pmatrix}

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

and

H = \begin{pmatrix} 7 \\ 1 \end{pmatrix}

, find

F + 3G

in terms of

x

Answer this when you sit the paper.

Question 2702

[2 marks]Matrices

F = \begin{pmatrix} 3 & x \\ -4 & -6 \end{pmatrix}

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

and

H = \begin{pmatrix} 7 \\ 1 \end{pmatrix}

, find the value of

x

if the determinant of

F

-14

Answer this when you sit the paper.

Question 2703

[2 marks]Matrices

F = \begin{pmatrix} 3 & x \\ -4 & -6 \end{pmatrix}

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

and

H = \begin{pmatrix} 7 \\ 1 \end{pmatrix}

, find

GH

Answer this when you sit the paper.

Mathematics Paper 1 November 2015

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 503

Question 601

Question 701

Question 801

Question 901

Question 902

Question 1001

Question 1002

Question 1101

Question 1102

Question 1103

Question 1201

Question 1301

Question 1302

Question 1401

Question 1402

Question 1403

Question 1501

Question 1502

Question 1503

Question 1601

Question 1602

Question 1701

Question 1702

Question 1801

Question 1802

Question 1803

Question 1901

Question 1902

Question 2001

Question 2002

Question 2003

Question 2101

Question 2102

Question 2201

Question 2202

Question 2203

Question 2301

Question 2302

Question 2401

Question 2402

Question 2501

Question 2502

Question 2601

Question 2602

Question 2603

Question 2604

Question 2701

Question 2702

Question 2703

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