ZIMSEC O Level Mathematics Paper 1 June 2015

Question 101

[1 marks]Approximations & Estimations

Express 0,0978 correct to two decimal places.

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Question 102

[1 marks]Approximations & Estimations

Express 0,0978 correct to 2 significant figures.

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Question 103

[1 marks]Ordinary and Standard Form

Express 0,0978 in standard form.

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Question 201

[1 marks]Fractions, Decimals & Percentages

Evaluate

39,6 + 0,09

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Question 202

[2 marks]Fractions, Decimals & Percentages

Simplify

\left(\frac{2}{3} - \frac{1}{2}\right) \times \frac{3}{4}

, giving the answer in its lowest terms.

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Question 301

[1 marks]Change of Units

Express 2323 in 12-hour notation.

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Question 302

[2 marks]Change of Units

A jet plane leaves Harare for Praia at 2323. The journey takes 5 hours 33 minutes and Praia's time is 2 hours behind Harare's time. Find the time in Praia when the jet arrives.

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Question 401

[1 marks]Number Bases

Write down

1 \times 2^4 + 1 \times 2^3 + 1 \times 2^1

as a number in base 2.

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Question 402

[2 marks]Substitution

Given that

a = -3

b = 3

and

c = -1

, evaluate

\left(\frac{c-a}{b-a}\right)^2

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

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Question 501

[1 marks]Number

Find

\sqrt[3]{0,027}

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Question 502

[2 marks]Polygons, Symmetry & Circles

The size of each interior angle of a regular polygon is

168^\circ

. Find the number of sides of the polygon.

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Question 601

[1 marks]Vectors

Given that

\mathbf{a} = \begin{pmatrix} -1 \\ -2 \end{pmatrix}

and

\mathbf{b} = \begin{pmatrix} -3 \\ -4 \end{pmatrix}

, express

\mathbf{a} - \mathbf{b}

as a column vector.

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Question 602

[2 marks]Vectors

Given that

\mathbf{b} = \begin{pmatrix} -3 \\ -4 \end{pmatrix}

, find

|\mathbf{b}|

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Question 701

[2 marks]Sets

A is the set of perfect square numbers less than 50, and the elements of A are whole numbers. List the elements of set A.

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Question 702

[1 marks]Sets

A is the set of perfect square numbers less than 50 and B is the set of even numbers not greater than 20. The elements of both sets are whole numbers. Find

n(A \cap B)

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Question 801

[3 marks]Quadratic Equations

Solve the equation

\frac{3}{x} = x - 2

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Question 901

[1 marks]Trigonometry, Bearing & Distances

B is East of A. State the three figure bearing of A from B.

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Question 902

[2 marks]Trigonometry, Bearing & Distances

Express

33,55^\circ

in degrees and minutes.

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Question 1001

[1 marks]Circle Geometry

In the diagram P, Q, R and T are points on the circumference of a circle. PTS and QRS are straight lines. PR is a diameter,

Q\hat{S}P = 28^\circ

and

R\hat{P}S = 50^\circ

. Calculate

P\hat{R}T

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Question 1002

[1 marks]Circle Geometry

In the diagram P, Q, R and T are points on the circumference of a circle. PTS and QRS are straight lines. PR is a diameter,

Q\hat{S}P = 28^\circ

and

R\hat{P}S = 50^\circ

. Calculate

Q\hat{T}S

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Question 1003

[1 marks]Circle Geometry

In the diagram P, Q, R and T are points on the circumference of a circle. PTS and QRS are straight lines. PR is a diameter,

Q\hat{S}P = 28^\circ

and

R\hat{P}S = 50^\circ

. Calculate

Q\hat{T}R

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Question 1101

[3 marks]Simultaneous Equations

Solve the simultaneous equations

3x - y = 7

and

y = 5 - x

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Question 1201

[1 marks]Variation

It is given that y varies directly as the square root of z. Write down the equation connecting y, z and a constant k.

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Question 1202

[1 marks]Variation

y varies directly as the square root of z, so that

y = k\sqrt{z}

. Find k when

y = 3

and

z = 4

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Question 1203

[1 marks]Variation

y varies directly as the square root of z, and

y = 3

when

z = 4

. Find y when

z = 16

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Question 1301

[1 marks]Trigonometry, Bearing & Distances

In the diagram triangle ACD is right angled at C,

AD = 6

cm,

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

and

D\hat{A}C = 30^\circ

, and ABC is a straight line. Calculate CD, in centimetres. [sin 30° = 0,50; cos 30° = 0,87; tan 30° = 0,58; sin 45° = 0,71; cos 45° = 0,71; tan 45° = 1,00]

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Question 1302

[2 marks]Trigonometry, Bearing & Distances

In the diagram triangle ACD is right angled at C,

AD = 6

cm,

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

and

D\hat{A}C = 30^\circ

, and ABC is a straight line. Calculate AB, giving the answer correct to 1 decimal place, in centimetres. [sin 30° = 0,50; cos 30° = 0,87; tan 30° = 0,58; sin 45° = 0,71; cos 45° = 0,71; tan 45° = 1,00]

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Question 1401

[2 marks]Laws of Indices

Simplify

(2a)^{-2} \times 3a^2

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Question 1402

[2 marks]Logarithms

Simplify

\log 8 + \log 4

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Question 1501

[2 marks]Matrices

Given that

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

, find the determinant of

\mathbf{A}

in terms of x, in its simplest form.

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Question 1502

[2 marks]Matrices

Given that

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

and

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

, find

\mathbf{BA}

in terms of x, in its simplest form.

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Question 1601

[2 marks]Consumer Arithmetic

On a day when the exchange rate was R9,03 to 1 USD, a trader exchanged 600 USD for rands. Find the amount, in rands, the trader received.

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Question 1602

[2 marks]Change of Subject of Formula

Given that

f = \frac{mv - mu}{t}

, express m in terms of f, v, u and t.

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Question 1701

[2 marks]Travel Graphs

An object starts from rest and accelerates at

4\ \text{m/s}^2

for 5 seconds until it reaches a speed of 20 m/s. It then travels at this speed for 30 seconds, after which it decelerates uniformly and comes to rest in a further 10 seconds. Calculate the total distance travelled, in metres.

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Question 1801

[2 marks]Probability

9 white and 6 yellow identical tennis balls are placed in a box. Kuda picks balls at random one at a time. Find the probability that the first and second balls picked are both white.

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Question 1802

[2 marks]Probability

9 white and 6 yellow identical tennis balls are placed in a box. Kuda picks balls at random one at a time. Find the probability that the first and second balls picked are of different colours.

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Question 1901

[1 marks]Measures & Mensuration

In the diagram OABC is a sector of a circle centre O and radius

3\frac{1}{2}

cm, right angled at O, and the region between the chord AC and the arc ABC is shaded. State the name given to the shaded region.

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Question 1902

[3 marks]Measures & Mensuration

In the diagram OABC is a sector of a circle centre O and radius

3\frac{1}{2}

cm, right angled at O. Calculate the area of the shaded region between the chord AC and the arc ABC, in

\text{cm}^2

. Take

\pi

to be

\frac{22}{7}

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Question 2001

[4 marks]Consumer Arithmetic

A rural district council increases the value of land by 5 % every year. If the value of a piece of land is $4 600, calculate its value in 2 years' time, in dollars.

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Question 2101

[4 marks]Algebraic Fractions

Simplify

\frac{x^2 - y^2}{x^2 + xy} + \frac{2y - 2x}{xy}

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Question 2201

[2 marks]Linear Equations

Solve the equation

3 - (2n - 5) = 32

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Question 2202

[2 marks]Algebraic Fractions

Express

\frac{7x+2}{5} - \frac{5x+3}{6}

as a single fraction in its simplest form.

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Question 2301

[1 marks]Transformations

On the grid, P is the point

(1; -2)

and Q is the point

(3; -2)

. Write down the coordinates of the image of P, if P is translated by the vector

\begin{pmatrix} -1 \\ 4 \end{pmatrix}

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Question 2302

[3 marks]Transformations

On the grid, P is the point

(1; -2)

, Q is the point

(3; -2)

P_2

is the point

(-2; -1)

and

Q_2

is the point

(-2; -3)

. Which single transformation maps PQ onto

P_2Q_2

AA reflection in the line $y = x$ .
BA rotation through $90^\circ$ clockwise about the origin.
CA rotation through $90^\circ$ anticlockwise about the origin.
DA translation by the vector $\begin{pmatrix} -3 \\ 1 \end{pmatrix}$ .

Question 2401

[1 marks]Statistics

Ten students walk to Chitsa High School every day. The distances they walk, to the nearest kilometre, are 1 km (4 students), 2 km (2 students), 3 km (2 students), 4 km (1 student) and 5 km (1 student). State the least possible distance walked by a student, in kilometres.

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Question 2402

[1 marks]Statistics

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Question 2403

[1 marks]Statistics

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Question 2404

[2 marks]Statistics

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Question 2601

[1 marks]Scales & Simple Map Problems

The scale of the plan of a house is 1:500. Find the length, in centimetres, of a room on the plan which measures 8 m.

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Question 2602

[1 marks]Scales & Simple Map Problems

The scale of the plan of a house is 1:500. Calculate the actual height, in metres, of a wall which is represented by 3,6 cm on the plan.

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Question 2603

[3 marks]Scales & Simple Map Problems

The scale of the plan of a house is 1:500. Find the actual area, in

\text{m}^2

, of a room which has an area of

1,6\ \text{cm}^2

on the plan.

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Question 2701

[2 marks]Quadratic Equations

The diagram shows the graph of

y = 6 - x - x^2

. Use the graph to solve the equation

6 - x - x^2 = 0

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Question 2702

[1 marks]Quadratic Equations

The diagram shows the graph of

y = 6 - x - x^2

. Use the graph to state the equation of the line of symmetry of the curve.

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Question 2703

[1 marks]Quadratic Equations

The diagram shows the graph of

y = 6 - x - x^2

. Use the graph to estimate the maximum value of the function.

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Question 2704

[2 marks]Quadratic Equations

The diagram shows the graph of

y = 6 - x - x^2

. Use the graph to estimate the area bounded by the curve, the x-axis, the line

x = -1

and the line

x = 1

, in square units.

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Mathematics Paper 1 June 2015

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The questions

Question 101

Question 102

Question 103

Question 201

Question 202

Question 301

Question 302

Question 401

Question 402

Question 501

Question 502

Question 601

Question 602

Question 701

Question 702

Question 801

Question 901

Question 902

Question 1001

Question 1002

Question 1003

Question 1101

Question 1201

Question 1202

Question 1203

Question 1301

Question 1302

Question 1401

Question 1402

Question 1501

Question 1502

Question 1601

Question 1602

Question 1701

Question 1801

Question 1802

Question 1901

Question 1902

Question 2001

Question 2101

Question 2201

Question 2202

Question 2301

Question 2302

Question 2401

Question 2402

Question 2403

Question 2404

Question 2601

Question 2602

Question 2603

Question 2701

Question 2702

Question 2703

Question 2704

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