ZIMSEC O Level Mathematics Paper 2 November 2018

Question 101

[2 marks]Algebraic Expressions

Simplify

ax - x(a - b) + 2bx

Answer this when you sit the paper.

Question 102

[2 marks]Algebraic Expressions

Simplify

(x - 2)^2 - x^2

Answer this when you sit the paper.

Question 103

[2 marks]Algebraic Expressions

Given that

P = \frac{1}{2}[a + d(a + d)]

, evaluate

P

when

a = \frac{1}{2}

and

d = 1

Answer this when you sit the paper.

Question 104

[3 marks]Algebraic Fractions

Express

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

as a single fraction in its lowest terms.

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Question 201

[2 marks]Consumer Arithmetic

Bright Link (Pvt) Ltd sells channel blocks in 5 kg boxes at $50 a box. Calculate the price of channel blocks per kilogram.

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Question 202

[2 marks]Consumer Arithmetic

A twenty-litre bucket of floor polish is priced at $50 on the Bright Link (Pvt) Ltd list, and all the prices on that list include 15% Value Added Tax (VAT). Calculate the Value Added Tax on the bucket of floor polish.

Answer this when you sit the paper.

Question 203

[3 marks]Consumer Arithmetic

Bright Link (Pvt) Ltd charges $50 for 20 litres of floor polish, $30 for 20 litres of toilet dip, $28 for 20 litres of sanitiser, $50 for a 5 kg box of channel blocks and $28 for 20 litres of dish washer, and gives 10% discount on any order placed between 1 January and 28 February. On the fourth of January a school ordered two 20 litre buckets of floor polish, one 20 litre container of toilet dip, two 20 litre containers of dish washer, one 20 litre container of sanitiser and three 5 kg boxes of channel blocks. Calculate the total discount the school got.

Answer this when you sit the paper.

Question 204

[3 marks]Consumer Arithmetic

A man invested $400 in a bank that offers 3% per annum compound interest. Calculate the total amount he would get at the end of 3 years.

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Question 301

[3 marks]Inequalities

Solve the inequality

4x - 2 \le 5x + 2 < 2x + 8

, giving your answer in the form

a \le x < b

, where

a

and

b

are integers.

Answer this when you sit the paper.

Question 302

[3 marks]Change of Subject of Formula

Make

x

the subject of the formula

R = \sqrt{\dfrac{ax - p}{Q + bx}}

Answer this when you sit the paper.

Question 303

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

Factorise completely

2m^3n^2 + 3m^2n - 2m

Answer this when you sit the paper.

Question 304

[1 marks]Inequalities

Solving the inequality

4x - 2 \le 5x + 2 < 2x + 8

gives

-4 \le x < 2

. Which of these describes the correct illustration of that answer on a number line?

AA shaded segment from $-4$ to 2, with open circles at both $-4$ and 2
BA shaded segment from $-4$ to 2, with a filled circle at $-4$ and an open circle at 2
CA shaded segment from $-4$ to 2, with an open circle at $-4$ and a filled circle at 2
DA shaded segment from $-4$ to 2, with filled circles at both $-4$ and 2

Question 401

[1 marks]Constructions & Loci

In triangle ABC the angle

B\hat{C}A

is bisected using ruler and compasses. Which of these describes the locus represented by that bisector?

AThe locus of points equidistant from the points B and A
BThe locus of points a fixed distance from the point C
CThe locus of points equidistant from the lines CB and CA
DThe locus of points equidistant from the lines AB and AC

Question 501

[2 marks]Sets

The universal set is

\xi = \{x : 1 \le x \le 10,\ x \text{ is an integer}\}

and A is the set of perfect square numbers in

\xi

. List all the elements of set A.

Answer this when you sit the paper.

Question 502

[1 marks]Sets

The universal set is

\xi = \{x : 1 \le x \le 10,\ x \text{ is an integer}\}

, A is the set of perfect square numbers in

\xi

and B is the set of multiples of 4 in

\xi

. List all the elements of set

A \cap B

Answer this when you sit the paper.

Question 503

[1 marks]Sets

The universal set is

\xi = \{x : 1 \le x \le 10,\ x \text{ is an integer}\}

, A is the set of perfect square numbers in

\xi

and B is the set of multiples of 4 in

\xi

. Find

n(A \cup B)

Answer this when you sit the paper.

Question 504

[1 marks]Sets

It is given that

P \subset Q

and

Q \subset R

. Write in set notation the relationship between set P and set R.

Answer this when you sit the paper.

Question 505

[2 marks]Sets

It is given that

P \subset Q

and

Q \subset R

. Which of these describes a correct Venn diagram for the three sets P, Q and R?

AP and R overlapping each other, with Q drawn entirely outside both
BThree circles that all overlap one another in one common region
CThree circles one inside the other, with P inside Q and Q inside R
DThree separate circles that do not touch one another

Question 506

[1 marks]Statistics & Probability

A bag contains 10 buttons that are identical except for colour, 7 red and 3 blue. Two buttons are drawn at random, one after the other without replacement. The first button drawn is red. Find the probability that the second button is blue.

Answer this when you sit the paper.

Question 507

[2 marks]Statistics & Probability

A bag contains 10 buttons that are identical except for colour, 7 red and 3 blue. Two buttons are drawn at random, one after the other without replacement. Find the probability that both buttons are red.

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Question 508

[2 marks]Statistics & Probability

Answer this when you sit the paper.

Question 509

[1 marks]Statistics & Probability

A bag contains 10 buttons that are identical except for colour, 7 red and 3 blue. Two buttons are drawn at random, one after the other without replacement. The first button drawn is blue. Find the probability that the second button is red.

Answer this when you sit the paper.

Question 601

[3 marks]Statistics & Probability

The ages of vehicles parked at a stadium are grouped as follows.

0 < x \le 5

: 10 vehicles;

5 < x \le 10

: 12 vehicles;

10 < x \le 15

: 37 vehicles;

15 < x \le 20

: 51 vehicles;

20 < x \le 25

: 10 vehicles. Calculate an estimate of the mean age of the vehicles, in years.

Answer this when you sit the paper.

Question 602

[1 marks]Statistics & Probability

The ages of 120 vehicles are grouped as

0 < x \le 5

: 10;

5 < x \le 10

: 12;

10 < x \le 15

: 37;

15 < x \le 20

: 51;

20 < x \le 25

: 10. In the cumulative frequency table the entry for

x < 15

is written as

n

. Find the value of

n

Answer this when you sit the paper.

Question 603

[2 marks]Statistics & Probability

A cumulative frequency curve is drawn for the ages of 120 vehicles, using the points (5; 10), (10; 22), (15; 59), (20; 110) and (25; 120). Use the curve to find an estimate of the median age, in years.

Answer this when you sit the paper.

Question 604

[2 marks]Statistics & Probability

A cumulative frequency curve is drawn for the ages of 120 vehicles, using the points (5; 10), (10; 22), (15; 59), (20; 110) and (25; 120). Use the curve to find an estimate of the upper quartile, in years.

Answer this when you sit the paper.

Question 701

[1 marks]Trigonometry, Bearing & Distances

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

075^\circ

and the bearing of C from A is

140^\circ

. Calculate

B\hat{A}C

, in degrees.

Answer this when you sit the paper.

Question 702

[2 marks]Trigonometry, Bearing & Distances

In triangle ABC on level ground,

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

A\hat{B}C = 80^\circ

and B is 9 km from C. Calculate the distance from A to C, in kilometres.

Answer this when you sit the paper.

Question 703

[2 marks]Trigonometry, Bearing & Distances

In triangle ABC on level ground,

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

A\hat{B}C = 80^\circ

and B is 9 km from C. Calculate the shortest distance from B to AC, in kilometres.

Answer this when you sit the paper.

Question 704

[2 marks]Circle Geometry

P, Q, R and S are points on the circumference of a circle. The chords PQ and QS are equal and

S\hat{Q}P = 72^\circ

. Calculate

P\hat{S}Q

, in degrees.

Answer this when you sit the paper.

Question 705

[1 marks]Circle Geometry

P, Q, R and S are points on the circumference of a circle, with R and Q on the same arc cut off by the chord SP. Given that

S\hat{Q}P = 72^\circ

, calculate

S\hat{R}P

, in degrees.

Answer this when you sit the paper.

Question 706

[2 marks]Circle Geometry

P, Q, R and S are points on the circumference of a circle centre O, and POR is a diameter. Given that

S\hat{R}P = 72^\circ

, calculate

S\hat{P}R

, in degrees.

Answer this when you sit the paper.

Question 707

[2 marks]Circle Geometry

P and S are points on a circle and the tangents to the circle at P and at S meet at T outside the circle. R is a point on the major arc PS and

S\hat{R}P = 72^\circ

. Calculate

P\hat{T}S

, in degrees.

Answer this when you sit the paper.

Question 801

[2 marks]Variation

It is given that

y

varies inversely as the square root of

x

, and that

y = 2

when

x = 9

. Find the equation connecting

y

and

x

Answer this when you sit the paper.

Question 802

[2 marks]Variation

It is given that

y = \frac{6}{\sqrt{x}}

. Find

x

when

y = \frac{1}{2}

Answer this when you sit the paper.

Question 803

[3 marks]Quadratic Equations

Solve the equation

3x^2 - 8x - 13 = 0

, giving your answers correct to one decimal place.

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Question 804

[3 marks]Logarithms

Show that

\log(3x + 1) + \log(x - 3) = 1

reduces to a quadratic equation, and write that equation in the form

ax^2 + bx + c = 0

Answer this when you sit the paper.

Question 901

[1 marks]Vector Geometry

In triangle ABC,

\vec{AB} = a

and

\vec{AC} = b

. Express

\vec{BC}

in terms of

a

and/or

b

Answer this when you sit the paper.

Question 902

[1 marks]Vector Geometry

In triangle ABC,

\vec{AB} = a

and

\vec{AC} = b

. N lies on BC such that

BN = \frac{1}{3}BC

. Express

\vec{BN}

in terms of

a

and/or

b

Answer this when you sit the paper.

Question 903

[2 marks]Vector Geometry

In triangle ABC,

\vec{AB} = a

and

\vec{AC} = b

. N lies on BC such that

BN = \frac{1}{3}BC

. Express

\vec{AN}

in terms of

a

and/or

b

Answer this when you sit the paper.

Question 904

[1 marks]Vector Geometry

In triangle ABC,

\vec{AB} = a

and

\vec{AC} = b

. M is the midpoint of AC. Express

\vec{BM}

in terms of

a

and/or

b

Answer this when you sit the paper.

Question 905

[2 marks]Vector Geometry

In triangle ABC,

\vec{AB} = a

\vec{AC} = b

and M is the midpoint of AC, so that

\vec{BM} = -a + \frac{1}{2}b

. X lies on BM with

\vec{BX} = h\vec{BM}

. Express

\vec{AX}

in terms of

a

b

and

h

Answer this when you sit the paper.

Question 906

[1 marks]Vector Geometry

In triangle ABC,

\vec{AB} = a

and

\vec{AC} = b

, and N lies on BC with

\vec{AN} = \frac{2}{3}a + \frac{1}{3}b

. Given that

\vec{AX} = k\vec{AN}

, express

\vec{AX}

in terms of

a

b

and

k

Answer this when you sit the paper.

Question 907

[3 marks]Vector Geometry

In triangle ABC the vectors

a

and

b

are not parallel, and the point X satisfies both

\vec{AX} = (1 - h)a + \frac{h}{2}b

and

\vec{AX} = \frac{2k}{3}a + \frac{k}{3}b

. Find the value of

h

and the value of

k

Answer this when you sit the paper.

Question 1001

[2 marks]Functional Graphs

A table of values for

y = 2x + 3 - x^2

gives

y = -5

x = -2

y = p

x = -1

y = 3

x = 0

y = q

x = 1

y = 3

x = 2

y = 0

x = 3

and

y = -5

x = 4

. Find the value of

p

and the value of

q

Answer this when you sit the paper.

Question 1002

[2 marks]Functional Graphs

The graph of

y = 2x + 3 - x^2

and the line

y = -x

are drawn on the same axes for

-3 \le x \le 5

. Use the graphs to find an estimate of the solution to the equation

-x^2 + 2x + 3 = -x

, giving each value correct to one decimal place.

Answer this when you sit the paper.

Question 1003

[3 marks]Functional Graphs

The curve

y = 2x + 3 - x^2

and the line

y = -x

are drawn on the same axes. Find an estimate of the area bounded by the curve, the lines

x = 0

x = 1

and

y = -x

, in square units.

Answer this when you sit the paper.

Question 1101

[3 marks]Measures & Mensuration

A solid aluminium alloy casting for a pulley consists of 3 discs each

1\frac{1}{2}

cm thick, of diameters 4 cm, 6 cm and 8 cm, stacked on a common axis, with a central hole 2 cm in diameter drilled right through. Calculate the volume of aluminium used to make the casting, in cm

^3

Answer this when you sit the paper.

Question 1102

[2 marks]Measures & Mensuration

An aluminium alloy casting has a volume of 122,5 cm

^3

. Calculate its mass, in grammes, if the density of the alloy is 2,8 g/cm

^3

Answer this when you sit the paper.

Question 1103

[2 marks]Consumer Arithmetic

An aluminium alloy casting has a mass of 343 grammes. Calculate the total price of the casting if the alloy costs $7,50 per gramme.

Answer this when you sit the paper.

Question 1104

[3 marks]Measures & Mensuration

A triangular plot has two of its boundaries measuring 400 m and 440 m with an included angle of

46^\circ

. Calculate the area of the plot, giving the answer in hectares.

Answer this when you sit the paper.

Question 1201

[2 marks]Geometrical Transformation

Triangle P has vertices at (1; 2), (1; 4) and (2; 4). Triangle P is mapped onto triangle Q by an enlargement of factor -2, centre the origin. Write down the vertices of triangle Q.

Answer this when you sit the paper.

Question 1202

[2 marks]Geometrical Transformation

Triangle P has vertices at (1; 2), (1; 4) and (2; 4). Triangle P is mapped onto triangle R by a translation through

\begin{pmatrix} -3 \\ -5 \end{pmatrix}

. Write down the vertices of triangle R.

Answer this when you sit the paper.

Question 1203

[3 marks]Matrices

Triangle P has vertices at (1; 2), (1; 4) and (2; 4). Triangle N is the image of triangle P under the transformation represented by the matrix

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

. Write down the vertices of triangle N.

Answer this when you sit the paper.

Question 1204

[3 marks]Geometrical Transformation

Triangle P has vertices at (1; 2), (1; 4) and (2; 4). Triangle S has vertices at (2; 2), (2; 4) and (4; 4). Which of these describes fully the single transformation which maps triangle P onto triangle S?

AA stretch parallel to the $x$ axis with factor 2, the $y$ axis invariant
BAn enlargement of factor 2, centre the origin
CA stretch parallel to the $y$ axis with factor 2, the $x$ axis invariant
DA shear parallel to the $x$ axis with factor 2, the $y$ axis invariant

Mathematics Paper 2 November 2018

Sit this paper online

The questions

Question 101

Question 102

Question 103

Question 104

Question 201

Question 202

Question 203

Question 204

Question 301

Question 302

Question 303

Question 304

Question 401

Question 501

Question 502

Question 503

Question 504

Question 505

Question 506

Question 507

Question 508

Question 509

Question 601

Question 602

Question 603

Question 604

Question 701

Question 702

Question 703

Question 704

Question 705

Question 706

Question 707

Question 801

Question 802

Question 803

Question 804

Question 901

Question 902

Question 903

Question 904

Question 905

Question 906

Question 907

Question 1001

Question 1002

Question 1003

Question 1101

Question 1102

Question 1103

Question 1104

Question 1201

Question 1202

Question 1203

Question 1204

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