ZIMSEC O Level Mathematics Paper 2 June 2015

Question 101

[2 marks]Fractions, Decimals and Standard Form

Express

\frac{5}{16}

as a percentage.

Answer this when you sit the paper.

Question 102

[2 marks]Fractions, Decimals and Standard Form

Simplify

27^{\frac{2}{3}} - \left(\frac{1}{8}\right)^{\frac{1}{3}}

Answer this when you sit the paper.

Question 103

[3 marks]Fractions, Decimals and Standard Form

Simplify

3\frac{4}{5} - \left(1\frac{2}{3} + \frac{7}{15}\right)

, giving the answer in its lowest terms.

Answer this when you sit the paper.

Question 104

[2 marks]Fractions, Decimals and Standard Form

Given that

p = 0,045

and

r = 2,513 \times 10^{-4}

, evaluate

pr

giving the answer in standard form correct to three significant figures.

Answer this when you sit the paper.

Question 201

[2 marks]Sets and Linear Equations

It is given that

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

and

B = \{x : x \text{ is a factor of } 20\}

. List all the elements of B.

A $\{1, 2, 4, 5, 10\}$ , the factors of 20 that lie inside the universal set
B $\{1, 2, 4, 5, 10, 20\}$ , every factor of 20 including 20 itself
C $\{2, 4, 6, 8, 10\}$ , the multiples of 2 that lie inside the universal set
D $\{2, 4, 10\}$ , the even factors of 20 that lie inside the universal set

Question 202

[2 marks]Sets and Linear Equations

It is given that

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

A = \{x : x \text{ is a prime number}\}

and

B = \{x : x \text{ is a factor of } 20\}

. List all the elements of

(A \cup B)'

A $\{6, 8, 9\}$ , the members of $\xi$ that are in neither A nor B
B $\{2, 5\}$ , the members of $\xi$ that belong to both A and B at once
C $\{1, 4, 6, 8, 9, 10\}$ , the members of $\xi$ that are not prime numbers
D $\{3, 6, 7, 8, 9\}$ , the members of $\xi$ that are not factors of 20

Question 203

[2 marks]Sets and Linear Equations

It is given that

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

A = \{x : x \text{ is a prime number}\}

and

B = \{x : x \text{ is a factor of } 20\}

. List all the elements of

A \cap B

Answer this when you sit the paper.

Question 204

[3 marks]Sets and Linear Equations

Solve the equation

\frac{3x + 1}{3} - \frac{x - 4}{5} = \frac{1}{2}

Answer this when you sit the paper.

Question 301

[2 marks]Ratio and Consumer Arithmetic

It is given that 300 cattle are to be shared in the ratio

12 : 10 : 8

. Express the ratio in its simplest form.

Answer this when you sit the paper.

Question 302

[3 marks]Ratio and Consumer Arithmetic

It is given that 300 cattle are to be shared in the ratio

12 : 10 : 8

. Calculate the difference between the largest and smallest shares.

Answer this when you sit the paper.

Question 303

[2 marks]Ratio and Consumer Arithmetic

A shop advertises 25% off all red shirts. The red shirts were originally marked at

\$25,00

each. Calculate the amount that Joko paid for one red shirt.

Answer this when you sit the paper.

Question 304

[3 marks]Ratio and Consumer Arithmetic

Red shirts marked at

\$25,00

each are on sale at 25% off. Tindo bought 10 such shirts at the sale price and sold them at

\$23,00

each. Calculate the total profit Tindo made.

Answer this when you sit the paper.

Question 401

[2 marks]Circle Geometry and Number Bases

In the diagram A, B, C and D lie on a circle centre O, EAF is a tangent to the circle at A, and D, O and B lie on a straight line. Given that

B\hat{A}F = 40^\circ

and

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

, calculate

A\hat{D}B

A $50^\circ$ , from the angles of triangle ADB after taking $D\hat{A}B$ as $40^\circ$
B $40^\circ$ , equal to the tangent-chord angle $B\hat{A}F$ in the alternate segment
C $20^\circ$ , taking the angle at the circumference as half of $B\hat{A}F$
D $80^\circ$ , taking the angle at the circumference as twice $B\hat{A}F$

Question 402

[2 marks]Circle Geometry and Number Bases

In the diagram A, B, C and D lie on a circle centre O, EAF is a tangent to the circle at A, and D, O and B lie on a straight line that meets the tangent at F. Given that

B\hat{A}F = 40^\circ

, calculate

A\hat{B}F

in degrees.

Answer this when you sit the paper.

Question 403

[2 marks]Circle Geometry and Number Bases

In the diagram A, B, C and D lie on a circle centre O, EAF is a tangent to the circle at A, and D, O and B lie on a straight line. Given that

B\hat{A}F = 40^\circ

and

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

, calculate

C\hat{D}B

in degrees.

Answer this when you sit the paper.

Question 404

[2 marks]Circle Geometry and Number Bases

Convert

65_{10}

to a number in base 3.

Answer this when you sit the paper.

Question 405

[3 marks]Circle Geometry and Number Bases

Simplify

3102_4 + 11101_2

, giving the answer in base 4.

Answer this when you sit the paper.

Question 501

[2 marks]Functional Notation and Change of Subject of Formula

Given that

f(x) = 3x^2 - 7x + 1

, evaluate

f(-1)

Answer this when you sit the paper.

Question 502

[3 marks]Functional Notation and Change of Subject of Formula

Given that

f(x) = 3x^2 - 7x + 1

, find the values of

x

when

f(x) = -1

Answer this when you sit the paper.

Question 503

[2 marks]Functional Notation and Change of Subject of Formula

Given that

P = \frac{n}{2}\{2a + (n - 1)d\}

, express

a

in terms of

d

n

and

P

A $a = \frac{P}{n} - \frac{(n - 1)d}{2}$ , halving both terms after dividing by $n$
B $a = \frac{P - (n - 1)d}{2n}$ , subtracting the $(n - 1)d$ term before dividing by $n$
C $a = \frac{2P}{n} - (n - 1)d$ , dividing the whole bracket by 2 at the end
D $a = 2Pn - \frac{(n - 1)d}{2}$ , multiplying by $n$ instead of dividing

Question 504

[3 marks]Functional Notation and Change of Subject of Formula

Given that

P = \frac{n}{2}\{2a + (n - 1)d\}

, find the value of

a

when

n = 10

d = 4

and

P = 20

Answer this when you sit the paper.

Question 601

[2 marks]Constructions and Loci

A construction is to be drawn using a scale of 1 cm to represent 2 metres. Two points, M and N, are 10 metres apart on level ground. How far apart should M and N be drawn?

A10 cm, by drawing one centimetre for each metre on the ground
B5 cm, since each centimetre stands for 2 metres of ground
C2 cm, by reading the scale as 2 cm to every 10 metres
D20 cm, by multiplying the 10 metres by the 2 in the scale

Question 602

[3 marks]Constructions and Loci

From a point M on level ground the angle of elevation of a bird on top of a vertical pole is

30^\circ

. From a point N, 10 metres closer to the pole and on the same side, the angle of elevation of the same bird is

45^\circ

. Find the height of the pole in metres, correct to three significant figures.

Answer this when you sit the paper.

Question 603

[3 marks]Constructions and Loci

From a point M on level ground the angle of elevation of a bird on top of a vertical pole is

30^\circ

. From a point N, 10 metres closer to the pole and on the same side, the angle of elevation of the same bird is

45^\circ

. Find the distance of M from the bottom of the pole in metres, correct to three significant figures.

Answer this when you sit the paper.

Question 701

[3 marks]Variation and Mensuration

M

is directly proportional to

(d - 1)^2

. Given that

M = 12

when

d = 4

, calculate

M

when

d = 7

Answer this when you sit the paper.

Question 702

[2 marks]Variation and Mensuration

ABCDE is the cross-section of a tobacco shed, with ABDE a rectangle and BCD a triangular roof.

AB = BC = CD = DE = 5

m and

AE = 8

m. Calculate the perpendicular height of C above the side BD, in metres.

Answer this when you sit the paper.

Question 703

[2 marks]Variation and Mensuration

ABCDE is the cross-section of a tobacco shed, with ABDE a rectangle and BCD a triangular roof of perpendicular height 3 m.

AB = DE = 5

m and

AE = BD = 8

m. Calculate the area of the cross-section ABCDE, in square metres.

Answer this when you sit the paper.

Question 704

[2 marks]Variation and Mensuration

A tobacco shed 20 m long has a uniform cross-section of area 52 m

^2

. Calculate the volume of the shed, in cubic metres.

Answer this when you sit the paper.

Question 705

[3 marks]Variation and Mensuration

A tobacco shed is 20 m long. Its cross-section ABDE below the roof line BD is a rectangle 8 m wide and 5 m high, with the roof above BD. Calculate the number of bales of tobacco that can be stored in the shed up to BD, given that each bale has a volume of 4 m

^3

Answer this when you sit the paper.

Question 801

[2 marks]Inequalities and Linear Programming

A girl is given

\$6,00

to buy fireworks. She buys

x

rockets at 60 c each and

y

crackers at 30 c each. Which inequality states that she does not spend more than she has?

A $60x + 30y \ge 600$ , requiring her to spend at least the whole amount
B $60x + 30y \le 6$ , comparing the cost in cents with 6 dollars
C $30x + 60y \le 600$ , pricing the rockets at 30 c and the crackers at 60 c
D $60x + 30y \le 600$ , comparing the cost in cents with 600 c

Question 802

[2 marks]Inequalities and Linear Programming

A girl buys

x

rockets and

y

crackers. She wants at least 4 rockets, and the number of crackers should be more than or equal to twice the number of rockets. Write down two inequalities that satisfy these conditions.

A $x > 4$ and $y > 2x$ , since more than is what both of the conditions ask for here
B $x \ge 4$ and $y \ge 2x$ , taking at least and more than or equal as inclusive
C $x \ge 4$ and $2y \ge x$ , taking twice as applying to the crackers
D $x \le 4$ and $y \ge 2x$ , reading at least 4 as a limit of 4 rockets

Question 803

[3 marks]Inequalities and Linear Programming

A girl has

\$6,00

and buys

x

rockets at 60 c each and

y

crackers at 30 c each, subject to

2x + y \le 20

x \ge 4

and

y \ge 2x

. Find the least amount of money, in dollars, that she can spend.

Answer this when you sit the paper.

Question 804

[3 marks]Inequalities and Linear Programming

A girl is given

\$6,00

and buys 4 rockets at 60 c each and 8 crackers at 30 c each, which is the cheapest combination allowed. Find the change she would get.

Answer this when you sit the paper.

Question 805

[2 marks]Inequalities and Linear Programming

A girl spends the whole of her

\$6,00

x

rockets at 60 c each and

y

crackers at 30 c each, so that

2x + y = 20

. Find the value of

y

when she buys 5 rockets.

Answer this when you sit the paper.

Question 901

[2 marks]Geometrical Transformation

Quadrilateral ABCD has vertices at A(1; 0), B(2; 0), C(2; 2) and D(1; 2). State the special name given to quadrilateral ABCD.

AA trapezium, because only one pair of opposite sides of the shape is parallel
BA square, because all four sides are of equal length and all angles are right angles
CA rectangle, because the angles are right angles and one side is 1 unit and the next 2
DA rhombus, because opposite sides are parallel and the diagonals cross at right angles

Question 902

[3 marks]Geometrical Transformation

Quadrilateral ABCD has vertices A(1; 0), B(2; 0), C(2; 2), D(1; 2). Quadrilateral

ABC_1D_1

has vertices A(1; 0), B(2; 0),

C_1

(6; 2),

D_1

(5; 2). Describe fully the single transformation that maps ABCD onto

ABC_1D_1

AA translation of 4 units in the positive $x$ direction, applied to all four vertices
BA shear with the $x$ -axis invariant and shear factor 2, moving C and D 4 units right
CA stretch with the $x$ -axis invariant and stretch factor 3, taking C to $(6; 2)$
DA rotation about the origin through $90^\circ$ , which fixes the points A and B

Question 903

[3 marks]Geometrical Transformation

Quadrilateral ABCD has vertices A(1; 0), B(2; 0), C(2; 2) and D(1; 2). It is mapped onto

A_2B_2C_2D_2

by a reflection in the line

y = x + 2

. Write down the coordinates of

C_2

, the image of C.

Answer this when you sit the paper.

Question 904

[3 marks]Geometrical Transformation

Quadrilateral ABCD has vertices A(1; 0), B(2; 0), C(2; 2) and D(1; 2).

A_3B_3C_3D_3

is its image under an enlargement of scale factor

-1

with

(-1; -1)

as centre. Write down the coordinates of

C_3

, the image of C.

Answer this when you sit the paper.

Question 1001

[2 marks]Vector Geometry

The point M has coordinates

(7; -3)

and

\overrightarrow{RM} = \begin{pmatrix} 6 \\ 4 \end{pmatrix}

. Calculate the coordinates of R.

Answer this when you sit the paper.

Question 1002

[2 marks]Vector Geometry

The point M has coordinates

(7; -3)

and

\overrightarrow{RM} = \begin{pmatrix} 6 \\ 4 \end{pmatrix}

. Find

\overrightarrow{MR}

A $\begin{pmatrix} -6 \\ 4 \end{pmatrix}$ , reversing only the horizontal component of $\overrightarrow{RM}$
B $\begin{pmatrix} 1 \\ -7 \end{pmatrix}$ , the position vector of the point R found earlier
C $\begin{pmatrix} -6 \\ -4 \end{pmatrix}$ , the reverse of $\overrightarrow{RM}$ , so both components change sign
D $\begin{pmatrix} 6 \\ 4 \end{pmatrix}$ , the same as $\overrightarrow{RM}$ because M and R are the same pair of points

Question 1003

[2 marks]Vector Geometry

ORST is a quadrilateral in which

\overrightarrow{OR} = \boldsymbol{u}

\overrightarrow{OT} = 2\boldsymbol{v}

and

\overrightarrow{TS} = 2\boldsymbol{u} + \boldsymbol{v}

. Express

\overrightarrow{OS}

in terms of

\boldsymbol{u}

and

\boldsymbol{v}

Answer this when you sit the paper.

Question 1004

[3 marks]Vector Geometry

ORST is a quadrilateral in which

\overrightarrow{OR} = \boldsymbol{u}

and

\overrightarrow{OT} = 2\boldsymbol{v}

. Express

\overrightarrow{RT}

in terms of

\boldsymbol{u}

and

\boldsymbol{v}

Answer this when you sit the paper.

Question 1005

[3 marks]Vector Geometry

In quadrilateral ORST the diagonals OS and RT meet at P, where

\overrightarrow{RP} = (2k - 1)\boldsymbol{u} + 3k\boldsymbol{v}

and also

\overrightarrow{RP} = h\overrightarrow{RT}

with

\overrightarrow{RT} = -\boldsymbol{u} + 2\boldsymbol{v}

. Calculate the value of

k

Answer this when you sit the paper.

Question 1101

[3 marks]Simultaneous Equations, Bearings and Trigonometry

Solve the simultaneous equations

3x - 2y = 8

and

5x - 4y = 12

Answer this when you sit the paper.

Question 1102

[3 marks]Simultaneous Equations, Bearings and Trigonometry

P is 4 km north of Q, and R is 6 km from P on a bearing of

073^\circ

. Calculate QR in km, correct to three significant figures.

Answer this when you sit the paper.

Question 1103

[3 marks]Simultaneous Equations, Bearings and Trigonometry

P is 4 km north of Q, and R is 6 km from P on a bearing of

073^\circ

, with

QR = 8,13

km. Calculate

P\hat{Q}R

in degrees, correct to one decimal place.

Answer this when you sit the paper.

Question 1104

[3 marks]Simultaneous Equations, Bearings and Trigonometry

P is 4 km north of Q, and R is 6 km from P on a bearing of

073^\circ

. Given that

P\hat{Q}R = 44,9^\circ

, find the bearing of R from Q to the nearest degree.

Answer this when you sit the paper.

Question 1201

[3 marks]Statistics and Probability

The cumulative frequency of Mathematics marks for 500 students is: 10 students scored

x \le 10

, 50 scored

x \le 20

, 150 scored

x \le 30

, 245 scored

x \le 40

, 325 scored

x \le 50

, 400 scored

x \le 60

, 465 scored

x \le 70

, 490 scored

x \le 80

, 495 scored

x \le 90

and 500 scored

x \le 100

. Find the median mark, correct to the nearest whole mark.

Answer this when you sit the paper.

Question 1202

[3 marks]Statistics and Probability

For 500 students the cumulative frequency of Mathematics marks is: 10 at

x \le 10

, 50 at

x \le 20

, 150 at

x \le 30

, 245 at

x \le 40

, 325 at

x \le 50

, 400 at

x \le 60

, 465 at

x \le 70

, 490 at

x \le 80

, 495 at

x \le 90

and 500 at

x \le 100

. Find the inter-quartile range, correct to the nearest whole mark.

Answer this when you sit the paper.

Question 1203

[3 marks]Statistics and Probability

Of 500 students in a Mathematics examination, 325 scored marks less than or equal to 50. Two students are chosen at random, one after the other and without replacement. Find the probability that both students got marks less than or equal to 50, correct to three significant figures.

Answer this when you sit the paper.

Question 1204

[2 marks]Statistics and Probability

In a Mathematics examination taken by 500 students, 325 of them scored marks less than or equal to 50. How many students scored more than 50 marks?

A75, the difference between the 325 students and the 250 halfway mark
B250, taking half of the 500 students who sat the examination
C325, the same count as the students who scored 50 marks or less
D175, the 500 students less the 325 who scored 50 marks or less

Mathematics Paper 2 June 2015

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 402

Question 403

Question 404

Question 405

Question 501

Question 502

Question 503

Question 504

Question 601

Question 602

Question 603

Question 701

Question 702

Question 703

Question 704

Question 705

Question 801

Question 802

Question 803

Question 804

Question 805

Question 901

Question 902

Question 903

Question 904

Question 1001

Question 1002

Question 1003

Question 1004

Question 1005

Question 1101

Question 1102

Question 1103

Question 1104

Question 1201

Question 1202

Question 1203

Question 1204

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