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ZIMSEC O Level · 4008/2, 4028/2 · J2001

Mathematics Paper 2 June 2001

Questions
55
Total marks
124
Time allowed
150 min
Syllabus code
4008/2, 4028/2

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Questions
55
Pass mark
33
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 101

[2 marks]Ratio, indices, simple interest, proportion
If 18 200 m² of land is shared in the ratio 2:3:8, calculate the area of the smallest share.

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Question 102

[1 marks]Ratio, indices, simple interest, proportion
Given that x≥2912x \geq 29\frac{1}{2}, state the least possible value of xx if xx is a perfect cube.

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Question 103

[1 marks]Ratio, indices, simple interest, proportion
Given that x≥2912x \geq 29\frac{1}{2}, state the least possible value of xx if xx is a rational number.

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Question 104

[3 marks]Ratio, indices, simple interest, proportion
Calculate the time that $2000 would take to amount to $3645 if invested at 2312%23\frac12\% per annum simple interest.

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Question 105

[2 marks]Ratio, indices, simple interest, proportion
A girl bought 72 g of chocolates for $10,80. Calculate the amount she would have paid for 0,5 kg (500 g) of the same type of chocolates.

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Question 201

[2 marks]Algebra, functions, parallel lines
Given that a=3a=3, b=−2b=-2 and c=10c=10, calculate ac2ac^2.

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Question 202

[1 marks]Algebra, functions, parallel lines
Given that a=3a=3 and b=−2b=-2, calculate aba^b.

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Question 203

[3 marks]Algebra, functions, parallel lines
Express 4p−31−5p\dfrac{4}{p} - \dfrac{3}{1-5p} as a single fraction in its simplest form.

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Question 204

[2 marks]Algebra, functions, parallel lines
Given that f(x)=2x−3f(x)=2x-3, calculate the value of kk when f(k)=−21f(k)=-21.

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Question 205

[2 marks]Algebra, functions, parallel lines
In the diagram, MNP is parallel to CD. Angle PND = 59°, and angle CDQ = r° lies on the straight line at D on the same side as N and P. Calculate the value of rr.

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Question 206

[1 marks]Algebra, functions, parallel lines
In the diagram, MNP is parallel to CD, with MC as a transversal between them. Angle NMC = u° and angle MCD = v°. Express vv in terms of uu.

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Question 301

[2 marks]Wages, mensuration (prism)
A man earns $30 per hour for the first 35 hours and $40 for each additional hour he works in a week. In a week he earned $1290 in total, of which $1050 came from the first 35 hours. Calculate the number of additional hours he worked at the $40 rate.

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Question 302

[2 marks]Wages, mensuration (prism)
A man earns $30 per hour for the first 35 hours and $40 for each additional hour he works in a week. If he earned $1290 in a week, calculate the total number of hours he worked.

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Question 303

[2 marks]Wages, mensuration (prism)
A uniform triangular prism is 27 cm long. Its cross-section is a right-angled triangle PQR with PQ = RQ = 6 cm and angle PQR = 90°. Calculate the length PR.

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Question 304

[2 marks]Wages, mensuration (prism)
The prism's cross-section is a right-angled triangle with legs PQ = RQ = 6 cm and angle PQR = 90°, and the prism is 27 cm long. Calculate the volume of the prism.

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Question 305

[3 marks]Wages, mensuration (prism)
A prism has cross-section PQR with PQ=RQ=6 cm, angle PQR=90°, hypotenuse PR=8,485 cm, and the prism is 27 cm long. Calculate the total surface area of the prism.

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Question 401

[2 marks]Constructions & Loci
ABCD is a parallelogram with AB=9 cm, AD=7 cm and angle BAD=60°. P is the point on DC such that P is equidistant from AB and AD. Calculate the length of BP.

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Question 402

[2 marks]Constructions & Loci
In a construction, ABCD is a parallelogram with AB=9 cm, AD=7 cm and angle BAD=60°. Describe the locus that the perpendicular bisector of BC represents.
  1. APoints equidistant from A and D
  2. BPoints equidistant from B and C
  3. CPoints equidistant from lines AB and AD
  4. DPoints equidistant from A and C

Question 501

[1 marks]Sets, Venn diagrams, probability
Each of 37 pupils ordering an ice cream chose at least one of vanilla, chocolate, peppermint. The number choosing peppermint only is (21-x) and the number choosing both chocolate and peppermint only is x. Write down the total number of pupils who chose a peppermint.

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Question 502

[2 marks]Sets, Venn diagrams, probability
For the 37 pupils: vanilla-only = y, vanilla-and-chocolate-only = 2, chocolate-only = 2x, chocolate-and-peppermint-only = x, peppermint-only = (21-x). Express y in terms of x in its simplest form.

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Question 503

[1 marks]Sets, Venn diagrams, probability
For the 37 pupils, chocolate-only = 2x and peppermint-only = (21-x). The number who chose peppermint only was three more than the number who chose chocolate only. Write down an equation in x.

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Question 504

[1 marks]Sets, Venn diagrams, probability
Solve the equation 21−x−3=2x21-x-3=2x for xx.

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Question 505

[2 marks]Sets, Venn diagrams, probability
Given that chocolate-only = 2x pupils and x=6, determine the number of pupils who chose chocolate only.

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Question 506

[2 marks]Sets, Venn diagrams, probability
Of the 37 pupils, the number who chose both vanilla and chocolate only is 2. Find the probability that a pupil who had a vanilla also had a chocolate.

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Question 507

[3 marks]Sets, Venn diagrams, probability
Of the 37 pupils, 21 chose peppermint. Two pupils are chosen at random from all 37, without replacement. Calculate the probability that both chosen pupils had peppermint, giving your answer as a fraction in its lowest terms.

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Question 601

[1 marks]Graphs (linear), rates and charges
A firm's delivery charge for parcels over 5 kg is a fixed minimum charge plus an amount proportional to the mass in excess of 5 kg. Parcels of 15 kg and 23 kg cost $28,50 and $40,50 respectively. Calculate the fixed minimum charge.

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Question 602

[1 marks]Graphs (linear), rates and charges
A firm's delivery charge for parcels over 5 kg is a fixed minimum charge plus an amount proportional to the mass in excess of 5 kg. Parcels of 15 kg and 23 kg cost $28,50 and $40,50 respectively. Calculate the rate per kilogram charged for the mass by which a parcel exceeds 5 kg.

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Question 603

[2 marks]Graphs (linear), rates and charges
A firm charges a fixed minimum charge of $13,50 for parcels up to 5 kg, plus $1,50 for each kg by which a parcel exceeds 5 kg. Calculate the mass of a parcel that would cost $38,50 to dispatch.

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Question 604

[2 marks]Graphs (linear), rates and charges
A firm charges a fixed minimum charge of $13,50 for parcels up to 5 kg, plus $1,50 for each kg by which a parcel exceeds 5 kg. Calculate the charge for a parcel of mass 75 kg.

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Question 701

[1 marks]Mensuration (sector, rectangle)
PQRS is a sector of a circle, centre P, with PQ=PS=8 cm and arc QRS=14 cm. Calculate the perimeter of the sector PQRS.

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Question 702

[3 marks]Mensuration (sector, rectangle)
A sector PQRS has centre P, radius PQ=PS=8 cm, and arc QRS=14 cm. Calculate the angle SPQ (take π=3,142).

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Question 703

[2 marks]Mensuration (sector, rectangle)
A sector PQRS has centre P, radius 8 cm, and angle SPQ=100,2°. Calculate the area of the sector PQRS (take π=3,142).

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Question 704

[3 marks]Mensuration (sector, rectangle)
In the diagram, ABCD is a rectangle and PQRS is a sector of a circle, centre P, where P is the midpoint of AB. PQ=PS=8 cm and angle SPQ=100,2°, with R touching side DC of the rectangle. Calculate the area of the rectangle ABCD.

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Question 705

[2 marks]Mensuration (sector, rectangle)
In the diagram, the sector PQRS (area 56,01 cm²) sits inside rectangle ABCD (area 98,23 cm²); the shaded region is the part of the rectangle outside the sector. Calculate the area of the shaded region.

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Question 801

[3 marks]Trigonometry, Bearing & Distances
In triangle ABC, BC=9 cm, angle ABC=68° and angle BAC=42°. Calculate the length of AC.

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Question 802

[3 marks]Trigonometry, Bearing & Distances
In triangle ABC, angle BAC=42°. H is on AC with AH=4,1 cm and G is on AB with AG=4,7 cm. Calculate the length of HG.

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Question 803

[3 marks]Trigonometry, Bearing & Distances
In triangle AHG, AH=4,1 cm, AG=4,7 cm and angle HAG=42°. Calculate the area of triangle AHG.

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Question 804

[2 marks]Trigonometry, Bearing & Distances
In triangle ABC, BC=9 cm, angle BAC=42° and angle ABC=68°. Calculate the perpendicular distance from B to AC.

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Question 901

[1 marks]Circle geometry, similar triangles, quadratic equations
A circle has diameter CB. TC is the tangent to the circle at C, and angle TCE=35°, where E is a point on the circle. Calculate angle CBE.

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Question 902

[1 marks]Circle geometry, similar triangles, quadratic equations
A circle has diameter CB, with E on the circle and angle CBE=35°. Calculate angle BCE.

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Question 903

[1 marks]Circle geometry, similar triangles, quadratic equations
In the diagram, CBDE is a cyclic quadrilateral with angle BCE=55°, and ED produced meets CB produced at A. Calculate angle BDA.

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Question 904

[1 marks]Circle geometry, similar triangles, quadratic equations
In the diagram, A is the point where ED and CB, both produced, meet. Triangle ADB shares the angle at A with another triangle, and angle ACE = angle ADB. Name, in the correct order, the triangle that is similar to triangle ADB.

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Question 905

[1 marks]Circle geometry, similar triangles, quadratic equations
In the diagram, triangle ACE is similar to triangle ADB, with AB=(x+3) cm, AE=8 cm, BD=1 cm and CE=x cm. From the similar triangles, AB/AE = BD/CE. Write down this equation before simplifying it.

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Question 906

[3 marks]Circle geometry, similar triangles, quadratic equations
Solve the equation x2+3x−8=0x^2+3x-8=0 for xx, a length in cm, giving the answer correct to 2 significant figures.

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Question 1101

[2 marks]Transformations, matrices
Triangle ABC has vertices A(1,1), B(3,1) and C(2,3). Triangle A1B1C1 is the image of triangle ABC under a reflection in the y-axis. State the coordinates of A1, B1 and C1.

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Question 1102

[3 marks]Transformations, matrices
Triangle ABC has vertices A(1,1), B(3,1) and C(2,3). Triangle A2B2C2 is the image of triangle ABC under an enlargement, scale factor -2, centre (2,0). State the coordinates of A2, B2 and C2.

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Question 1103

[3 marks]Transformations, matrices
Triangle ABC has vertices A(1,1), B(3,1), C(2,3). Its image under a certain single transformation has vertices A3(-1,-3), B3(-1,-1), C3(-3,-2). Describe fully this single transformation.
  1. ARotation 90° anticlockwise, centre (2,-2)
  2. BReflection in the horizontal line y = -2
  3. CRotation 90° clockwise, centre (2,-2)
  4. DRotation of 180°, about the centre (2,-2)

Question 1104

[2 marks]Transformations, matrices
Under a certain matrix transformation, triangle ABC with vertices A(1,1), B(3,1), C(2,3) maps to a triangle with vertices (1,-2), (3,-2), (2,-6). Find the matrix that produces this transformation.

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Question 1201

[1 marks]Vectors, matrices
In the diagram, OA⃗=a\vec{OA}=\mathbf{a} and OB⃗=b\vec{OB}=\mathbf{b}. Express AB⃗\vec{AB} in terms of a\mathbf{a} and b\mathbf{b}.

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Question 1202

[1 marks]Vectors, matrices
In the diagram, OA⃗=a\vec{OA}=\mathbf{a}, OB⃗=b\vec{OB}=\mathbf{b}, and P is the point such that AP=2PB. Express AP⃗\vec{AP} in terms of a\mathbf{a} and b\mathbf{b}.

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Question 1203

[2 marks]Vectors, matrices
In the diagram, OA⃗=a\vec{OA}=\mathbf{a}, OB⃗=b\vec{OB}=\mathbf{b}, and P is the point such that AP=2PB. Express OP⃗\vec{OP} in terms of a\mathbf{a} and b\mathbf{b}.

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Question 1204

[1 marks]Vectors, matrices
In the diagram, OA⃗=a\vec{OA}=\mathbf{a}, OB⃗=b\vec{OB}=\mathbf{b}, and Q is the point such that AB=BQ. Express AQ⃗\vec{AQ} in terms of a\mathbf{a} and b\mathbf{b}.

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Question 1205

[3 marks]Vectors, matrices
M is a 2x2 matrix such that M−2(1−101)=3(11−10)M - 2\begin{pmatrix}1&-1\\0&1\end{pmatrix} = 3\begin{pmatrix}1&1\\-1&0\end{pmatrix}. Find M.

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Question 1206

[2 marks]Vectors, matrices
N is a 2x2 matrix such that N(10)=(−31)N\binom{1}{0}=\binom{-3}{1} and N(01)=(x2)N\binom{0}{1}=\binom{x}{2}. Find the matrix N in terms of x.

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Question 1207

[2 marks]Vectors, matrices
For the matrix N=(−3x12)N=\begin{pmatrix}-3&x\\1&2\end{pmatrix}, find the value of x for which N has no inverse.

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