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ZIMSEC O Level · 4008/2, 4028/2 · J1999

Mathematics Paper 2 June 1999

Questions
33
Total marks
136
Time allowed
150 min
Syllabus code
4008/2, 4028/2

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Questions
33
Pass mark
20
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 101

[1 marks]Number, percentages, interest
Evaluate 2 1/2 - 3/5 ÷ 2/3.

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Question 102

[1 marks]Number, percentages, interest
Tendai is paid $12,40 an hour for a basic week of 40 hours, and $18,60 an hour for overtime beyond 40 hours. Calculate his total pay for a week in which he works 48 hours.
  1. A$595,20
  2. B$644,80
  3. C$843,20
  4. D$892,80

Question 103

[1 marks]Number, percentages, interest
Calculate the simple interest earned on $1200 invested at a rate of 15% per annum for 6 months.

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Question 201

[1 marks]Algebra, factorising, indices
Factorise completely ax + x - 3a - 3.

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Question 202

[1 marks]Algebra, factorising, indices
Factorise 2x² - 7x + 3.
  1. A(x-1)(2x-3)
  2. B(2x+1)(x+3)
  3. C(2x-3)(x+1)
  4. D(2x-1)(x-3)

Question 203

[1 marks]Algebra, factorising, indices
Given that 2p = ∛(6q+5), find the value of p when q = 20.

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Question 301

[1 marks]Statistics & Probability
In a survey of pupils who went on a trip to Great Zimbabwe, Form 1 had 25 pupils, Form 2 had 16, Form 3 had 75 and Form 4 had 64. What was the modal form?
  1. AForm 2
  2. BForm 3
  3. CForm 4
  4. DForm 1

Question 302

[1 marks]Statistics & Probability
For a trip with 25, 16, 75 and 64 pupils from Forms 1-4 respectively, find the mean number of pupils per form.

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Question 303

[1 marks]Statistics & Probability
Of the pupils who went on a school trip, 16 were from Form 2 and 64 from Form 4, out of 1080 pupils at the whole school. Find, as a single fraction in its lowest terms, the probability that a pupil chosen at random from the whole school went on the trip and was in either Form 2 or Form 4.

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Question 401

[1 marks]Matrices, simultaneous equations, vectors, coordinate geometry
Find the value of r for which the matrix [[r,24],[-4,3]] is singular.

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Question 402

[1 marks]Matrices, simultaneous equations, vectors, coordinate geometry
Given that [[3,2],[1,-1]] multiplied by the column vector (x,y) equals (16,7), find the value of x.
  1. A-1
  2. B6
  3. C7
  4. D9

Question 403

[1 marks]Matrices, simultaneous equations, vectors, coordinate geometry
W and X are points with coordinates (-2,3) and (4,6) respectively; Y is (8,1). Find |XY|, the magnitude of vector XY.

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Question 501

[1 marks]Constructions & Loci
In the construction of quadrilateral ABCD with AB=9,0 cm, angle DAB=90°, angle ABC=60°, AD=7,5 cm and BC=6,3 cm, the marking scheme gives the measured value of angle BCD as approximately:
  1. A139°
  2. B151°
  3. C90°
  4. D120°

Question 601

[1 marks]Sets
In a survey of 200 people about beef, chicken and pork: Beef and Chicken = 60, and all three = 28. Find the number of people who liked Beef and Chicken only.

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Question 602

[1 marks]Sets
In a survey of 200 people: Beef only = 16, Beef-and-Chicken only = 32, Chicken-and-Pork only = 18, Beef-and-Pork only = 4. How many people liked exactly two types of meat?
  1. A18
  2. B32
  3. C54
  4. D60

Question 603

[1 marks]Sets
Of 200 people surveyed about beef, chicken and pork, 60 people liked none of the three. Give this as a fraction of the total surveyed, in its lowest terms.

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Question 701

[1 marks]Algebra, quadratic equations, area
Rectangle M has sides (x+4) cm and (7-x) cm; right triangle N has legs x cm and (3x+1) cm. Given the area of M is twice the area of N, this leads to the equation 2x²-x-14=0. Solve this equation, giving the positive root correct to 3 significant figures.

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Question 702

[1 marks]Algebra, quadratic equations, area
Rectangle M has sides (x+4) cm and (7-x) cm, where x=2,91 (3 s.f.). Write down the length of rectangle M, (x+4) cm, correct to the nearest millimetre.
  1. A4,1 cm
  2. B6,8 cm
  3. C6,9 cm
  4. D7,0 cm

Question 703

[1 marks]Algebra, quadratic equations, area
Rectangle M has sides (x+4) cm and (7-x) cm, where x=2,91 (3 s.f.). Write down the width of rectangle M, (7-x) cm, correct to the nearest millimetre.

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Question 801

[1 marks]Transformations, matrices
Triangle ABC has vertices A(-3,2), B(-1,2), C(-1,3). Triangle A1B1C1 has vertices A1(-2,-3), B1(-2,-1), C1(-3,-1). Describe fully the single transformation that maps triangle ABC onto triangle A1B1C1.
  1. AReflection in the line y=x
  2. BEnlargement, centre the origin, scale factor -1
  3. CTranslation by vector (1,-5)
  4. DRotation of 90° anticlockwise about the origin

Question 802

[1 marks]Transformations, matrices
Triangle ABC (A(-3,2), B(-1,2), C(-1,3)) is mapped onto triangle A2B2C2 by the matrix [[-2,0],[0,-2]]. Find the coordinates of A2.

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Question 803

[1 marks]Transformations, matrices
Triangle A3B3C3 has vertices A3(3,2), B3(5,2), C3(8,3), the image of triangle ABC (A(-3,2), B(-1,2), C(-1,3)). Describe fully the single transformation that maps ABC onto A3B3C3.
  1. AShear, x-axis invariant, shear factor 3
  2. BStretch, x-axis invariant, factor 3
  3. CShear, y-axis invariant, shear factor 3
  4. DEnlargement, centre the origin, factor 3

Question 901

[1 marks]Similar triangles, sine and cosine rule
AB is parallel to DE and AE is parallel to PQ, with ACE and BCPD straight lines and AC=PQ. Given AC = 1/4 AE and the area of triangle ABC is 2 square units, find the area of PQEC.

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Question 902

[1 marks]Similar triangles, sine and cosine rule
In quadrilateral JKLM, JM=5 m, KM=8 m and angle MJK=50°. Calculate angle JKM.

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Question 903

[1 marks]Similar triangles, sine and cosine rule
In quadrilateral JKLM, angle MKL=95° and KL=11 m, with KM=8 m. Calculate the length of ML.

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Question 1001

[1 marks]Rates of work, mensuration (cylinder, cube, sphere)
Working 8 hours a day, 45 men could do a job in 12 days. How many men, working at the same rate for 7 1/2 hours a day, should be employed to do the job in 9 days?

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Question 1002

[1 marks]Rates of work, mensuration (cylinder, cube, sphere)
A cylindrical hole of radius 3 cm was drilled completely through a metal cube of side 15 cm, perpendicular to a face. Taking π=3,142, calculate the volume of metal removed.
  1. A397,1 cm³
  2. B424,2 cm³
  3. C450,0 cm³
  4. D381,8 cm³

Question 1003

[1 marks]Rates of work, mensuration (cylinder, cube, sphere)
Metal of volume 424,2 cm³, removed by drilling a hole through a cube, was melted and made into 45 identical solid spheres (volume of sphere = 4/3 πr³). Calculate the radius of each sphere, correct to the nearest tenth of a millimetre.

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Question 1101

[1 marks]Graphs, kinematics (velocity-time)
The velocity of a ball, v m/s, after time t seconds is given by v=4+5t-t². Given v=4,8,10,10,8,4 at t=0,1,2,3,4,5, find the value of p, the velocity at t=6.

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Question 1102

[1 marks]Graphs, kinematics (velocity-time)
For a ball whose velocity is v=4+5t-t², what does the gradient of the velocity-time graph at t=4 represent?
  1. AThe ball's acceleration (deceleration) at t=4 s
  2. BThe distance travelled by the ball up to t=4 s
  3. CThe ball's initial velocity
  4. DThe average speed over the first 4 seconds

Question 1201

[1 marks]Linear programming, inequalities
Each Ordinary seat costs 40 cents and each Superior seat costs $1, with x rows of Ordinary seats (25 seats/row) and y rows of Superior seats (20 seats/row). Write down, in terms of x and y, an expression for the total income in dollars.

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Question 1202

[1 marks]Linear programming, inequalities
There were x rows of Ordinary seats and y rows of Superior seats for a school play, with income 10x+20y dollars, and the largest permitted audience occupying all seats at (x,y)=(8,10). Find the greatest possible income satisfying all the conditions.

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Question 1203

[1 marks]Linear programming, inequalities
There were x rows of Ordinary seats (25 seats each) and y rows of Superior seats (20 seats each), subject to 5x+4y≤80, x+y≤18 and x≥5. With all seats occupied, which point (x,y) represents the largest permitted audience?
  1. A(18,0)
  2. B(5,13)
  3. C(8,10)
  4. D(12,5)

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