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ZIMSEC O Level · 4004/2 · N2019

Mathematics Paper 2 November 2019 (topical set)

Questions
49
Total marks
136
Time allowed
150 min
Syllabus code
4004/2

These questions are attributed to this sitting but were printed in a topical collection, so this is not the whole paper as it was sat.

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Questions
49
Pass mark
30
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 5

[11 marks]Constructions & Loci
Use ruler and compasses only for all constructions and show clearly all construction lines and arcs. All constructions should be done in a single diagram. ABCD is a trapezium in which AB = 6,5 cm, AD = 5,2 cm, angle ABC = 120 degrees and AD is perpendicular to AB. DC is parallel to AB. (a) (i) Construct the trapezium ABCD. [6] (ii) Construct the bisector of angle ABC. [2] (b) Describe the locus of points that the bisector of angle ABC represents. [2] (c) Measure and write down the length of BC. [1]

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Question 7

[12 marks]Consumer Arithmetic
(a) During a sale, all prices were reduced by 15%. Calculate the original price of a jacket that was bought for $55. [3] (b) An extract from MS Neto's bank statement for the month of May is shown. 01.05.17 Balance Brought Forward, balance 10.00;29.05.17Salary10.00; 29.05.17 Salary 402.00, balance $412.00; 30.05.17 Bank charges of 1% on Current Account Balance, amount X, balance Y; 31.05.17 Withdrawal, amount Z, balance $292.88. Calculate the value of (i) X, [1] (ii) Y, [1] (iii) Z. [1] (c) Omega decides to invest her pension of $600. OPTION A: She can invest it in a bank that offers 4% per year Simple Interest. OPTION B: She can invest it in a money market fund that offers 4% per year Compound Interest. Calculate (i) Omega's interest under Option A at the end of 3 years, [2] (ii) Omega's interest under Option B at the end of 3 years, [3] (iii) the difference between the amounts of interest from the two options. [1]

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Question 101

[1 marks]Fractions, Decimals & Percentages
Simplify 4 - (1 3/4 + 1 2/3).

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Question 102

[2 marks]Approximations & Estimations
It is given that y = 5.3 and z = 4.2, both given to 1 decimal place. Find the minimum possible value of yz. Give the answer correct to 2 decimal places.

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Question 103

[5 marks]Ratios, Rates & Proportions
A hotel has Executive rooms and General rooms in the ratio 3 : 5 respectively. A General room costs $19.00 per day. On a certain day, all the 2 928 rooms were occupied by both Executive and General customers and the total takings from the rooms amounted to $66 612.00. (i) Find the number of General rooms in the hotel. [2] (ii) Calculate the cost per day of an Executive room. [3]

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Question 201

[5 marks]Matrices
Matrix A = (x + 2, 14; 3, 3). The determinant of matrix A is less than 7. (i) Find the largest integer value of x. (ii) Find A^-1, the inverse of matrix A, using the value of x in (a)(i).

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Question 202

[5 marks]Vector Geometry
In the diagram, PQ = 3x and QW = y. N is a point on PR such that PN = 2NR. QW is produced to R such that QW : WR = 1 : 5. Express the following in terms of x and/or y (i) QR, [1] (ii) PR, [1] (iii) PN, [1] (iv) QN. [2]

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Question 401

[4 marks]Measures & Mensuration
A sweet shop sells cylindrical sweets each of diameter 3,8 cm and length 4,9 cm. In this question take pi to be 22/7. (i) Calculate the volume of one sweet. (ii) If the mass of 1 cm^3 of the sweet is 0,63 g, calculate the mass of a sweet, giving the answer to the nearest gramme.

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Question 402

[7 marks]Measures & Mensuration
The diagram shows an arrow for a signpost cut from a rectangular sheet of metal measuring 30 cm by 20 cm. The tail of the arrow is a rectangle 15 cm long whose top and bottom edges are each 7 cm from the edges of the sheet, and the head is a triangle whose base is the full 20 cm height and whose apex is 15 cm to the right. Calculate the (i) area of the arrow, (ii) perimeter of the arrow.

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Question 601

[2 marks]Laws of Indices
Solve the equation 3^k = (81^2 x 3^5)/3^11.

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Question 602

[4 marks]Factorisation, H.C.F & L.C.M
Factorise completely (i) 6y^2 - 10y + 4, (ii) ax + b + a + bx.

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Question 603

[3 marks]Algebraic Fractions
Express 6/(2x - x^2) - 3/x as a single fraction in its simplest form.

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Question 604

[3 marks]Variation
It is given that p is proportional to t^-3 and that p = 4 when t = 2. (i) Find a formula connecting p and t. [2] (ii) Find the value of t when p = 1/2. [1]

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Question 802

[5 marks]Quadratic Equations
(ii) Solve the equation 3x^2 - 4x - 16 = 0, giving the answers correct to 3 significant figures.

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Question 901

[1 marks]Statistics & Probability
The pie chart represents the time, t hours, spent by 240 people on charity work. The chart has four sectors: 0 < t <= 2 with an angle of 120 degrees, 6 < t <= 8 and 2 < t <= 4 each marked as a right angle, and 4 < t <= 6 with an angle of x. Find the value of x.

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Question 903

[3 marks]Statistics & Probability
The pie chart represents the time, t hours, spent by 240 people on charity work. The frequencies are: 0 < t <= 2: 80, 2 < t <= 4: 60, 4 < t <= 6: 40, 6 < t <= 8: 60. Calculate an estimate of the mean time spent on charity work.

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Question 904

[2 marks]Statistics & Probability
The pie chart represents the time, t hours, spent by 240 people on charity work. The frequencies are: 0 < t <= 2: 80, 2 < t <= 4: 60, 4 < t <= 6: 40, 6 < t <= 8: 60. Two people are chosen at random from the whole group, find the probability that they both spent more than 4 hours doing charity work.

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Question 905

[3 marks]Statistics & Probability
The time, t hours, spent by 240 people on charity work is grouped as 0 < t <= 2: 80 people, 2 < t <= 4: 60 people, 4 < t <= 6: 40 people, 6 < t <= 8: 60 people. A frequency polygon is drawn by plotting each frequency at the mid-point of its class. State the coordinates of the point plotted for the class 6 < t <= 8.

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Question 1001

[1 marks]Functional Graphs
The following is a table of values for the function f(x) = x^3 - 4x^2 + 4, with x = -1, -1/2, 0, 1/2, 1, 1 1/2, 2, 2 1/2, 3, 3 1/2, 4 giving f(x) = -1, 2,9, 4, 3,1, 1, -1,6, -4, -5,4, p, -2,1, 4. Find the value of p.

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Question 1002

[4 marks]Functional Graphs
State the coordinates of the point where the graph of f(x) = x^3 - 4x^2 + 4 crosses the y axis.

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Question 1101

[1 marks]Inequalities & Linear Programming
A school's agriculture department intends to plant beans and peas in its 5-hectare field. Let x be the area in hectares required for beans and y the area in hectares under peas. Write down an inequality in x and y which satisfies this condition.

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Question 1102

[2 marks]Inequalities & Linear Programming
Beans require 2 bags of fertilizers per hectare while peas require 4 bags of fertilizers per hectare. The department has 16 bags of fertilizers for this project. Write down another inequality in x and y and show that it reduces to x + 2y <= 8.

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Question 1103

[2 marks]Inequalities & Linear Programming
The department wishes to plant at least one hectare of each crop. Write down two inequalities, one in x and the other in y, that satisfy these conditions.

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Question 1104

[4 marks]Inequalities & Linear Programming
The lines x = 1 and x + 2y = 8 are drawn on the same axes. Calculate the coordinates of the point where they cross.

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Question 1202

[3 marks]Geometrical Transformation
Triangle B has vertices at (2; 3), (2; 0) and (4; 0). Triangle C is the image of triangle B under an enlargement with centre (2; -1) and enlargement factor of -1 1/2. Draw and label triangle C.

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Question 1203

[1 marks]Geometrical Transformation
Point (-2; 2) is translated onto (6; -2). Find the translation vector.

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Question 1204

[3 marks]Geometrical Transformation
Triangle A has vertices at (-5; 2), (-2; 2) and (-2; 4). Triangle D is the image of triangle A under a transformation represented by the matrix (1 0; -2 1). Find the coordinates of the vertices of triangle D.

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Question 1205

[3 marks]Geometrical Transformation
Triangle A has vertices at (-5; 2), (-2; 2) and (-2; 4) and triangle B has vertices at (2; 3), (2; 0) and (4; 0). Describe fully the single transformation that maps triangle A onto triangle B.

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Question 30101

[1 marks]Circle Geometry
In the diagram, P, Q, R and S are points on the circumference of a circle centre O. POQ is a diameter of the circle. Arcs PS and SR are equal. angle QPS = 57. Name the angle which is equal to angle SQR.

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Question 30102

[1 marks]Circle Geometry
In the diagram, P, Q, R and S are points on the circumference of a circle centre O. POQ is a diameter of the circle. Arcs PS and SR are equal. angle QPS = 57. Find angle PQS.

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Question 30103

[1 marks]Circle Geometry
In the diagram, P, Q, R and S are points on the circumference of a circle centre O. POQ is a diameter of the circle. Arcs PS and SR are equal. angle QPS = 57. Find angle QRS.

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Question 30104

[2 marks]Circle Geometry
In the diagram, P, Q, R and S are points on the circumference of a circle centre O. POQ is a diameter of the circle. Arcs PS and SR are equal. angle QPS = 57. Find angle QSR.

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Question 30201

[2 marks]Trigonometry, Bearing & Distances
In the diagram, triangle PQS is right-angled at Q. SRQ is a straight line. PQ = 3,7 cm, PR = 5,2 cm and angle PSR = 22,3 degrees. Calculate the length of PS.

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Question 30202

[2 marks]Trigonometry, Bearing & Distances
In the diagram, triangle PQS is right-angled at Q. SRQ is a straight line. PQ = 3,7 cm, PR = 5,2 cm and angle PSR = 22,3 degrees. Calculate angle SPR.

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Question 30203

[2 marks]Trigonometry, Bearing & Distances
In the diagram, triangle PQS is right-angled at Q. SRQ is a straight line. PQ = 3,7 cm, PR = 5,2 cm and angle PSR = 22,3 degrees. Calculate angle QPR.

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Question 80101

[2 marks]Change of Subject of Formula
It is given that A = h(12 + b)/2. Find the value of A when b = 1,5 and h = 0,8.

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Question 80102

[3 marks]Change of Subject of Formula
It is given that A = h(12 + b)/2. Express h in terms of A and b.

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Question 80201

[3 marks]Trigonometry, Bearing & Distances
In the diagram, ABC is a triangle in which AB = 4 cm, BC = x cm, AC = 2x cm and angle ABC = 120 degrees. Form an equation in x and show that it reduces to 3x^2 - 4x - 16 = 0.

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Question 90201

[1 marks]Statistics & Probability
The pie chart represents the time, t hours, spent by 240 people on charity work. The sector 0 < t <= 2 has an angle of 120 degrees, the sectors 6 < t <= 8 and 2 < t <= 4 are right angles and the sector 4 < t <= 6 has an angle of 60 degrees. The following table shows the information contained in the pie chart.
Time (t hours): 0 < t <= 2, 2 < t <= 4, 4 < t <= 6, 6 < t <= 8
Frequency: 80, p, q, r
Find the value of p.

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Question 90202

[1 marks]Statistics & Probability
The pie chart represents the time, t hours, spent by 240 people on charity work. The sector 0 < t <= 2 has an angle of 120 degrees, the sectors 6 < t <= 8 and 2 < t <= 4 are right angles and the sector 4 < t <= 6 has an angle of 60 degrees. The following table shows the information contained in the pie chart.
Time (t hours): 0 < t <= 2, 2 < t <= 4, 4 < t <= 6, 6 < t <= 8
Frequency: 80, p, q, r
Find the value of q.

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Question 90203

[1 marks]Statistics & Probability
The pie chart represents the time, t hours, spent by 240 people on charity work. The sector 0 < t <= 2 has an angle of 120 degrees, the sectors 6 < t <= 8 and 2 < t <= 4 are right angles and the sector 4 < t <= 6 has an angle of 60 degrees. The following table shows the information contained in the pie chart.
Time (t hours): 0 < t <= 2, 2 < t <= 4, 4 < t <= 6, 6 < t <= 8
Frequency: 80, p, q, r
Find the value of r.

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Question 100301

[1 marks]Functional Graphs
Use the graph of f(x) = x^3 - 4x^2 + 4 to find the coordinates of the minimum turning point of the graph.

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Question 100302

[3 marks]Functional Graphs
Use the graph of f(x) = x^3 - 4x^2 + 4 to find the roots of the equation x^3 - 4x^2 + 4 = 0.

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Question 100303

[2 marks]Functional Graphs
Use the graph of f(x) = x^3 - 4x^2 + 4 to find the area bounded by the graph, the x-axis and the lines x = 2 and x = 3.

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Question 100304

[1 marks]Functional Graphs
Use the graph of f(x) = x^3 - 4x^2 + 4 to find the range of values of x for which f(x) < -4.

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Question 110501

[2 marks]Inequalities & Linear Programming
The estimated profit is $30,00 per hectare for beans and $40,00 per hectare for peas. Find the area of each crop that should be planted for maximum profit to be realized.

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Question 110502

[1 marks]Inequalities & Linear Programming
Find the expected maximum profit that may be realized, given a profit of $30,00 per hectare for beans and $40,00 per hectare for peas.

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Question 120101

[1 marks]Geometrical Transformation
Triangle A has vertices at (-5; 2), (-2; 2) and (-2; 4). Calculate the area of triangle A.

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Question 120102

[1 marks]Geometrical Transformation
Triangle B has vertices at (2; 3), (2; 0) and (4; 0). State the coordinates of the midpoint of the side joining (2; 3) and (4; 0).

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