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ZIMSEC O Level · 4004/2 · J2019

Mathematics Paper 2 June 2019 (topical set)

Questions
44
Total marks
143
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
44
Pass mark
27
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 1

[2 marks]Prime Numbers, Sequences & Types of Numbers
(a) Write down the next term in the sequence below. 1/3 ; 2/4 ; 3/5 ; 4/6 ; ___ [1] (b) Express 10 as a sum of two different prime numbers. [1]

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Question 3

[11 marks]Consumer Arithmetic
(a) Tariro bought US$7.00 for 91.70 Pula from a bank. (i) Find the exchange rate in the form US$1 : m Pula. [1] (ii) The bank charged 1% commission for the transaction. Calculate the amount of money Tariro received. [2] (b) In a sale, the original price of a suit is reduced by 16% to $210. Calculate the original price of the suit before the sale. [3] (c) William invested $P, at a rate of 3% per annum simple interest. After 5 years he got $2010 simple interest. Calculate the value of $P. [2] (d) John invested $600 for 3 years at 4% per annum compound interest. Calculate the total amount he received after 3 years. [3]

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Question 5

[12 marks]Constructions & Loci
Triangle ABC is such that AB = BC = 7 cm and angle ABC = 120 degrees. Calculate the length of AC, giving your answer correct to 1 decimal place.

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Question 11

[12 marks]Measures & Mensuration
The diagram shows the cross-section of a garden shed. The cross-section ABCDE is made up of a rectangle measuring 2 m by 2,2 m and an isosceles triangle with a perpendicular height of 0,6 m and a base of 2 m. (a) Calculate the area of the cross-section. (b) If the shed is 3 m long, calculate the volume of the shed. (c) It is given that 23 m^2 of the surface area of the shed need to be painted and that one tin of paint covers an area of 4,5 m^2. Calculate the number of tins of paint that have to be bought to cover the 23 m^2. (d)(i) Calculate the length of the edge DE. (ii) The sloping roof is to be covered by roofing material which costs $6.40 per square metre. Calculate the cost of roofing material needed to cover the sloping roof.

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Question 12

[13 marks]Vector Geometry
(a) It is given that u = (3; 9) and v = (-3; 1). (i) Simplify u - 3v. [2] (ii) Evaluate |u - 3v|. [1] (b) In the diagram, OA = p, AB = q and M is the midpoint of AB. OB is produced to C such that OB = BC. Express the following in terms of p and/or q, (i) OC, [1] (ii) OM, [1] (iii) AC. [1] (iv) OM is produced to a point T (not in the diagram) such that OT = kOM, where k is a constant. Express OT in terms of k, p and q. [1] (v) If point T is on AC and is such that AT = hAC, form and simplify another expression for OT in terms of h, p and q. [1] (vi) Using your answers in (iv) and (v), find the value of h and the value of k. [3] (vii) Hence, find the ratio of MT : OT. [1]

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Question 16

[4 marks]Variation
The table shows some corresponding values of h and V such that V is proportional to h^3. h: 1, 2, 3, ..., q and the matching V: 3, 24, 81, ..., 648. Find the (a) equation connecting V and h, [2] (b) value of q. [2]

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Question 102

[2 marks]Fractions, Decimals & Percentages
Express 1 hectare as a percentage of 0,25 km^2.

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Question 103

[5 marks]Ratios, Rates & Proportions
(i) Increase $105 by 12%. [2] (ii) Tendai and Chipo share $105.00 in the ratio 4 : 3 in that order. Find Tendai's share and Chipo's share. [3]

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Question 201

[2 marks]Trigonometry, Bearing & Distances
sin theta = cos 40 degrees. Find the 2 possible values of theta if 0 < theta < 180 degrees.

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Question 401

[3 marks]Algebraic Fractions
Express 3 - (x + 2)/(x - 1) as a single fraction in its simplest form.

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Question 403

[3 marks]Change of Subject of Formula
Given that sqrt(ax + b) = d, express x in terms of a, b and d.

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Question 602

[10 marks]Probability
In a test the probability that a learner gets the first question correct is 3/5. If a learner gets it correct the probability of getting the second one correct becomes 4/5. If the learner fails the first question, the probability of getting the second one correct becomes 1/5. (i) Complete the probability tree diagram. [3] (ii) Hence or otherwise find the probability that the learner who answers two questions, gets both questions correct. [2] (iii) Hence or otherwise find the probability that the learner, who answers two questions, gets none of the two questions correct. [2] (iv) Hence or otherwise find the probability that the learner, who answers two questions, gets only one of the questions correct. [3]

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Question 901

[2 marks]Trigonometry, Bearing & Distances
In the diagram, ABCD is a quadrilateral in which BD is a diagonal. AB = 26 cm, BD = 24 cm, angle ABD = angle CBD = 40 degrees and angle CDB = 30 degrees. Calculate the area of triangle ABD.

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Question 902

[4 marks]Trigonometry, Bearing & Distances
In the diagram, ABCD is a quadrilateral in which BD is a diagonal. AB = 26 cm, BD = 24 cm, angle ABD = angle CBD = 40 degrees and angle CDB = 30 degrees. Calculate the length of AD.

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Question 903

[4 marks]Trigonometry, Bearing & Distances
In the diagram, ABCD is a quadrilateral in which BD is a diagonal. AB = 26 cm, BD = 24 cm, angle ABD = angle CBD = 40 degrees and angle CDB = 30 degrees. Calculate the length of BC.

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Question 904

[2 marks]Trigonometry, Bearing & Distances
In the diagram, ABCD is a quadrilateral in which BD is a diagonal. AB = 26 cm, BD = 24 cm, angle ABD = angle CBD = 40 degrees and angle CDB = 30 degrees. Calculate the shortest distance from C to BD.

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Question 1002

[3 marks]Statistics & Probability
The table shows information about the heights of a group of 42 learners.
Height (h) cm: 150 < h <= 160, 160 < h <= 165, 165 < h <= 180, 180 < h <= 190
Frequency: 5, 9, 18, 10
Calculate an estimate of the mean height of the learners.

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Question 1003

[3 marks]Statistics & Probability
The table shows information about the heights of a group of 42 learners.
Height (h) cm: 150 < h <= 160, 160 < h <= 165, 165 < h <= 180, 180 < h <= 190
Frequency: 5, 9, 18, 10
Two learners are chosen at random from the group. Find the probability that both have heights that are more than 160 cm but less than or equal to 180 cm.

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Question 1004

[3 marks]Statistics & Probability
The table shows information about the heights of a group of 42 learners.
Height (h) cm: 150 < h <= 160, 160 < h <= 165, 165 < h <= 180, 180 < h <= 190
Frequency: 5, 9, 18, 10
A histogram is drawn for this data. Calculate the frequency density of the class 165 < h <= 180.

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Question 20201

[2 marks]Trigonometry, Bearing & Distances
In the diagram, ABC is a triangle in which AP is perpendicular to BC. AB = 9,4 cm, angle ABC = 37 degrees and angle PAC = 42 degrees. Calculate the length of AP.

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Question 20202

[2 marks]Trigonometry, Bearing & Distances
In the diagram, ABC is a triangle in which AP is perpendicular to BC. AB = 9,4 cm, angle ABC = 37 degrees and angle PAC = 42 degrees. Calculate the length of AC.

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Question 20301

[1 marks]Circle Geometry
In the diagram, A, B and C are points on the circumference of a circle centre O. angle AOC = 3y and angle ABC = 4y + 4. Write down an expression, in terms of y, for reflex angle AOC.

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Question 20302

[3 marks]Circle Geometry
In the diagram, A, B and C are points on the circumference of a circle centre O. angle AOC = 3y and angle ABC = 4y + 4. Find the value of y.

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Question 40201

[3 marks]Functional Notation
It is given that the functions f(x) = x^2 + 3x - 8, g(x) = 3x + 1 and h(x) = 2^x. Find the values of x for which f(x) = g(x).

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Question 40202

[3 marks]Functional Notation
It is given that the functions f(x) = x^2 + 3x - 8, g(x) = 3x + 1 and h(x) = 2^x. Find the value of x given that h(x) = 0,25.

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Question 60101

[1 marks]Sets
The universal set (xi) has subsets P and Q such that n(xi) = 59, n(P) = 15, n(Q) = 35 and n((P union Q)') = 9. Write down n(P intersect Q).

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Question 60102

[1 marks]Sets
The universal set (xi) has subsets P and Q such that n(xi) = 59, n(P) = 15, n(Q) = 35 and n((P union Q)') = 9. Write down n(P union Q).

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Question 70101

[3 marks]Inequalities
Solve the following inequality giving the answer in the form a <= x < b where a and b are constants to be found: 5x - 13 <= x - 6 < 9 + 4x.

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Question 70102

[1 marks]Inequalities
State the largest integer value of x that satisfies 5x - 13 <= x - 6 < 9 + 4x.

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Question 70103

[1 marks]Inequalities
Write down the smallest integer value of x that satisfies the inequality 5x - 13 <= x - 6 < 9 + 4x.

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Question 70201

[1 marks]Trigonometry, Bearing & Distances
Triangle ABC is such that angle ABC = 90 degrees, AB = (x + 2) cm and AC = (2x + 3) cm. Write down an expression in terms of x for sin ACB.

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Question 70202

[1 marks]Trigonometry, Bearing & Distances
Triangle ABC is such that angle ABC = 90 degrees, AB = (x + 2) cm and AC = (2x + 3) cm. Given that sin ACB = 9/16, form an equation in x.

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Question 70203

[2 marks]Trigonometry, Bearing & Distances
Triangle ABC is such that angle ABC = 90 degrees, AB = (x + 2) cm and AC = (2x + 3) cm. Given that sin ACB = 9/16, solve the equation in b(ii).

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Question 70204

[1 marks]Trigonometry, Bearing & Distances
Triangle ABC is such that angle ABC = 90 degrees, AB = (x + 2) cm and AC = (2x + 3) cm with x = 2,5. Hence find the length of side AC.

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Question 70205

[2 marks]Trigonometry, Bearing & Distances
Triangle ABC is such that angle ABC = 90 degrees, AB = (x + 2) cm and AC = (2x + 3) cm with x = 2,5. Hence, calculate the length of side BC.

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Question 80101

[1 marks]Functional Graphs
The following is an incomplete table of values for the function y = x^2 - 4x, with x = -2, -1, 0, 1, 2, 3, 4, 5, 6 giving y = 12, 5, 0, p, -4, -3, 0, q, 12. Find the value of p.

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Question 80102

[1 marks]Functional Graphs
The following is an incomplete table of values for the function y = x^2 - 4x, with x = -2, -1, 0, 1, 2, 3, 4, 5, 6 giving y = 12, 5, 0, p, -4, -3, 0, q, 12. Find the value of q.

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Question 80201

[4 marks]Functional Graphs
State the coordinates of the minimum point of the graph of y = x^2 - 4x.

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Question 80202

[2 marks]Functional Graphs
State the coordinates of the point where the line y = 3 - x crosses the y axis.

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Question 80301

[2 marks]Functional Graphs
Use the graph to solve the equation x^2 - 4x = 3 - x.

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Question 80302

[2 marks]Functional Graphs
Use the graph to find the equation of the line of symmetry of the curve y = x^2 - 4x.

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Question 100101

[1 marks]Statistics & Probability
The table shows information about the heights of a group of 42 learners.
Height (h) cm: 150 < h <= 160, 160 < h <= 165, 165 < h <= 180, 180 < h <= 190
Frequency: 5, 9, 18, 10
Frequency Density: 0,5 1,8 1,2 1
State the modal class.

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Question 100102

[1 marks]Statistics & Probability
The table shows information about the heights of a group of 42 learners.
Height (h) cm: 150 < h <= 160, 160 < h <= 165, 165 < h <= 180, 180 < h <= 190
Frequency: 5, 9, 18, 10
State the class that contains the median height.

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Question 100103

[1 marks]Statistics & Probability
The table shows information about the heights of a group of 42 learners.
Height (h) cm: 150 < h <= 160, 160 < h <= 165, 165 < h <= 180, 180 < h <= 190
Frequency: 5, 9, 18, 10
State the class that contains the lower quartile.

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