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ZIMSEC O Level · 4030/2 · N2017

Mathematics Paper 2 November 2017 (topical set)

Questions
41
Total marks
124
Time allowed
150 min
Syllabus code
4030/2

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
41
Pass mark
25
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 6

[9 marks]Constructions & Loci
Use pencil, ruler and compasses only for all constructions and show clearly all construction lines and arcs. All constructions should be on a single diagram. (a) (i) Construct, in a single diagram, triangle AXB such that AX = 5 cm, BX = 7,5 cm and angle AXB = 60 degrees. [3] (ii) Construct the locus of points which are 1. equidistant from XA and XB, [2] 2. 3,5 cm from X. [1] (iii) Show by shading, the region R, in the triangle, such that R is closer to XA than XB and XR is less than or equal to 3,5 cm. [2] (b) Measure and write down the length of AB. [1]

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Question 12

[12 marks]Vector Geometry
In the diagram, OQR, OMP, PTQ and RTM are straight lines such that OM = (1/3)OP and PT = (3/4)PQ. It is given that OP = 12a and OQ = 4b. (a) Express as simply as possible, in terms of a and/or b (i) PQ, [1] (ii) PT, [1] (iii) OT, [1] (iv) MT. [2] (b) It is given that MR = h MT. Express OR in terms of a and/or b and a constant h. [2] (c)(i) It is given that OR = k OQ. Express OR in terms of a and/or b and a constant k. [1] (ii) Use the expressions for OR in (b) and (c)(i) to find the values of h and k. [3] (d) Write down the numerical value of MT:TR. [1]

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Question 101

[2 marks]Fractions, Decimals & Percentages
Evaluate 1,36 - 7/8, giving the answer as a decimal.

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Question 102

[2 marks]Measures & Mensuration
The diagram shows a rectangle ABCD with DC = 10 cm and BC = 6 cm. Right-angled triangle PQR has been cut off, such that AP = 2 cm, PQ = 3 cm and BR = 4 cm. Calculate the perimeter of the shape APQRBCD.

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Question 103

[3 marks]Factorisation, H.C.F & L.C.M
(i) Factorise completely x^2 - 6x. (ii) Factorise completely (m - 1)^2 - 9.

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Question 104

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

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Question 201

[5 marks]Polygons, Symmetry & Circles
(i) Three interior angles of a hexagon are each x° and the remaining three interior angles are each y°. Form an equation in x and y that satisfies this condition. [2] (ii) Given also that 5x = 7y, use this equation and the equation in (i) to find the values of x and y. [3]

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Question 203

[3 marks]Change of Subject of Formula
Given that ax = sqrt(b^2 - x^2), express x in terms of a and b.

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Question 301

[5 marks]Matrices
It is given that matrix P = (3 -2 1; 0 -1 4) and matrix Q = (-2 3; -4 5). (i) State the order of matrix P. (ii) 1. Calculate Q^2. 2. Calculate Q^-1, the inverse of matrix Q.

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Question 302

[3 marks]Variation
M varies directly as the square of r and inversely as the square root of h. (i) Express M in terms of r, h and a constant k. [1] (ii) Find the value of k when r = h = 4 and M = 12. [2]

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Question 402

[5 marks]Co-ordinate Geometry
4y - 3x = -8 is an equation of a straight line. (i) Find the gradient of the line. (ii) Find the coordinates of the point where the straight line crosses the y-axis. (iii) Find the equation of a line parallel to 4y - 3x = -8 passing through the point (0; 3).

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Question 403

[3 marks]Similarity & Congruency
A jug 20 cm high has a capacity of 125 ml when full. Calculate the height of a similar jug which has a capacity of 1 litre when full.

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Question 501

[4 marks]Consumer Arithmetic
A trader made a profit of 16% on the cost price by selling a handset for $29,00. (i) Calculate the cost price of the handset. [2] (ii) Calculate the selling price of the handset if a loss of 30% was realized. [2]

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Question 503

[4 marks]Prime Numbers, Sequences & Types of Numbers
Study the number pattern. First row: 0, 0, 2, 2. Second row: 1, 3, 2, 5. Third row: 2, 6, 2, 8. Fourth row: 3, 9, 2, 11. Fifth row: ---, ---, ---, ---. n th row: ---, ---, ---, x. (i) Complete the fifth row. [2] (ii) Express x in terms of n. [2]

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Question 702

[2 marks]Ratios, Rates & Proportions
Three people can complete a certain task in 6 days. Calculate the number of people, working at the same rate, who can complete the same task in 9 days.

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Question 801

[2 marks]Inequalities & Linear Programming
Mr. Moyo wants to plant mango and guava trees in his plot. He wants at least 4 mango trees and at least 2 guava trees. Let x be the number of mango trees and y be the number of guava trees. Form two inequalities that satisfy the given conditions.

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Question 802

[1 marks]Inequalities & Linear Programming
There is enough space in his plot for not more than 9 trees. Write down an inequality in x and y that satisfies the given condition, where x is the number of mango trees and y the number of guava trees.

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Question 803

[2 marks]Inequalities & Linear Programming
Mango trees cost $14,00 each and guava trees cost $24,00 each. Mr. Moyo has $168,00 for the purchase of trees. Form an inequality in x and y that satisfies this condition and show that it reduces to 7x + 12y <= 84.

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Question 804

[4 marks]Inequalities & Linear Programming
State the coordinates of the point where the line 7x + 12y = 84 crosses the y axis.

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Question 805

[1 marks]Inequalities & Linear Programming
The lines x + y = 9 and y = 2 are drawn on the same axes. Calculate the coordinates of the point where they cross.

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Question 806

[2 marks]Inequalities & Linear Programming
Use the graph to find the number of trees that will use the greatest amount of money, where mango trees cost $14,00 each and guava trees cost $24,00 each.

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Question 901

[1 marks]Statistics & Probability
A survey was carried out to find the ages of 60 patients at a hospital. The table shows the information collected.
age x (years): 0 < x <= 10, 10 < x <= 20, 20 < x <= 30, 30 < x <= 35, 35 < x <= 40, 40 < x <= 45, 45 < x <= 50, 50 < x <= 60
Frequency: 0, 4, m, 11, 15, 10, 5, 7
Find the value of m.

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Question 902

[1 marks]Statistics & Probability
A survey was carried out to find the ages of 60 patients at a hospital. The table shows cumulative frequency of the same 60 patients.
age x (years): x <= 10, x <= 20, x <= 30, x <= 35, x <= 40, <= 45, x <= 50, x <= 60
cumulative frequency: 0, 4, n, 23, 38, 48, 53, 60
Find the value of n.

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Question 903

[2 marks]Statistics & Probability
A survey was carried out to find the ages of 60 patients at a hospital. The cumulative frequencies are:
age x (years): x <= 10, x <= 20, x <= 30, x <= 35, x <= 40, <= 45, x <= 50, x <= 60
cumulative frequency: 0, 4, 12, 23, 38, 48, 53, 60
Find the probability that 2 patients chosen at random will both be less than or equal to 45 years in age.

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Question 904

[4 marks]Statistics & Probability
A survey found the ages of 60 patients at a hospital. The cumulative frequencies are:
age x (years): x <= 10, x <= 20, x <= 30, x <= 35, x <= 40, x <= 45, x <= 50, x <= 60
cumulative frequency: 0, 4, 12, 23, 38, 48, 53, 60
Find the number of patients who were more than 45 years old.

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Question 1001

[6 marks]Measures & Mensuration
The diagram shows the cross-section OPQR of a cylindrical wooden block centre O that was cut with PORSTV removed, such that angle POR = 120 degrees. The radius, OP, is 10 cm and the block is 15 cm high. [Take pi to be 22/7.] (i) Calculate the area of the cross-section OPQR. (ii) Calculate the volume of the block. (iii) Calculate the curved surface area of the block.

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Question 1002

[4 marks]Consumer Arithmetic
A Zimbabwean motorist travels to Botswana on holiday. The motorist travels a total distance of 3 600 km in Botswana. The motorist's car consumes petrol at a rate of 9 km per litre of petrol. (i) Calculate the amount of petrol used in Botswana. [2] (ii) Petrol costs 6,5 pula per litre in Botswana. Calculate the total cost of petrol used in US dollars if the exchange rate was US$1 = 8 pula. [2]

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Question 1003

[2 marks]Functional Notation
Given that f(x) = 4 - x^2, calculate f(-1).

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Question 20201

[2 marks]Circle Geometry
The diagram shows points A, B and T on the circumference of a circle centre O. PT is a tangent to the circle at T. AB is parallel to TO and angle ATB = 40. Name two angles equal to angle ABT.

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Question 20202

[2 marks]Circle Geometry
The diagram shows points A, B and T on the circumference of a circle centre O. PT is a tangent to the circle at T. AB is parallel to TO and angle ATB = 40. Calculate angle BAT.

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Question 30301

[1 marks]Geometrical Transformation
ABC is a scalene triangle with angle ABC = 90 degrees. Write down the special name of a quadrilateral that is formed by triangle ABC and its image after a reflection in the line AC.

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Question 30302

[1 marks]Geometrical Transformation
ABC is a scalene triangle with angle ABC = 90 degrees. Write down the special name of a quadrilateral that is formed by triangle ABC and its image after a rotation through 180 degrees about the mid-point of AC.

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Question 40101

[1 marks]Sets
The Venn diagram shows the universal set xi and its subsets A, B and C. The number of elements in each region is 12 in A only, 7 - x in A intersect B only, 5 in B only, x in the region common to all three, 8 - x in A intersect C only, 6 in B intersect C only and 4 + x in C only. Find n(B).

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Question 40102

[1 marks]Sets
The Venn diagram shows subsets A, B and C with 12 in A only, 7 - x in A intersect B only, 5 in B only, x common to all three, 8 - x in A intersect C only, 6 in B intersect C only and 4 + x in C only. Find n(A' intersect B intersect C), where A' is the complement of set A.

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Question 40103

[2 marks]Sets
The Venn diagram shows subsets A, B and C with 12 in A only, 7 - x in A intersect B only, x common to all three and 8 - x in A intersect C only. Find the value of x given that n(A) = 23.

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Question 50201

[2 marks]Logarithms
Solve the equation log_x 81 = 2.

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Question 50202

[2 marks]Ordinary & Standard Form
Simplify (3 x 10^2) - (2 x 10^-1), giving the answer in standard form.

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Question 70101

[5 marks]Circle Geometry
In the diagram ABCD is a cyclic quadrilateral in which AB = 1 cm, BC = 4 cm, CD = 3 cm and angle ABC = 115. Calculate AC.

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Question 70102

[5 marks]Circle Geometry
In the diagram ABCD is a cyclic quadrilateral in which AB = 1 cm, BC = 4 cm, CD = 3 cm and angle ABC = 115. Calculate angle DAC.

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Question 90501

[2 marks]Statistics & Probability
A survey was carried out to find the ages of 60 patients at a hospital. The cumulative frequencies are:
age x (years): x <= 10, x <= 20, x <= 30, x <= 35, x <= 40, <= 45, x <= 50, x <= 60
cumulative frequency: 0, 4, 12, 23, 38, 48, 53, 60
Use the graph to estimate the median.

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Question 90502

[2 marks]Statistics & Probability
A survey was carried out to find the ages of 60 patients at a hospital. The cumulative frequencies are:
age x (years): x <= 10, x <= 20, x <= 30, x <= 35, x <= 40, <= 45, x <= 50, x <= 60
cumulative frequency: 0, 4, 12, 23, 38, 48, 53, 60
Use the graph to estimate the upper quartile.

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