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ZIMSEC O Level · 4004/1 · J2019

Mathematics Paper 1 June 2019 (topical set)

Questions
41
Total marks
100
Time allowed
150 min
Syllabus code
4004/1

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 1

[3 marks]Fractions, Decimals & Percentages
Express (a) 12/25 as a decimal fraction, (b) 2/5 as a percentage, (c) 0.0375 as a fraction in its lowest terms.

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Question 2

[3 marks]Prime Numbers, Sequences & Types of Numbers
Write down the next term in each of the following sequences. (a) 1 ; 4 ; 9 ; 16 ; 25 ; 36 ; ___ [1] (b) sqrt(2) ; sqrt(3) ; sqrt(5) ; sqrt(7) ; sqrt(11) ; ___ [1] (c) 16 ; 8 ; 4 ; 2 ; 1 ; ___ [1]

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Question 3

[3 marks]Ratios, Rates & Proportions
Three girls aged 12 years, 13 years and 15 years share $100.00 in the ratio of their ages. Calculate the amount of money that each girl receives.

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Question 4

[3 marks]Number Bases
(a) Convert (i) 434_5 to base ten, [1] (ii) 75_10 to base two. [1] (b) Evaluate 377_8 + 411_8, leaving the answer in base 8. [1]

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Question 6

[3 marks]Sets
P, Q and R are three sets that overlap one another, so a Venn diagram of them has seven regions inside the circles. How many of those seven regions make up the set (P' intersect R) union (R' intersect Q)?

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Question 7

[3 marks]Consumer Arithmetic
(a) Convert 647 cents to dollars. [1] (b) The exchange rate for converting United States dollars to South African rand is US$1 : R13.80. Calculate the equivalent of US$75.90 in Rands. [2]

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Question 8

[3 marks]Simultaneous Equations
Solve the simultaneous equations: 5x - 2y = 26, 3x + 4y = 0.

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Question 9

[3 marks]Measures & Mensuration
The sides of a parallelogram are of lengths 10 cm and 8 cm. One of the interior angles of the parallelogram is 150 degrees. Calculate the area of the parallelogram. Use as much of the information given below as is necessary. [tan 30 = 0,577; cos 30 = 0,866; sin 30 = 0,5]

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Question 10

[3 marks]Probability
A box contains 20 sweets which are identical in shape and size except for colour. Eight of the sweets are yellow and twelve are green. (a) Calculate the probability of picking a yellow sweet. [1] (b) Two sweets are picked at random from the box. Calculate the probability that the sweets are of the same colour. [2]

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Question 11

[3 marks]Polygons, Symmetry & Circles
In the diagram, all the circles are of equal radii. State the (a) total number of circles, [1] (b) number of lines of symmetry, [1] (c) order of rotational symmetry. [1]

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Question 12

[4 marks]Logarithms
It is given that log 6 = 0.7781 and log 5 = 0.6990. Calculate (a) log 30, (b) log 1 200 000.

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Question 13

[4 marks]Polygons, Symmetry & Circles
(a) Calculate the size of one exterior angle of an 18-sided regular polygon. [2] (b) Calculate the sum of the interior angles of a heptagon (7-sided polygon). [2]

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Question 14

[4 marks]Variation
The number of people, N, who favour a certain type of energy drink varies directly as the population size, S. In a population of 1 000 people, only 40 people were reported to favour that type of energy drink. (a) Form an equation connecting N and S. [2] (b) Find the population size, S from which 180 people favour that type of energy drink. [2]

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Question 17

[4 marks]Factorisation, H.C.F & L.C.M
(a) Factorise (i) p^2 - 4, (ii) 2p^2 + 7p + 6. (b) Hence or otherwise, find the Highest Common Factor (H.C.F) of p^2 - 4 and 2p^2 + 7p + 6.

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Question 18

[4 marks]Measures & Mensuration
A right circular cone has a base diameter of 24 cm and a slant height of 15 cm. Calculate the (a) vertical height of the cone, (b) volume of the cone in terms of pi. [volume of cone = (1/3) pi r^2 h]

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Question 22

[4 marks]Ordinary & Standard Form
(a) Express in standard form (i) 618 000, [1] (ii) 0.000 423. [1] (b) Evaluate (8.76 x 10^-2) + (7.89 x 10^-2), leaving the answer in standard form. [2]

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Question 23

[4 marks]Vector Geometry
The diagram shows two intersecting straight lines AOB and XOY. OA = p and OX = q. AO/OB = XO/OY = 1/3. (a) Express in terms of p and/or q (i) AX, [1] (ii) BY. [1] (b) State any two relationships between the lines AX and YB. [2]

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Question 501

[1 marks]Circle Geometry
In the diagram, ABCD is a cyclic quadrilateral in which AB = AD and BC = DC. AC is the diameter of the circle and angle ADB = 10. State the special name given to the cyclic quadrilateral ABCD.

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Question 502

[1 marks]Circle Geometry
In the diagram, ABCD is a cyclic quadrilateral in which AB = AD and BC = DC. AC is the diameter of the circle and angle ADB = 10. Find angle ACD.

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Question 503

[1 marks]Circle Geometry
In the diagram, ABCD is a cyclic quadrilateral in which AB = AD and BC = DC. AC is the diameter of the circle and angle ADB = 10. Find angle ADC.

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Question 1501

[1 marks]Trigonometry, Bearing & Distances
In a rectangle ABCD, AB = 12 cm and BC = 5 cm. Express as a common fraction, tan ACD.

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Question 1502

[2 marks]Trigonometry, Bearing & Distances
In a rectangle ABCD, AB = 12 cm and BC = 5 cm. Express as a common fraction, cos DAC.

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Question 1503

[1 marks]Trigonometry, Bearing & Distances
In a rectangle ABCD, AB = 12 cm and BC = 5 cm. Express as a common fraction, sin BDC.

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Question 1601

[1 marks]Statistics & Probability
The masses of 6 bags of mealie-meal on the shelf of a shop were as follows:
5 kg; 5 kg; 10 kg; 10 kg; 10 kg; 20 kg.
Find the modal mass.

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Question 1602

[1 marks]Statistics & Probability
The masses of 6 bags of mealie-meal on the shelf of a shop were as follows:
5 kg; 5 kg; 10 kg; 10 kg; 10 kg; 20 kg.
Find the median mass.

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Question 1603

[2 marks]Statistics & Probability
The masses of 6 bags of mealie-meal on the shelf of a shop were as follows:
5 kg; 5 kg; 10 kg; 10 kg; 10 kg; 20 kg.
Find the mean mass.

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Question 1901

[1 marks]Functional Notation
It is given that f(x) = 3x^2 - 2x - 8. Find f(-4).

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Question 1902

[3 marks]Functional Notation
It is given that f(x) = 3x^2 - 2x - 8. Find the values of x for which f(x) = 0.

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Question 2001

[2 marks]Laws of Indices
Solve the equation x^(2/3) = 4.

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Question 2002

[2 marks]Linear Equations
Solve the equation 2/(x - 2) = 3/(x + 2).

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Question 2101

[2 marks]Inequalities & Linear Programming
The unshaded region of a linear programming graph is bounded by three straight lines: the xx-axis, the line through the origin and the point (100;200)(100; 200), and a broken line through (0;300)(0; 300) and (300;0)(300; 0). The point (150;50)(150; 50) lies inside the region. Write down the inequality that the broken line contributes.

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Question 2102

[2 marks]Inequalities & Linear Programming
A region is defined by y≥0y\geq0, y≤2xy\leq2x and x+y<300x+y<300. Find the greatest value of x+yx+y, given that xx and yy are integers.

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Question 2401

[1 marks]Trigonometry, Bearing & Distances
Moyo village is 5 km away from Dube village on a bearing of 020 degrees. Ncube village is 6 km away from Dube village on a bearing of 060 degrees. Find the bearing of Dube village from Moyo village.

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Question 2402

[3 marks]Trigonometry, Bearing & Distances
Moyo village is 5 km away from Dube village on a bearing of 020 degrees. Ncube village is 6 km away from Dube village on a bearing of 060 degrees. Find the distance from Moyo village to Ncube village, leaving the answer in surd form. [cos 40 = 0,77; sin 40 = 0,64; tan 40 = 0,84]

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Question 2501

[2 marks]Similarity & Congruency
Two similar bottles are of heights 8 cm and 16 cm. The bases of the similar bottles are also similar. The surface area of the base of the smaller bottle is 1.44 cm^2. Find the surface area of the base of the bigger bottle.

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Question 2502

[2 marks]Similarity & Congruency
Two similar bottles are of heights 8 cm and 16 cm. Find the volume of the smaller bottle if the volume of the bigger bottle is 16 cm^3.

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Question 2601

[3 marks]Geometrical Transformation
The diagram shows two quadrilaterals ABCD and A1B1C1D1 on the Cartesian plane. ABCD has vertices A(-1; 1), B(-2; 2), C(-3; 1) and D(-2; 3). A1B1C1D1 has vertices A1(-1; -1), B1(-2; -2), C1(-1; -3) and D1(-3; -2). Describe fully the single transformation which maps ABCD onto A1B1C1D1.

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Question 2602

[2 marks]Geometrical Transformation
The diagram shows two quadrilaterals ABCD and A1B1C1D1 on the Cartesian plane. ABCD has vertices A(-1; 1), B(-2; 2), C(-3; 1) and D(-2; 3). Point A2(1; -2) is the image of A under a translation. Find the translation vector.

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Question 2701

[2 marks]Travel Graphs
The diagram is a velocity-time graph of an object which decelerates uniformly from a velocity of 90 m/s to a velocity of 60 m/s in 10 seconds. It then decelerates uniformly to rest in a further 5 seconds. Calculate the total distance covered by the object during the 15 seconds.

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Question 2702

[2 marks]Travel Graphs
The diagram is a velocity-time graph of an object which decelerates uniformly from a velocity of 90 m/s to a velocity of 60 m/s in 10 seconds. It then decelerates uniformly to rest in a further 5 seconds. Calculate the average velocity of the object during the 15 seconds.

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Question 2703

[2 marks]Travel Graphs
The diagram is a velocity-time graph of an object which decelerates uniformly from a velocity of 90 m/s to a velocity of 60 m/s in 10 seconds. It then decelerates uniformly to rest in a further 5 seconds. Calculate the deceleration of the object during the last five seconds.

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