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ZIMSEC O Level · 4008/1 · J2012

Mathematics Paper 1 June 2012 (topical set)

Questions
43
Total marks
104
Time allowed
150 min
Syllabus code
4008/1

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
43
Pass mark
26
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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
(a) Find 3% of $70. (b) Evaluate 4,01 - 3,4 x 1,08.

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Question 4

[3 marks]Simultaneous Equations
Solve the simultaneous equations: 4x - 2y = 16, 3x + 2y = 19.

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Question 5

[3 marks]Number Bases
Find p in base eight such that p_8 + 234_5 = 421_5.

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Question 7

[3 marks]Matrices
(a) State the reason why the matrix (6 -3; -2 1) has no inverse. (b) Find the 2 x 2 matrix M such that (2 -3; -1 6) - (2 -6; 5 0) = 3M.

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Question 8

[1 marks]Geometrical Transformation
Triangle ABC is reflected in the line PQ, and its image is triangle A'B'C'. Write down the single transformation that maps triangle A'B'C' back onto triangle ABC.

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Question 11

[3 marks]Points, Lines & Angles
In the diagram, AB is parallel to DE. DB is parallel to EF. ACF and DCB are straight lines. Given that angle DEF = 140°, calculate (a) angle CDE, [1] (b) angle ABC, [1] (c) the size of angle DCF which makes CDEF a cyclic quadrilateral. [1]

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Question 12

[6 marks]Measures & Mensuration
A rectangle measures (5x - 2) cm and (x + 1) cm. (a) Write down an expression for the area of the rectangle in terms of x. (b) Given that the area of the rectangle is 12 cm^2, form an equation and show that it reduces to 5x^2 + 3x - 14 = 0. (c) Solve the equation 5x^2 + 3x - 14 = 0. (d) Hence find the length of the rectangle.

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Question 13

[4 marks]Consumer Arithmetic
One litre of paraffin costs $1,00. Calculate (a) the cost of 750 millilitres of paraffin, [2] (b) the number of 750-millilitre bottles of paraffin which can be obtained from a full 30-litre container. [2]

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Question 15

[4 marks]Variation
It is given that y varies inversely as (2x + 3) and that y = 1 when x = 1. (a) Express y in terms of x. [2] (b) Find the value of x when y = 5. [2]

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Question 18

[5 marks]Polygons, Symmetry & Circles
Below are three shapes labelled figure A (a regular nine-sided polygon), figure B (a parallelogram) and figure C (a circle). (a) State the order of rotational symmetry of the shape labelled (i) figure A, [1] (ii) figure B. [1] (b) State the number of lines of symmetry of the shape labelled (i) figure A, [1] (ii) figure B, [1] (iii) figure C. [1]

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Question 19

[4 marks]Constructions & Loci
PQ and QR are two straight lines meeting at Q. Name the locus of the points inside angle PQR which are the same distance from the line PQ as they are from the line QR.

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Question 21

[5 marks]Inequalities & Linear Programming
Find the three inequalities which define the unshaded region in the diagram above.

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Question 24

[6 marks]Probability
A box contains twelve tennis balls which are identical except for colour. Three of the tennis balls are yellow, four are green and five are white. (a) Find the probability that a ball picked at random from the box is (i) white, [1] (ii) black. [1] (b) Two balls are picked at random from the box. Find the probability that they are (a) of the same colour, [2] (b) of different colours. [2]

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Question 201

[2 marks]Inequalities
Solve the inequality 3x + 17 < 5 - 3x.

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Question 202

[1 marks]Inequalities
Write down the maximum possible integer value of x such that 3x - 17 <= 5 - 3x.

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Question 301

[2 marks]Approximations & Estimations
A cube has an edge of length 1.99 cm correct to three significant figures. Estimate correct to one significant figure, the volume of the cube.

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Question 302

[1 marks]Approximations & Estimations
A cube has an edge of length 1.99 cm correct to three significant figures. State the lower limit of the length of the edge in centimetres.

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Question 601

[3 marks]Co-ordinate Geometry
A is the point (0; 6) and B is the point (4; 2). Find (a) AB in column form, (b) the gradient of the line AB, (c) the equation of the line AB.

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Question 602

[3 marks]Vector Geometry
A is the point (0 ; 6) and B is the point (4 ; 2). Find (a) AB in column form, [1] (b) the gradient of the line AB, [1] (c) the equation of the line AB. [1]

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Question 901

[1 marks]Statistics & Probability
A boy picked up some stones as he was playing. The table below shows the number of stones picked and their respective mass ranges.
Mass (m) in grammes: 0 < m <= 2, 2 < m <= 4, 4 < m <= 6, 6 < m <= 8
Number of stones: 2, 6, 5, 3
Use the table to find the number of stones which had a mass of more than 4 grammes.

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Question 902

[1 marks]Statistics & Probability
A boy picked up some stones as he was playing. The table below shows the number of stones picked and their respective mass ranges.
Mass (m) in grammes: 0 < m <= 2, 2 < m <= 4, 4 < m <= 6, 6 < m <= 8
Number of stones: 2, 6, 5, 3
Use the table to find the modal class interval.

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Question 903

[1 marks]Statistics & Probability
A boy picked up some stones as he was playing. The table below shows the number of stones picked and their respective mass ranges.
Mass (m) in grammes: 0 < m <= 2, 2 < m <= 4, 4 < m <= 6, 6 < m <= 8
Number of stones: 2, 6, 5, 3
Use the table to find an estimate of the mean mass.

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Question 1001

[1 marks]Laws of Indices
Simplify sqrt((5p + 2)^2).

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Question 1002

[2 marks]Factorisation, H.C.F & L.C.M
Factorise 9x^2 - 12x + 4.

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Question 1201

[1 marks]Fractions, Decimals & Percentages
A boy completes a 400-metre race in one minute. Express 400 metres as a percentage of a kilometre.

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Question 1202

[2 marks]Change of Units
A boy completes a 400-metre race in one minute. Express his speed in kilometres per hour.

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Question 1401

[4 marks]Laws of Indices
Simplify the following, giving your answers in standard form. (a) sqrt(6250000), (b) 5^-2.

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Question 1402

[4 marks]Ordinary & Standard Form
Simplify the following, giving your answers in standard form. (a) sqrt(6250000) [2] (b) 5^-2 [2]

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Question 1601

[2 marks]Change of Subject of Formula
Given that p = (x - q)(x + q), express q in terms of x and p.

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Question 1602

[2 marks]Change of Subject of Formula
Given that p = (x - q)(x + q), find the values of q when x = 3 and p = -7.

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Question 1701

[1 marks]Functional Graphs
The diagram shows the graph of the function f(x) = 2x^2 + 3x - 4. Use the graph to find the minimum value of the function f(x).

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Question 1702

[1 marks]Functional Graphs
The diagram shows the graph of the function f(x) = 2x^2 + 3x - 4. Use the graph to find the gradient of the curve at x = 1.

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Question 1703

[1 marks]Functional Graphs
The diagram shows the graph of the function f(x) = 2x^2 + 3x - 4. Use the graph to find the area between the curve, the x-axis, the y-axis and the line x = -2.

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Question 1704

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

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Question 2001

[2 marks]Similarity & Congruency
In the diagram, AB = 6 cm, BC = 4 cm, BE = 3 cm and BE is parallel to CD. Find the length of CD.

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Question 2002

[1 marks]Similarity & Congruency
In the diagram, AB = 6 cm, BC = 4 cm, BE = 3 cm and BE is parallel to CD. Express the ratio BE : CD in its simplest form.

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Question 2003

[2 marks]Similarity & Congruency
In the diagram, AB = 6 cm, BC = 4 cm, BE = 3 cm and BE is parallel to CD. Express the ratio area of triangle ABE : area of quadrilateral BCDE in its simplest form.

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Question 2201

[4 marks]Logarithms
Evaluate (i) log_10 1 - log_10 0.0001, (ii) log_2 sqrt(2).

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Question 2202

[2 marks]Laws of Indices
Express (9^2 x 9^3) as a power of 3.

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Question 2501

[1 marks]Travel Graphs
The diagram is the velocity-time graph of an object which accelerates uniformly from rest and attains a velocity of 20 m/s in 2s. The object maintains a constant velocity for a further 4s and then accelerates uniformly again for 4s after which it reaches a velocity of 40 m/s. Calculate the acceleration of the object during the first 2 seconds.

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Question 2502

[3 marks]Travel Graphs
The diagram is the velocity-time graph of an object which accelerates uniformly from rest and attains a velocity of 20 m/s in 2s. The object maintains a constant velocity for a further 4s and then accelerates uniformly again for 4s after which it reaches a velocity of 40 m/s. Calculate the distance covered by the object during the 10 seconds.

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Question 2503

[1 marks]Travel Graphs
The diagram is the velocity-time graph of an object which accelerates uniformly from rest and attains a velocity of 20 m/s in 2s. The object maintains a constant velocity for a further 4s and then accelerates uniformly again for 4s after which it reaches a velocity of 40 m/s. Calculate the average speed of the object during the 10 seconds.

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Question 2504

[1 marks]Travel Graphs
The diagram is the velocity-time graph of an object which accelerates uniformly from rest and attains a velocity of 20 m/s in 2s. The object maintains a constant velocity for a further 4s and then accelerates uniformly again for 4s after which it reaches a velocity of 40 m/s. Calculate the velocity of the object 9 seconds from rest.

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