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ZIMSEC O Level · 4008/1 · N2012

Mathematics Paper 1 November 2012 (topical set)

Questions
49
Total marks
101
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
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 3

[3 marks]Vector Geometry
The points P and Q are shown on the grid, with Q at (-2, 4) and P in the fourth quadrant. (a)(i) Write down the co-ordinates of P. [1] (ii) Write PQ as a column vector. [1] (b) Given QM = (5; -3), draw QM on the grid. [1]

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Question 6

[3 marks]Change of Subject of Formula
Make y the subject of the formula x = sqrt(cy - d).

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Question 7

[3 marks]Simultaneous Equations
Solve the simultaneous equations: 4x + 9y = 33, 2x - 3y = -6.

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Question 8

[3 marks]Ratios, Rates & Proportions
Jojo works in the afternoons only for 5 days a week. He starts work at 1.15 pm and finishes at 7.45 pm. (a) Express 7.45 pm as time in the 24-hour notation. [1] (b) If he is paid $1,20 per hour, calculate his weekly wage. [2]

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Question 9

[3 marks]Factorisation, H.C.F & L.C.M
Factorise completely (i) 7pq - 14q, (ii) x^2 - 7x + 10.

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Question 12

[3 marks]Co-ordinate Geometry
In the diagram, the line through A is parallel to the line y = 12 - 4x and the distance AB = 5 units. (a) Write down the x-coordinate of B. (b) Find the equation of the line through A parallel to the line y = 12 - 4x.

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Question 13

[3 marks]Number Bases
If 120_3 = 13_n + 10_n, find the value of n.

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Question 14

[3 marks]Laws of Indices
(a) Find the exact value of (4/3)^-2. (b) Simplify 3^(-1/2) x 9^(1/4).

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Question 15

[3 marks]Statistics & Probability
The mean of 10 numbers is 54,6. If the number (x + 6) is added to the 10 numbers, the mean becomes 51. Find the value of x.

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Question 16

[3 marks]Trigonometry, Bearing & Distances
In the diagram, PQ = 8 cm, QR = 12 cm and PR = 10 cm. Express cos P as a common fraction.

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Question 17

[4 marks]Matrices
Given that C = (2 -3; 0 4) and D = (5 -2; -7 1), express as a single matrix (a) C - 2D, (b) D^2.

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Question 20

[4 marks]Probability
In this question give all probabilities as common fractions. Eight identical cards are numbered 2 ; 3 ; 5 ; 6 ; 7 ; 8 ; 8 and 9. (a) One of the cards is chosen at random. (i) Write down the number whose probability of being chosen is 1/4. [1] (ii) Find the probability of choosing a card with a prime number. [1] (b) Two of the eight cards are taken at random. Find the probability that the sum of the two numbers is 5. [2]

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Question 21

[4 marks]Constructions & Loci
A and B are two fixed points. Name the line which separates the points that are nearer to A from the points that are nearer to B.

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Question 22

[4 marks]Variation
F is inversely proportional to the square of d. (a) Express F in terms of d and a constant k. [1] (b) Find (i) the value of k when F = 60 and d = 3. [2] (ii) the value of F when d = 6. [1]

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Question 24

[5 marks]Polygons, Symmetry & Circles
(a) Write down the special name of the regular polygon which has three lines of symmetry. [1] (b) AB, BC and CD are sides of a 12-sided polygon. PB, BC and CR are sides of a regular n-sided polygon and angle PBC = 140°. Find (i) the value of n, [2] (ii) the size of angle DCR. [2]

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Question 102

[1 marks]Ordinary & Standard Form
Express 754.96 in standard form.

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Question 202

[1 marks]Trigonometry, Bearing & Distances
In the diagram, triangle JKL is right-angled at K. Write down the special name given to the side JL.

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Question 401

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

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Question 402

[2 marks]Algebraic Expressions
Simplify 4x^2 - 3x(2x - 5).

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Question 501

[1 marks]Trigonometry, Bearing & Distances
Write down the supplement of 35 degrees.

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Question 502

[2 marks]Trigonometry, Bearing & Distances
The diagram shows the positions of two TV masts P and Q. The bearing of Q from P is 125 degrees. Find the 3-figure bearing of P from Q.

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Question 801

[1 marks]Change of Units
Express 7.45 pm as time in the 24-hour notation.

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Question 1001

[2 marks]Inequalities
Solve the inequality 4 - 5x < 19.

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Question 1002

[1 marks]Inequalities
The solution of the inequality 4 - 5x < 19 is shown as a region on a Cartesian plane. Write down the equation of the vertical line that forms the boundary of that region.

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Question 1101

[1 marks]Trigonometry, Bearing & Distances
In the diagram, AB = 12 cm, AC = 9 cm and BC = 7 cm. Express the ratio AC : AB in its simplest form.

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Question 1102

[2 marks]Trigonometry, Bearing & Distances
In the diagram, AB = 12 cm, AC = 9 cm and BC = 7 cm. Find the area of triangle ABC. [sin A = 0,58; cos A = 0,81; tan A = 0,71]

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Question 1801

[2 marks]Logarithms
Given that log 3 = 0.477 and log 5 = 0.699, find log 45.

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Question 1802

[2 marks]Sets
Two sets A and B are such that A intersect B is not empty, A union B = xi, n(A) = 15, n(B) = 25 and n(A union B) = 30. Find n(A intersect B).

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Question 1901

[1 marks]Scales & Simple Map Problems
Express a scale of 2 cm to 5 m in the form 1 : n, where n is a whole number.

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Question 2301

[1 marks]Circle Geometry
ABCDEF is a circle centre O. TBM is a tangent to the circle at B. angle EBC = 52, angle CBM = 20 and AB is parallel to ED. Find angle EFC.

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Question 2302

[1 marks]Circle Geometry
ABCDEF is a circle centre O. TBM is a tangent to the circle at B. angle EBC = 52, angle CBM = 20 and AB is parallel to ED. Find angle BEC.

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Question 2303

[1 marks]Circle Geometry
ABCDEF is a circle centre O. TBM is a tangent to the circle at B. angle EBC = 52, angle CBM = 20 and AB is parallel to ED. Find angle ABE.

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Question 2304

[2 marks]Circle Geometry
ABCDEF is a circle centre O. TBM is a tangent to the circle at B. angle EBC = 52, angle CBM = 20 and AB is parallel to ED. Find angle CED.

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Question 2502

[2 marks]Functional Notation
Given also that the line of symmetry of the graph of f(x) = x^2 + 3x + 2 is x = -1 1/2, find the coordinates of the turning point of this graph.

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Question 2601

[3 marks]Travel Graphs
A car decelerates uniformly from 18 m/s at 2 m/s^2 for 6 seconds. Calculate the distance the car travels during these 6 seconds.

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Question 2602

[1 marks]Travel Graphs
A car decelerates from 18 m/s at 2 m/s^2 for 6 seconds. It then travels with a constant velocity for 10 seconds before it decelerates at h m/s^2 until it comes to rest in a further 8 seconds. Calculate the distance the car travels at constant velocity.

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Question 2603

[1 marks]Travel Graphs
A car decelerates from 18 m/s at 2 m/s^2 for 6 seconds. It then travels with a constant velocity for 10 seconds before it decelerates at h m/s^2 until it comes to rest in a further 8 seconds. Find the value of h.

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Question 2701

[1 marks]Geometrical Transformation
The diagram shows triangles A, B, C, D and PQR on the Cartesian plane. Triangle A has vertices (-3; -3), (-3; -5) and (0; -5). Triangle B has vertices (3; -5), (6; -5) and (6; -3). Triangle A is mapped onto triangle B by a reflection. Write down the equation of the line of reflection.

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Question 2702

[1 marks]Geometrical Transformation
The diagram shows triangles A, B, C, D and PQR on the Cartesian plane. Triangle B has vertices (3; -5), (6; -5) and (6; -3). Triangle C has vertices (2; 3), (4; 3) and (4; 0). Triangle B is mapped onto triangle C by an anticlockwise rotation through 90 degrees. Write down the coordinates of the centre of rotation.

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Question 10101

[1 marks]Approximations & Estimations
Express 754,96 correct to one decimal place.

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Question 10102

[1 marks]Approximations & Estimations
Express 754,96 correct to one significant figure.

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Question 20101

[1 marks]Trigonometry, Bearing & Distances
In the diagram, triangle JKL is right-angled at K. Measure and write down the length of KL correct to the nearest centimetre.

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Question 20102

[1 marks]Trigonometry, Bearing & Distances
In the diagram, triangle JKL is right-angled at K. Measure and write down the size of angle KJL correct to the nearest degree.

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Question 190201

[1 marks]Approximations & Estimations
The radius of a circle, r cm, is given as 11 cm correct to the nearest whole number. Find the limits between which r lies.

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Question 190202

[2 marks]Approximations & Estimations
The radius of a circle, r cm, is given as 11 cm correct to the nearest whole number. Find the least possible circumference of the circle in terms of pi.

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Question 250101

[1 marks]Functional Notation
It is given that f(x) = x^2 + 3x + 2. Find f(0).

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Question 250102

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

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Question 270301

[3 marks]Geometrical Transformation
The diagram shows triangles A, B, C, D and PQR on the Cartesian plane. Triangle C has vertices (2; 3), (4; 3) and (4; 0). Triangle D has vertices (-6; 3), (-3; 3) and (-6; 0). Describe fully the single transformation which maps triangle C onto triangle D.

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Question 270302

[3 marks]Geometrical Transformation
The diagram shows triangles A, B, C, D and PQR on the Cartesian plane. Triangle PQR has vertices P(1; 4), Q(5; 4) and R(5; -2). Triangle C has vertices (2; 3), (4; 3) and (4; 0). Describe fully the single transformation which maps triangle PQR onto triangle C.

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