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ZIMSEC O Level · 4008/1 · N2014

Mathematics Paper 1 November 2014 (topical set)

Questions
44
Total marks
95
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
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 5

[3 marks]Matrices
Given that (10 3; 4 2) - 2(-1 -3; u -5) = (v 9; -18 12), (a) find the value of (i) u, (ii) v. (b) Find the determinant of (10 3; 4 2).

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Question 6

[3 marks]Factorisation, H.C.F & L.C.M
(a) The product of a number k and 15 is 105. Find the number k. (b) Factorise completely 4x^2 + 12x - 7.

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Question 10

[3 marks]Measures & Mensuration
The density of a certain stone is known to be 2,5 g/cm^3. Calculate the volume, in cm^3, of a piece of the stone with a mass of 7,5 kg.

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Question 11

[3 marks]Variation
The time, T, hours, varies inversely as the speed, S, kilometres per hour. (a) Express T in terms of S and constant D. [1] (b) Calculate the constant D, when T = 12 minutes and S = 15 km/h. [2]

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Question 15

[4 marks]Consumer Arithmetic
On 1 March 2008 a farmer deposited $36 000 into a new bank account. On 30 June 2008 her account balance was $36 600. (a) Calculate (i) the time of investment as a fraction of a year in its simplest form, [1] (ii) the interest rate percent per annum. [2] (b) Given an exchange rate of 1toR7,50,convert1 to R7,50, convert 210 to rands. [1]

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Question 17

[6 marks]Ratios, Rates & Proportions
John, Ticha and Sharai share some sweets. John and Ticha's shares are in the ratio 1 : 2. Ticha and Sharai's shares are in the ratio 3 : 4. (a) Express the shares in the ratio John : Ticha : Sharai. [2] (b) Calculate (i) Ticha's share if Sharai got 24 sweets, [2] (ii) the total number of sweets shared. [2]

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Question 18

[5 marks]Vector Geometry
The co-ordinates of A, B and C are (4 ; 2), (0 ; -2) and (-3 ; 2) respectively. (a) Express as column vectors (i) OA, [1] (ii) -2BC. [2] (b) Calculate |BC|. [2]

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Question 21

[5 marks]Constructions & Loci
In triangle ABC, angle ABC = 135 degrees and BC = 6 cm. The perpendicular from C meets AB produced at X. Calculate the length of CX, correct to 1 decimal place. [sin 45 degrees = 0,7]

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Question 22

[5 marks]Probability
The probability that John passes a driving test is 3/4 and that of Peter passing is 2/x. (a) If the probability that they both pass the test is 3/28, find x. [2] (b) Calculate the probability that (i) Peter fails the test, [1] (ii) either John or Peter passes the test. [2]

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Question 101

[2 marks]Fractions, Decimals & Percentages
Simplify (i) 1 1/2 - 2/3, (ii) 0.45 x 2/9.

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Question 102

[1 marks]Approximations & Estimations
Express 0.0796 correct to 3 decimal places.

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Question 201

[1 marks]Fractions, Decimals & Percentages
Express 12,5% as a common fraction in its simplest form.

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Question 202

[2 marks]Factorisation, H.C.F & L.C.M
Find the Highest Common Factor (H.C.F) of 168 and 252.

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Question 301

[1 marks]Sets
It is given that xi = {1; 2; 3; 4; 5; 6; 7; 8; 9; 10}, where H is a set of prime numbers and K is a set of odd numbers. List the elements of set H.

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Question 302

[2 marks]Sets
It is given that xi = {1; 2; 3; 4; 5; 6; 7; 8; 9; 10}, where H is a set of prime numbers and K is a set of odd numbers. Find n(H union K).

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Question 402

[1 marks]Change of Units
Express 15 minutes before midnight as time in the 24-hour notation.

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Question 801

[1 marks]Circle Geometry
In the diagram, ABCD is a circle centre O. angle AOB = 80 and AB = BC. Calculate angle ACB.

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Question 802

[1 marks]Circle Geometry
In the diagram, ABCD is a circle centre O. angle AOB = 80 and AB = BC. Calculate angle ADC.

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Question 803

[1 marks]Circle Geometry
In the diagram, ABCD is a circle centre O. angle AOB = 80 and AB = BC. Calculate angle OAC.

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Question 902

[1 marks]Polygons, Symmetry & Circles
State the name of a polygon with rotational symmetry of order 2.

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Question 1301

[1 marks]Prime Numbers, Sequences & Types of Numbers
Write down the next term of the sequence 81/625 ; 27/125 ; 9/25 ;

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Question 1302

[2 marks]Ordinary & Standard Form
Simplify 1.11 x 10^5 divided by 3.7 x 10^-3, expressing your answer in standard form.

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Question 1401

[2 marks]Change of Subject of Formula
Given that V = (1/3) pi r^2 h, express r in terms of V, pi and h.

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Question 1402

[2 marks]Change of Subject of Formula
Given that V = (1/3) pi r^2 h, find r if pi = 22/7, V = 29 1/3 and h = 7.

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Question 1602

[3 marks]Statistics & Probability
The following is a list of marks obtained by a group of students.
20 ; 18 ; 12 ; 19 ; 18 ; 14 ; 18
If two more marks, x and x + 1, are included in the list, the mean becomes 16. Find x.

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Question 1901

[2 marks]Laws of Indices
Solve 3^y = 9^-2.

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Question 1902

[3 marks]Logarithms
Given that log_x 81 = log_2 16, find the value of x.

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Question 2001

[1 marks]Number Bases
Evaluate 212_3 + 122_3 giving your answer in base three.

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Question 2002

[4 marks]Points, Lines & Angles
In the diagram, LM and RS are two parallel straight lines and PQ cuts LM and RS at X and Y respectively. Given that angle MXY = 2u° and angle XYS = 3u°, calculate (i) the value of u, [2] (ii) angle XYS, [1] (iii) angle PXL. [1]

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Question 2301

[2 marks]Geometrical Transformation
The diagram shows triangles A and A2 drawn on the Cartesian plane. Triangle A has vertices (-7; 1), (-5; 1) and (-5; 5). Draw triangle A1, the image of triangle A under a reflection with mirror line x = -1.

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Question 2302

[3 marks]Geometrical Transformation
The diagram shows triangles A and A2 drawn on the Cartesian plane. Triangle A has vertices (-7; 1), (-5; 1) and (-5; 5). Triangle A2 has vertices (1; -5), (3; -5) and (3; -1). Describe fully the single transformation which maps triangle A onto triangle A2.

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Question 2402

[2 marks]Inequalities & Linear Programming
By considering integral values of x and y in the region defined by 3y >= 4x, y >= 0 and the third inequality, calculate the least value of x + y.

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Question 2501

[2 marks]Travel Graphs
The diagram shows a velocity-time graph of a particle which decelerates uniformly from a velocity of 40 m/s to a velocity of 25 m/s in 20 seconds. It further decelerates uniformly at a rate of 2,5 m/s^2 until it comes to rest. Given that the total time of the journey is T seconds, calculate the deceleration of the particle during the first 20 seconds.

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Question 2502

[2 marks]Travel Graphs
The diagram shows a velocity-time graph of a particle which decelerates uniformly from a velocity of 40 m/s to a velocity of 25 m/s in 20 seconds. It further decelerates uniformly at a rate of 2,5 m/s^2 until it comes to rest. Given that the total time of the journey is T seconds, calculate the value of T.

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Question 2503

[2 marks]Travel Graphs
The diagram shows a velocity-time graph of a particle which decelerates uniformly from a velocity of 40 m/s to a velocity of 25 m/s in 20 seconds. It further decelerates uniformly at a rate of 2,5 m/s^2 until it comes to rest. Given that the total time of the journey is T seconds, calculate the total distance covered in the T seconds.

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Question 2504

[1 marks]Travel Graphs
The diagram shows a velocity-time graph of a particle which decelerates uniformly from a velocity of 40 m/s to a velocity of 25 m/s in 20 seconds. It further decelerates uniformly at a rate of 2,5 m/s^2 until it comes to rest in a total time of T = 30 seconds. Calculate the average speed for the whole journey.

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Question 40101

[1 marks]Functional Notation
Given that f(x) = 3 - 4x, find f(-2).

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Question 40102

[1 marks]Functional Notation
Given that f(x) = 3 - 4x, find x if f(x) = 19.

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Question 90101

[1 marks]Trigonometry, Bearing & Distances
Given that sin theta = 5/13 and 90 < theta < 180 degrees, express as a common fraction cos theta.

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Question 90102

[1 marks]Trigonometry, Bearing & Distances
Given that sin theta = 5/13 and 90 < theta < 180 degrees, express as a common fraction tan theta.

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Question 160101

[1 marks]Statistics & Probability
The following is a list of marks obtained by a group of students.
20 ; 18 ; 12 ; 19 ; 18 ; 14 ; 18
Find the mode.

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Question 160102

[1 marks]Statistics & Probability
The following is a list of marks obtained by a group of students.
20 ; 18 ; 12 ; 19 ; 18 ; 14 ; 18
Find the median.

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Question 240101

[3 marks]Inequalities & Linear Programming
The diagram shows the region defined by three inequalities 3y >= 4x, y >= 0 and a third inequality. Find the third inequality.

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Question 240102

[1 marks]Inequalities & Linear Programming
The diagram shows the region defined by three inequalities 3y >= 4x, y >= 0 and a third inequality. Find the coordinates of point M, where the two lines intersect, shown on the diagram.

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