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ZIMSEC O Level · 4030/1 · J2018

Mathematics Paper 1 June 2018 (topical set)

Questions
43
Total marks
100
Time allowed
150 min
Syllabus code
4030/1

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 2

[3 marks]Fractions, Decimals & Percentages
(a) Find the exact value of (i) 7,03 - 2,145, (ii) 4,32 x 0,11. (b) Simplify 1 7/8 + 2 1/3, giving the answer as a mixed number.

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Question 4

[3 marks]Laws of Indices
Evaluate (a) cube root of 0.027, (b) (1 7/9)^(1/2), (c) 3^0 x 3^-2.

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Question 5

[3 marks]Polygons, Symmetry & Circles
(a) State the number of lines symmetry of a regular nonagon. [1] (b) The sum of interior angles of a regular polygon is 3 960°. Find the number of sides of the regular polygon. [2]

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Question 6

[3 marks]Number Bases
(a) Simplify 1044_8 - 175_8, giving the answer in base 8. [1] (b) Convert 10111_2 to a number in base 6. [2]

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Question 10

[3 marks]Variation
It is given that y varies directly as the square of (x - 3). (a) Express y in terms of x and a constant k. [1] (b) Given that y = 16 when x = 1, find y when x = 10. [2]

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Question 11

[3 marks]Simultaneous Equations
Solve the simultaneous equations: x + y = 5 1/2, x - 2y = 2 1/2.

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Question 12

[3 marks]Co-ordinate Geometry
It is given that 3x + 2y = 12 is an equation of a straight line. (a) Find the gradient of the straight line. (b) Find the coordinates of the point where the straight line crosses the y-axis.

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Question 13

[3 marks]Algebraic Fractions
Simplify 3x^2/(x^2 - 5x) divided by x/(x^2 - 25).

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Question 16

[4 marks]Factorisation, H.C.F & L.C.M
(a) Factorise completely (i) x^3 - x, (ii) x^2 + 2x + 1. (b) Hence or otherwise, find the Highest Common Factor (HCF) of x^3 - x and x^2 + 2x + 1.

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Question 17

[4 marks]Vector Geometry
It is given that vector p = (3; -4) and vector q = (-2; x). (a) Calculate p - q in terms of x. [1] (b) Find the value of (i) |p|, the magnitude of vector p. [1] (ii) x such that 2p = -3q. [2]

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Question 19

[4 marks]Probability
It is given that set P = {-11; -2; 0; 1; 2; 3; sqrt(11); 9; 17; 21}. (a) A number is chosen at random from set P. Find the probability that the number is either a negative number or a prime number. [2] (b) Two numbers are chosen at random from set P one after the other, without replacement. Find the probability that one is a perfect square and the other is a factor of 21. [2]

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Question 23

[5 marks]Measures & Mensuration
In the diagram, ABCDEF is a solid triangular prism. AB = 6 cm, BC = 20 cm, AF = 8 cm, FB = x cm and angle BAF = 90 degrees. (a) Find x. (b) Calculate the total surface area of the prism.

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Question 24

[6 marks]Logarithms
(a) Evaluate (i) log_3 45 - log_3 5, (ii) log 0.2 / log 5. (b) Express as a logarithm of a single number, 3 log 2 + (1/2) log 81.

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Question 25

[6 marks]Matrices
It is given that 3(p -1; 0 4) - (7 q; -2 2r) = (1/2)(16 8; 4 -12). Find the value of (i) p, (ii) q, (iii) r.

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Question 102

[1 marks]Approximations & Estimations
Find the approximate value of sqrt(3598).

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Question 301

[1 marks]Change of Units
Express the time 00 25 in 12-hour notation.

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Question 302

[2 marks]Measures & Mensuration
A goods train left Johannesburg at 2030 on a Wednesday and arrived in Beitbridge after travelling for 27 hours 45 minutes. (i) State the day on which the train arrived at Beitbridge. (ii) Find the time at which the train arrived at Beitbridge.

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Question 701

[1 marks]Circle Geometry
In the diagram W, X, Y and Z are points on the circumference of a circle centre O, WX = XY and angle XZW = 42. Calculate angle WYX.

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Question 702

[1 marks]Circle Geometry
In the diagram W, X, Y and Z are points on the circumference of a circle centre O, WX = XY and angle XZW = 42. Calculate angle YWZ.

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Question 703

[1 marks]Circle Geometry
In the diagram W, X, Y and Z are points on the circumference of a circle centre O, WX = XY and angle XZW = 42. Calculate angle WXY.

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Question 801

[1 marks]Linear Equations
Solve the equation (1/3)x - 1 = 7.

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Question 802

[2 marks]Laws of Indices
Solve the equation 4^(2n - 3) = 8.

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Question 901

[2 marks]Sets
Three sets A, B and C are such that A is a proper subset of B and C is a proper subset of A. Write down, in their simplest forms, the sets B intersect C and A union B, giving the answer as 'first, second'.

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Question 902

[1 marks]Sets
In the diagram, three sets P, Q and R are intersecting, with the P intersect Q lens and the P intersect R lens both shaded. Use set notation to describe the shaded region.

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Question 1401

[1 marks]Change of Subject of Formula
The formula for converting a temperature in degrees centigrade (C) to a temperature in degrees Fahrenheit (F) is F = 32 + 9C/5. Find F when C = 30.

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Question 1402

[2 marks]Change of Subject of Formula
The formula for converting a temperature in degrees centigrade (C) to a temperature in degrees Fahrenheit (F) is F = 32 + 9C/5. Make C the subject of the formula.

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Question 1501

[2 marks]Algebraic Expressions
Expand and simplify -3(x - 7) + 5(2 - 4x).

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Question 1502

[2 marks]Approximations & Estimations
The length of a side of a regular hexagon is 3,4 cm correct to one decimal place. Find the least possible perimeter of the regular hexagon.

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Question 1801

[1 marks]Statistics & Probability
The marks of 6 of the students who wrote a mathematics test are as follows:
15 ; 14 ; 9 ; 12 ; 11 ; 15.
Find the median mark for the 6 students.

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Question 1802

[3 marks]Statistics & Probability
The marks of 6 of the students who wrote a mathematics test are as follows:
15 ; 14 ; 9 ; 12 ; 11 ; 15.
A seventh student got x marks from the same test and the mean mark for the seven students was 13. Find x, the mark of the seventh student.

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Question 2002

[2 marks]Similarity & Congruency
Two similar bottles have heights 8 cm and 12 cm. The mass of the bottle of height 8 cm is 40 g. Find the mass of the similar bottle that has a height of 12 cm.

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Question 2101

[2 marks]Trigonometry, Bearing & Distances
ABC is a triangle with AB = 9 cm, BC = 4 cm and angle ABC = 120 degrees. Use as much of the information given below as is necessary. [tan 60 = 1,73; sin 60 = 0,87; cos 60 = 0,5] Find the area of triangle ABC.

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Question 2102

[3 marks]Trigonometry, Bearing & Distances
ABC is a triangle with AB = 9 cm, BC = 4 cm and angle ABC = 120 degrees. Find the length of AC leaving the answer in surd form.

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Question 2201

[1 marks]Travel Graphs
The diagram is a speed-time graph of an object whose initial speed is 12 m/s. The object accelerates uniformly for 4 seconds until it reaches a speed of 30 m/s. It then travels at this speed for 5 seconds and then decelerates at 6 m/s^2 until it comes to rest. Calculate the acceleration from t = 0 to t = 4.

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Question 2202

[2 marks]Travel Graphs
The diagram is a speed-time graph of an object whose initial speed is 12 m/s. The object accelerates uniformly for 4 seconds until it reaches a speed of 30 m/s. It then travels at this speed for 5 seconds and then decelerates at 6 m/s^2 until it comes to rest. Calculate the distance travelled from t = 0 to t = 9.

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Question 2203

[2 marks]Travel Graphs
The diagram is a speed-time graph of an object whose initial speed is 12 m/s. The object accelerates uniformly for 4 seconds until it reaches a speed of 30 m/s. It then travels at this speed for 5 seconds and then decelerates at 6 m/s^2 until it comes to rest. Calculate the value of T, the total time taken for the whole journey.

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Question 2601

[3 marks]Geometrical Transformation
The diagram shows three triangles ABC, A1B1C1 and A2B2C2. Triangle ABC has vertices A(2; 2), B(4; 2) and C(2; 6). Triangle A1B1C1 has vertices A1(5; -4), B1(7; -4) and C1(5; 0). Triangle ABC is mapped onto triangle A1B1C1 by a single transformation. Describe fully this transformation.

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Question 10101

[1 marks]Ordinary & Standard Form
Express 3598 as a number in standard form.

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Question 10102

[1 marks]Approximations & Estimations
Express 3598 correct to 2 significant figures.

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Question 200101

[2 marks]Inequalities
Solve the inequality 2(x - 3) < 7.

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Question 200102

[1 marks]Inequalities
Write down the largest perfect square that satisfies the inequality 2(x - 3) < 7.

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Question 260201

[1 marks]Geometrical Transformation
The diagram shows three triangles ABC, A1B1C1 and A2B2C2. Triangle ABC has vertices A(2; 2), B(4; 2) and C(2; 6). Triangle A2B2C2 has vertices A2(-2; -2), B2(-2; -4) and C2(-6; -2). Triangle ABC is mapped onto triangle A2B2C2 by a reflection. Find the equation of the axis of reflection.

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Question 260202

[2 marks]Geometrical Transformation
The diagram shows three triangles ABC, A1B1C1 and A2B2C2. Triangle ABC has vertices A(2; 2), B(4; 2) and C(2; 6). Triangle A2B2C2 has vertices A2(-2; -2), B2(-2; -4) and C2(-6; -2). Triangle ABC is mapped onto triangle A2B2C2 by a reflection. Find the matrix that represents this reflection.

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