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ZIMSEC O Level · 4030/1 · J2016

Mathematics Paper 1 June 2016 (topical set)

Questions
51
Total marks
101
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
51
Pass mark
31
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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
Evaluate (a) 1,4 + 0,04, (b) 5 1/4 ÷ 3 1/2.

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Question 5

[3 marks]Simultaneous Equations
Solve the simultaneous equations: 6y - 3x = 1, 3x + y = 13.

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Question 7

[3 marks]Number Bases
(a) Expand 1234_5 in powers of 5. [1] (b) Evaluate 1011_2 + 111_2, giving the answer in base 2. [2]

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Question 10

[3 marks]Change of Subject of Formula
Given that x = aq^2 + bq^2, express q in terms of a, b and x.

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Question 11

[3 marks]Variation
If V varies jointly as h and as the square of r, (a) write down the equation connecting V, r, h and a constant c. [1] (b) find c if V = 440, r = 2 and h = 35. [2]

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Question 13

[3 marks]Points, Lines & Angles
In the diagram AB, DC and FE are parallel. BC is parallel to GF. angle GBC = 60° and angle BAD = 80°. Find (a) angle BGD, [1] (b) angle ADG, [1] (c) angle DEF. [1]

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Question 14

[3 marks]Ordinary & Standard Form
Given that r = 9 x 10^6, evaluate, leaving the answers in standard form, (a) 2r, [1] (b) r^2, [1] (c) sqrt(r). [1]

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Question 16

[3 marks]Co-ordinate Geometry
The equation of a straight line, l, is 3x - 5y = 30. Find (a) the gradient of the line l, (b) the equation of a line parallel to line l passing through a point (-5; 3), in the form y = mx + c.

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Question 17

[3 marks]Scales & Simple Map Problems
The scale of a map is given as 1 : 250 000. Find (a) the distance on the ground, in km, represented by a length of 5 cm on the map, [1] (b) the actual area in km^2, represented by an area of 6 cm^2 on the map. [2]

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Question 18

[3 marks]Polygons, Symmetry & Circles
The size of each interior angle of a regular polygon is 135°. (a) Find (i) the size of each exterior angle, [1] (ii) the order of rotational symmetry of the regular polygon. [1] (b) State the special name of the regular polygon. [1]

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Question 19

[3 marks]Algebraic Fractions
Simplify 1/(a^2 - 3a + 2) divided by 1/(1 - a).

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Question 21

[4 marks]Matrices
The matrix A = (-2 14; 2 x) and |A| = -2. (a) Find the value of x. (b) Hence find A^-1.

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Question 22

[4 marks]Logarithms
(a) Given that log_b M = x, express M in terms of b and x. (b) Evaluate (i) log_4 (1/64), (ii) log 81 / log 27.

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Question 23

[3 marks]Probability
Two unbiased coins, coin 1 and coin 2 are tossed and the outcomes recorded in a table. (a) Complete the outcome table given, where H is a head and T is a tail. The table has Coin 1 across the top (H, T) and Coin 2 down the side (H, T), with HH and TT already entered. (b) Using the table or otherwise, find the probability of getting (i) 2 heads, [1] (ii) different outcomes, [1] (iii) at least one tail. [1]

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Question 26

[6 marks]Constructions & Loci
The diagram shows a triangle ABC, circle centre C of radius 4 cm and two straight lines L1 and L2. The lines L1 and L2 are each drawn parallel to AB, one on each side of it, at a distance of 2,5 cm from AB. (a) Describe fully the locus represented by the circle, centre C. [2] (b) Describe fully the locus represented by the lines L1 and L2. [2] (c) Describe the position of point D. [2]

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Question 202

[1 marks]Fractions, Decimals & Percentages
Express 7/30 as a recurring decimal fraction.

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Question 301

[1 marks]Prime Numbers, Sequences & Types of Numbers
It is given that 0 ; 1 ; 8 ; 27 ; ___ ; ... is a pattern. State the next term of the pattern.

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Question 302

[2 marks]Approximations & Estimations
A length h measured to 1 decimal place is given as 9,5 cm. State its limits.

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Question 401

[1 marks]Factorisation, H.C.F & L.C.M
Factorise completely x^2 - 1/36.

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Question 402

[2 marks]Algebraic Expressions
Remove brackets and simplify (4a + b)(5a - 3b).

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Question 601

[1 marks]Sets
It is given that xi = {0; 1; 2; 3; 4; 5; 6; 7; 8; 9}, A is a set of prime numbers and B is a set of factors of 12. List the elements of A.

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Question 602

[1 marks]Sets
It is given that xi = {0; 1; 2; 3; 4; 5; 6; 7; 8; 9}, A is a set of prime numbers and B is a set of factors of 12. List the elements of A intersect B.

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Question 603

[1 marks]Sets
It is given that xi = {0; 1; 2; 3; 4; 5; 6; 7; 8; 9}, A is a set of prime numbers and B is a set of factors of 12. Find n((A union B)').

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Question 801

[1 marks]Change of Units
Express 0,5 litres in cm^3.

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Question 802

[2 marks]Consumer Arithmetic
A woman earning $275 had her salary increased by 5%. Calculate her new salary. [2]

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Question 901

[1 marks]Functional Notation
If f(x) = 1/x^2, x is not 0, find f(-3).

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Question 902

[2 marks]Functional Notation
If f(x) = 1/x^2, x is not 0, find the values of x when f(x) = 1.

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Question 1201

[2 marks]Inequalities
Solve the inequality -2(2x - 7) >= 38.

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Question 1202

[1 marks]Inequalities
Illustrate the solution set of -2(2x - 7) >= 38 on the number line.

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Question 1501

[1 marks]Statistics & Probability
The table shows the sizes of shoes worn by pupils in a class.
shoe size: 5, 6, 7, 8, 9
frequency: 6, 14, 12, 8, 2
Find the total number of pupils in the class.

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Question 1502

[1 marks]Statistics & Probability
The table shows the sizes of shoes worn by pupils in a class.
shoe size: 5, 6, 7, 8, 9
frequency: 6, 14, 12, 8, 2
Find the modal shoe size.

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Question 1503

[1 marks]Statistics & Probability
The table shows the sizes of shoes worn by pupils in a class.
shoe size: 5, 6, 7, 8, 9
frequency: 6, 14, 12, 8, 2
Find the median shoe size.

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Question 2001

[1 marks]Change of Units
A motorist left Masvingo for Beitbridge at 2102. The motorist spent 1 hour 30 minutes mending a puncture and 3 hours driving. The motorist's average speed for the journey was 64 km/h. Express 2102 as a time on the 12-hour notation.

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Question 2002

[1 marks]Change of Units
A motorist left Masvingo for Beitbridge at 2102. The motorist spent 1 hour 30 minutes mending a puncture and 3 hours driving. Find the arrival time in Beitbridge in 24-hour notation.

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Question 2003

[3 marks]Measures & Mensuration
A motorist left Masvingo for Beitbridge at 2102. The motorist spent 1 hour 30 minutes mending a puncture and 3 hours driving. The motorist's average speed for the journey was 64 km/h. (a) Express 2102 as a time on the 12-hour notation. (b) Find the arrival time in Beitbridge in 24-hour notation. (c) Calculate the distance between Masvingo and Beitbridge.

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Question 2401

[2 marks]Consumer Arithmetic
On a certain day, US$100 was exchanged for R880. Calculate the equivalent value of R165 in US$ on that day. [2]

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Question 2501

[1 marks]Circle Geometry
In the diagram, points A, B, C and D are on the circumference of a circle with centre O. angle CDS = 50 and angle BDO = 20. Line TS is a tangent to the circle at D. Calculate angle DBC.

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Question 2502

[1 marks]Circle Geometry
In the diagram, points A, B, C and D are on the circumference of a circle with centre O. angle CDS = 50 and angle BDO = 20. Line TS is a tangent to the circle at D. Calculate angle DOC.

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Question 2503

[1 marks]Circle Geometry
In the diagram, points A, B, C and D are on the circumference of a circle with centre O. angle CDS = 50 and angle BDO = 20. Line TS is a tangent to the circle at D. Calculate angle ODC.

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Question 2504

[1 marks]Circle Geometry
In the diagram, points A, B, C and D are on the circumference of a circle with centre O. angle CDS = 50 and angle BDO = 20. Line TS is a tangent to the circle at D. Calculate angle ABD.

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Question 2505

[1 marks]Circle Geometry
In the diagram, points A, B, C and D are on the circumference of a circle with centre O. angle CDS = 50 and angle BDO = 20. Line TS is a tangent to the circle at D. Calculate angle DAC.

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Question 2701

[1 marks]Trigonometry, Bearing & Distances
Point Q is on a bearing of S35 degrees E from point P. Calculate the three-figure bearing of P from Q.

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Question 2802

[2 marks]Geometrical Transformation
The diagram shows triangles A, B and C. Triangle A has vertices (-2; 8), (-3; 5) and (1; 5). Triangle C has vertices (6; 8), (3; 5) and (7; 5). Triangle C is the image of triangle A under a transformation M. Describe fully transformation M.

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Question 20101

[1 marks]Approximations & Estimations
Express 31,095 correct to 2 decimal places.

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Question 20102

[1 marks]Approximations & Estimations
Express 31,095 correct to 2 significant figures.

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Question 240201

[2 marks]Change of Units
Express 90 km/h in m/s.

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Question 240202

[1 marks]Travel Graphs
An object starts from rest and accelerates uniformly until its speed is 90 km/h in 5 seconds. Calculate the acceleration of the object in m/s^2.

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Question 270201

[2 marks]Trigonometry, Bearing & Distances
In the diagram AB = 5 cm, AC = 10 cm and angle BAC = 120 degrees. Using as much of the information given below as is necessary, calculate the area of triangle ABC. [tan 60 = 1,73; sin 60 = 0,86; cos 60 = 0,50]

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Question 270202

[3 marks]Trigonometry, Bearing & Distances
In the diagram AB = 5 cm, AC = 10 cm and angle BAC = 120 degrees. Calculate the length of BC leaving the answer in surd form.

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Question 280101

[2 marks]Geometrical Transformation
The diagram shows triangles A, B and C. Triangle A has vertices (-2; 8), (-3; 5) and (1; 5). Triangle B has vertices (2; 5), (1; 2) and (5; 2). Triangle B is the image of A under a Translation T = (p; q). State the values of p and q.

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Question 280102

[2 marks]Geometrical Transformation
The diagram shows triangles A, B and C. Triangle B is the image of A under a Translation T = (4; -3). Find |T|.

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