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ZIMSEC O Level · 4008/1 · J2010

Mathematics Paper 1 June 2010 (topical set)

Questions
46 of 47
Total marks
105
Time allowed
150 min
Syllabus code
4008/1

We hold fewer questions than the paper printed. The rest are not in the bank yet.

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
46
Pass mark
28
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 1

[2 marks]Fractions, Decimals & Percentages
(a)(ii) Express 0.096 as a common fraction, giving your answer in its lowest terms. (b) Express 36 minutes as a percentage of two hours.

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Question 2

[3 marks]Ordinary & Standard Form
(a) Write down, in ordinary form, the value of 4.32 x 10^4. [1] (b) Given that M = 3.6 x 10^2 and N = 8 x 10^-1, find in standard form, the value of (i) MN, [1] (ii) M + N. [1]

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Question 4

[3 marks]Number Bases
(a) Convert 408 to a number in base 6. [1] (b) Write down 2 x 3^4 + 1 x 3^2 + 2 x 3^1 as a number in base 3. [1] (c) Given that 42_x + 53_x = 125_x, find the value of x. [1]

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Question 5

[3 marks]Laws of Indices
Given that m = 1/2, n = 0 and r = 3, evaluate (a) (mr)^n, (b) (2 1/4)^m, (c) the r-th root of -64.

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Question 6

[3 marks]Ratios, Rates & Proportions
(a) Given that 12 : d = 3 : 7, find the value of d. [1] (b) A sum of money is divided in the ratio 2 : 3 : 7. Given that the largest share is $224 000, calculate the smallest share. [2]

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Question 7

Sets
Given that n(xi) = 25, n(A) = 12, n(B') = 6 and n((A union B)') = 2, complete the Venn diagram to show the number of elements in each subset.

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Question 9

[3 marks]Simultaneous Equations
Solve the simultaneous equations: (1/2)x + 3y = 4, 3x + 2y = 8.

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Question 10

[3 marks]Consumer Arithmetic
A company director went to Britain and America on business. Her company gave her an allowance of £2000. (a) While in Britain she spent 1/5 of her allowance. Calculate the amount she spent. [1] (b) On arrival in America she converted all her remaining allowance into US$ at the rate of £1 to US$1,92. Calculate the amount she received in US$. [2]

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Question 13

[3 marks]Vector Geometry
It is given that p = (4; -6) and q = (6; x). Find (a) x if p is parallel to q, [1] (b) |p|, leaving your answer in surd form. [2]

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Question 14

[3 marks]Polygons, Symmetry & Circles
A quadrilateral has exactly one line of symmetry, and that line of symmetry is one of its diagonals. Write down the name of this quadrilateral.

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Question 16

[3 marks]Matrices
It is given that D is a 2 by 2 matrix such that D + (-6 -8; 3 4) = (0 0; 0 0). (a) Find D. (b) Write down the determinant of (-6 -8; 3 4).

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Question 18

[3 marks]Measures & Mensuration
The diagram shows a right pyramid whose base ABCDEF is a regular hexagon of centre O. OD = 8 m, VD = 10 m and the area of triangle DOC = 15,6 m^2. (a) Show that the height (VO) of the pyramid is 6 m. (b) Find the volume of the pyramid. [Volume of pyramid = (1/3) base area x height]

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Question 19

[4 marks]Variation
The graph shows the relationship between two variables t and d, a straight line through the origin passing through (2, 10), (4, 20), (6, 30), (8, 40) and (10, 50). Use the graph to find the value of (a) d when t = 7, [1] (b) t when d = 20, [1] (c) k when t = kd. [2]

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Question 20

[3 marks]Scales & Simple Map Problems
A map is drawn to a scale of 1 : 100 000. (a) Find the distance on the map between two villages which are 24 km apart on the ground, giving your answer in cm. [1] (b) Calculate the actual area of a farm in hectares, which is represented by 408 cm^2 on the map. [2]

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Question 22

[4 marks]Logarithms
Simplify as far as possible (a) log 9 / log 3, (b) 4 log 2 + log 20 - log 3,2.

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Question 23

[4 marks]Co-ordinate Geometry
(a) A line passes through the points A(2; 4) and B(x; y) and has gradient 1 1/2. Given that B lies on the y-axis, find the coordinates of B. (b) In the diagram, O is the origin, T is the point (8; 0) and R is the point (0; -6). Calculate the area of triangle TOR.

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Question 25

[3 marks]Measures & Mensuration
ABCD is an isosceles trapezium with AD = BC. (a) Given that AD = (2x - 4) cm and BC = (5 - x) cm, form an equation in x and solve it. (b) Given also that AB = (2x + 6) cm and DC = 14 cm, find the numerical value of the perimeter of the trapezium.

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Question 26

[4 marks]Constructions & Loci
In triangle XYZ, YZ = 9,5 cm, XY = 5,2 cm and ZX = 8,3 cm. N is the foot of the perpendicular from X to YZ. Calculate the length of XN, correct to 1 decimal place.

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Question 27

[4 marks]Polygons, Symmetry & Circles
AB, BC and CD are adjacent sides of a regular octagon with centre O. OB = 6 cm and BC is produced to N. Using as much of the information given below as is necessary, calculate (a) angle NBA, [1] (b) angle AOB, [1] (c) the area of triangle AOB. [2] [sin 45° = cos 45° = 0,7; tan 45° = 1]

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Question 301

[2 marks]Factorisation, H.C.F & L.C.M
For the expressions 12m^3n^2 and 18m^2n^3, find (i) the H.C.F, (ii) the L.C.M.

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Question 302

[1 marks]Algebraic Expressions
Simplify 6x + 12x / 3.

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Question 502

[1 marks]Substitution
Given that m = 1/2, n = 0 and r = 3, evaluate (2 1/4)^m.

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Question 503

[1 marks]Substitution
Given that m = 1/2, n = 0 and r = 3, evaluate the r-th root of -64.

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Question 801

[1 marks]Rational, Irrational Numbers & Surds
Simplify sqrt(50), leaving your answer in the form a sqrt(b).

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Question 802

[2 marks]Change of Units
Find, in km/h, the rate at which a car travels if it covers 24 metres in 1 second.

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Question 1101

[1 marks]Linear Equations
Solve the equation 3/y = 12/11.

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Question 1102

[2 marks]Quadratic Equations
Solve the equation x^2 + 5x = 24.

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Question 1201

[1 marks]Trigonometry, Bearing & Distances
In the diagram, angle ABC = angle ADC = 90 degrees, AB = BC = 5 cm and AD = 7 cm. Write down the value of tan BAC.

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Question 1202

[2 marks]Trigonometry, Bearing & Distances
In the diagram, angle ABC = angle ADC = 90 degrees, AB = BC = 5 cm and AD = 7 cm. Calculate the length of the line DC.

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Question 1501

[1 marks]Inequalities & Linear Programming
Given that x >= 0,5, state the least possible value of x if x is a prime number.

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Question 1502

[2 marks]Inequalities & Linear Programming
The diagram shows the region defined by three inequalities, two of which are x >= 0 and y >= 0. Find the third inequality.

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Question 1701

[1 marks]Trigonometry, Bearing & Distances
P, Q and R are three points on level ground. The bearing of R from Q is 160 degrees, the bearing of P from R is 300 degrees and angle QPR = 50 degrees. Find the three-figure bearing of Q from R.

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Question 1702

[2 marks]Trigonometry, Bearing & Distances
P, Q and R are three points on level ground. The bearing of R from Q is 160 degrees, the bearing of P from R is 300 degrees and angle QPR = 50 degrees. Find the three-figure bearing of Q from P.

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Question 2101

[1 marks]Similarity & Congruency
In the diagram, AEXD and BFXC are straight lines. AE = 2 cm, EX = 4 cm, XD = 6 cm and CD = 7 1/2 cm. AB, EF and CD are parallel. Name, in correct order, the triangle which is congruent to triangle XCD.

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Question 2102

[1 marks]Similarity & Congruency
In the diagram, AEXD and BFXC are straight lines, AE = 2 cm, EX = 4 cm, XD = 6 cm, CD = 7 1/2 cm and AB, EF and CD are parallel. Name, in correct order, the triangle which is similar to but not congruent to triangle XCD.

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Question 2103

[2 marks]Similarity & Congruency
In the diagram, AEXD and BFXC are straight lines, AE = 2 cm, EX = 4 cm, XD = 6 cm, CD = 7 1/2 cm and AB, EF and CD are parallel. Find the length of EF.

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Question 2401

[2 marks]Change of Subject of Formula
It is given that t = 2 pi sqrt(d/g). Find t when pi = 22/7, d = 490 and g = 10.

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Question 2402

[2 marks]Change of Subject of Formula
It is given that t = 2 pi sqrt(d/g). Make d the subject of the formula.

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Question 2801

[1 marks]Circle Geometry
In the diagram, COE is a diameter of the circle ABCDE, centre O and TA is a tangent to the circle at A. angle TAE = 60, angle ODC = 40 and arc AB = arc BC. Find angle CBE.

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Question 2802

[1 marks]Circle Geometry
In the diagram, COE is a diameter of the circle ABCDE, centre O and TA is a tangent to the circle at A. angle TAE = 60, angle ODC = 40 and arc AB = arc BC. Find angle ABE.

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Question 2803

[2 marks]Circle Geometry
In the diagram, COE is a diameter of the circle ABCDE, centre O and TA is a tangent to the circle at A. angle TAE = 60, angle ODC = 40 and arc AB = arc BC. Find angle BEC.

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Question 2804

[1 marks]Circle Geometry
In the diagram, COE is a diameter of the circle ABCDE, centre O and TA is a tangent to the circle at A. angle TAE = 60, angle ODC = 40 and arc AB = arc BC. Find angle EOD.

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Question 2901

[2 marks]Trigonometry, Bearing & Distances
In the diagram BCD is a straight line, AB = 8 cm, AC = 5 cm, CD = 6 cm and angle ACB = 23,6 degrees. Using as much of the information given below as is necessary, calculate the value of sin ABC, giving your answer as a common fraction in its lowest terms. [sin 23,6 = 0,40; cos 23,6 = 0,92; tan 23,6 = 0,44]

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Question 2902

[3 marks]Trigonometry, Bearing & Distances
In the diagram BCD is a straight line, AB = 8 cm, AC = 5 cm, CD = 6 cm and angle ACB = 23,6 degrees. Calculate AD^2. [sin 23,6 = 0,40; cos 23,6 = 0,92; tan 23,6 = 0,44]

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Question 10101

[1 marks]Approximations & Estimations
Express 0.096 correct to two decimal places.

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Question 50102

[1 marks]Substitution
Given that m = 1/2, n = 0 and r = 3, evaluate (mr)^n.

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