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ZIMSEC O Level · 4008/1, 4028/1 · N2000

Mathematics Paper 1 November 2000

Questions
63
Total marks
93
Time allowed
150 min
Syllabus code
4008/1, 4028/1

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Questions
63
Pass mark
38
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Answer every question in the printed order, get marked at the end, then see the answers.

The questions

Question 101

[1 marks]Number
Evaluate, giving your answer in decimal form, 1,549−0,072671,549 - 0,07267.

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Question 102

[1 marks]Number
Express as a fraction in its lowest terms, 38−29\frac{3}{8} - \frac{2}{9}.

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Question 103

[1 marks]Number
Express as a fraction in its lowest terms, 516+712\frac{5}{16} + \frac{7}{12}.

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Question 201

[1 marks]Algebra
Given that p=5p=5, q=−2q=-2 and r=1r=1, find the value of pq2rpq^2r.

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Question 202

[2 marks]Algebra
Given that p=5p=5, q=−2q=-2 and r=1r=1, find the value of 13−2(q−p)13-2(q-p).

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Question 301

[1 marks]Time
In terms of time, Japan is 7 hours ahead of Zimbabwe when Britain is 2 hours behind Zimbabwe. Calculate the difference in time between Britain and Japan.

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Question 302

[1 marks]Time
Japan is 7 hours ahead of Zimbabwe and Britain is 2 hours behind Zimbabwe. It is 1135 in Zimbabwe. Giving your answer as time on the 24 hour clock, calculate the time in Britain.

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Question 303

[1 marks]Time
Japan is 7 hours ahead of Zimbabwe and Britain is 2 hours behind Zimbabwe. It is 1135 in Zimbabwe. Giving your answer as time on the 24 hour clock, calculate the time in Japan.

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Question 401

[2 marks]Number
Calculate the highest common factor (H.C.F) of the three numbers 18, 30 and 42.

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Question 402

[1 marks]Number
Three uniform rods have lengths of 1,8m, 3,0m and 4,2m. Kuda cuts pieces of equal length from each of the rods. State the greatest possible length of each piece.

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Question 502

[2 marks]Sets
In the diagram, A, B and C are three overlapping sets drawn inside a rectangle representing the universal set. Use set notation to describe the shaded region shown in the diagram.

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Question 601

[1 marks]Approximations & Estimations
The number of pupils at a school, to the nearest 10, is 450. State the greatest possible number of pupils at the school.

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Question 602

[1 marks]Prime Numbers, Sequences & Types of Numbers
A magic square is an array of numbers with the special property that the sum of all the numbers in a row, or column, or along a diagonal, is always the same. This sum is called the magic number of the square. In the magic square with rows (401, 227, 179), (P, 269, 491) and (359, 311, 137), calculate the magic number of the square.

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Question 603

[1 marks]Prime Numbers, Sequences & Types of Numbers
Using the magic square with rows (401, 227, 179), (P, 269, 491) and (359, 311, 137), calculate the value of P.

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Question 701

[1 marks]Algebra
Simplify a3b4a4b2c\frac{a^3b^4}{a^4b^2c}.

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Question 702

[2 marks]Algebra
Solve the equation m2+7m−18=0m^2 + 7m - 18 = 0.

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Question 801

[2 marks]Ratios, Rates & Proportions
An orange syrup was diluted with water in the ratio 1:5 respectively. The volume of the orange syrup used was 350ml. Calculate the volume of the diluted drink.

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Question 802

[1 marks]Ratios, Rates & Proportions
An orange syrup was diluted with water in the ratio 1:5 respectively. The volume of the orange syrup used was 350ml, giving 2100ml of diluted drink. Calculate the number of people who can be served, if each is given exactly 80ml of the diluted drink.

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Question 901

[1 marks]Ordinary & Standard Form
A number in standard form is 6,714×10236,714 \times 10^{23}. State the number of zeros in the number when it is written in ordinary form.

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Question 902

[1 marks]Ordinary & Standard Form
A number in standard form is 6,714×10236,714 \times 10^{23}. Express in standard form twice the number.

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Question 903

[1 marks]Ordinary & Standard Form
A number in standard form is 6,714×10236,714 \times 10^{23}. Express in standard form one-millionth of the number.

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Question 1001

[1 marks]Number Bases
Convert 100121001_2 to a number in base ten.

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Question 1002

[1 marks]Number Bases
Subtract 32532_5 from 41541_5, giving your answer in base five.

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Question 1003

[1 marks]Number Bases
Convert 27 to a number in base five.

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Question 1101

[1 marks]Matrices
Evaluate (4  2)(5−17)(4\ \ 2)\begin{pmatrix}5\\-17\end{pmatrix}.

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Question 1102

[2 marks]Matrices
Express 3(26−14)−12(−6208)3\begin{pmatrix}2&6\\-1&4\end{pmatrix} - \frac{1}{2}\begin{pmatrix}-6&2\\0&8\end{pmatrix} as a single matrix.

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Question 1201

[2 marks]Functional Graphs
The graph shows straight lines l1l_1 and l2l_2 intersecting at A(2,6). O is the origin. Line l1l_1 cuts the x-axis at C(8,0), and line l2l_2 cuts the x-axis at B(-2,0). Find the area of triangle ABC.

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Question 1301

[1 marks]Laws of Indices
Evaluate −80-8^0.

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Question 1302

[2 marks]Laws of Indices
Evaluate log⁡432+log⁡42\log_4 32 + \log_4 2.

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Question 1401

[1 marks]Inequalities
Given that −5≤x≤1-5 \le x \le 1 and 6≤y≤176 \le y \le 17, find the greatest value of y−xy-x.

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Question 1402

[2 marks]Inequalities
Given that −5≤x≤1-5 \le x \le 1 and 6≤y≤176 \le y \le 17, find the least value of x3−yx^3-y.

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Question 1501

[1 marks]Scales & Simple Map Problems
A map is enlarged in the ratio 2:1. The original scale was 1:250 000. Calculate the new scale in the form 1:n.

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Question 1502

[2 marks]Scales & Simple Map Problems
A map is enlarged in the ratio 2:1. The original scale was 1:250 000. A lake has an area of 56cm² on the original map. Calculate the area of the lake on the enlarged map.

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Question 1601

[1 marks]Trigonometry, Bearing & Distances
In the diagram, ABC is a triangle and AD is perpendicular to BC produced. AC=5cm, AD=3cm, BC=7cm and CD=4cm. Find, as a common fraction, sin⁡AC^B\sin A\hat{C}B.

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Question 1602

[1 marks]Trigonometry, Bearing & Distances
In the diagram, ABC is a triangle and AD is perpendicular to BC produced. AC=5cm, AD=3cm, BC=7cm and CD=4cm. Find, as a common fraction, tan⁡AC^B\tan A\hat{C}B.

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Question 1603

[1 marks]Trigonometry, Bearing & Distances
In the diagram, ABC is a triangle and AD is perpendicular to BC produced. AC=5cm, AD=3cm, BC=7cm and CD=4cm. Write down the ratio of the area of triangle ABC to the area of triangle ACD, in its simplest form.

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Question 1702

[1 marks]Vector Geometry
In the diagram, OA→=a\overrightarrow{OA}=\mathbf{a} and OB→=b\overrightarrow{OB}=\mathbf{b}. The points C and D are also shown on the diagram. Write down OC→\overrightarrow{OC} in terms of a\mathbf{a} and b\mathbf{b}.

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Question 1801

[1 marks]Circle Geometry
P, Q, R and S are points on a circle, centre O. TS is the tangent to the circle and TPQ is a straight line that cuts the circle at P and Q. ST is parallel to RP. ST^P=26°S\hat{T}P=26° and SO^R=134°S\hat{O}R=134°. Calculate SP^RS\hat{P}R.

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Question 1802

[1 marks]Circle Geometry
P, Q, R and S are points on a circle, centre O. TS is the tangent to the circle and TPQ is a straight line that cuts the circle at P and Q. ST is parallel to RP. ST^P=26°S\hat{T}P=26° and SO^R=134°S\hat{O}R=134°. Calculate OS^PO\hat{S}P.

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Question 1803

[2 marks]Circle Geometry
P, Q, R and S are points on a circle, centre O. TS is the tangent to the circle and TPQ is a straight line that cuts the circle at P and Q. ST is parallel to RP. ST^P=26°S\hat{T}P=26° and SO^R=134°S\hat{O}R=134°. Calculate SP^TS\hat{P}T.

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Question 1901

[2 marks]Speed, distance and time
A sign post at a junction on the Bulawayo-Beitbridge road shows Bulawayo 66km in one direction, and Beitbridge 255km with Gwanda in the other direction. Calculate the distance between Gwanda and Beitbridge, given that Gwanda is 126km from Bulawayo.

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Question 1902

[2 marks]Speed, distance and time
A sign post at a junction on the Bulawayo-Beitbridge road shows Bulawayo 66km in one direction, and Beitbridge 255km in the other. Calculate the time taken by a motorist who travelled between Bulawayo and Beitbridge at an average speed of 107km/h.

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Question 2001

[2 marks]Change of Units
Express 1,5g/cm³ in kg/m³.

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Question 2002

[2 marks]Functional Notation
Given that f(x)=kx2+5x+6f(x)=kx^2+5x+6, calculate the value of k given that f(3)=−60f(3)=-60.

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Question 2101

[1 marks]Trigonometry, Bearing & Distances
A plane is flying on a bearing of 293°. It then changes direction through 83° anticlockwise. Calculate its new bearing.

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Question 2102

[1 marks]Polygons, Symmetry & Circles
In the diagram, AB and BC are adjacent sides of a square. AB and BX are adjacent sides of a regular n-sided polygon. Given that CB^X=126°C\hat{B}X=126°, calculate reflex CB^XC\hat{B}X.

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Question 2103

[1 marks]Polygons, Symmetry & Circles
In the diagram, AB and BC are adjacent sides of a square. AB and BX are adjacent sides of a regular n-sided polygon. Given that CB^X=126°C\hat{B}X=126°, calculate the exterior angle of the n-sided polygon.

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Question 2104

[1 marks]Polygons, Symmetry & Circles
In the diagram, AB and BC are adjacent sides of a square. AB and BX are adjacent sides of a regular n-sided polygon. Given that CB^X=126°C\hat{B}X=126°, calculate the value of n.

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Question 2202

[3 marks]Polygons, Symmetry & Circles
The parallel sides of an isosceles trapezium are of lengths 8cm and 18cm, and its perpendicular height is 12cm. Calculate the length of one of the non-parallel sides.

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Question 2301

[1 marks]Prime Numbers, Sequences & Types of Numbers
Study the pattern: Line 1: 2+3=52+3=5; Line 2: 2+6=82+6=8; Line 3: 2+9=112+9=11. Use the pattern to write down line 6.

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Question 2302

[1 marks]Prime Numbers, Sequences & Types of Numbers
Study the pattern: Line 1: 2+3=52+3=5; Line 2: 2+6=82+6=8; Line 3: 2+9=112+9=11; ...; Line n: 2+b=x2+b=x. Write down the value of b in terms of n.

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Question 2401

[2 marks]Measures & Mensuration
Figure A and Figure B have the same volume. Figure A is a cone of base radius 9cm and height 28cm. Taking π=227\pi=\frac{22}{7}, calculate the volume of the cone.

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Question 2402

[2 marks]Measures & Mensuration
Figure A and Figure B have the same volume (2376 cm³). Figure B is a prism whose length is 22cm, and whose cross-section is a right-angled isosceles triangle with the base and the height each equal to x cm. Calculate the value of x, leaving your answer in surd form.

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Question 2501

[2 marks]Measures & Mensuration
A rectangular concrete slab is 4m long, 1½m wide and 20cm thick. Calculate the total surface area of the slab, giving your answer in cm².

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Question 2502

[2 marks]Consumer Arithmetic
A rectangular concrete slab is 4m long, 1½m wide and 20cm thick, with total surface area 142 000 cm². The whole slab is to be painted at a cost of $15,00 per square metre. Calculate the cost of painting the slab.

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Question 2601

[2 marks]Fractions, Decimals & Percentages
A discount of 15% is given on all goods that are sold for cash in a shop. Calculate the cash price of an article that has a marked price of $68,00.

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Question 2602

[2 marks]Fractions, Decimals & Percentages
The price of a magazine was $16,50 in 1999. Given that this was an increase of 10% from the 1998 price, calculate the price of the magazine in 1998.

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Question 2701

[1 marks]Kinematics
The diagram shows the speed-time graph of a train which retards in two stages until it comes to rest after a time of t seconds: speed falls from 40 m/s to 10 m/s over the first 60 seconds, then falls from 10 m/s to rest. Calculate the retardation of the train during the first 60 seconds.

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Question 2702

[2 marks]Kinematics
The diagram shows the speed-time graph of a train which retards in two stages: speed falls from 40 m/s to 10 m/s over the first 60 seconds, then falls from 10 m/s to rest. Calculate the distance that the train covers in the first 60 seconds.

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Question 2703

[3 marks]Kinematics
The diagram shows the speed-time graph of a train which retards in two stages, from 40 m/s to 10 m/s over the first 60 seconds and then to rest after a further time. Given that the train covers a total distance of 3000m during the whole period of retardation, calculate the value of t, the total time taken to come to rest.

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Question 2801

[2 marks]Statistics & Probability
The table shows the frequency distribution of the number of instruments each member of a band could play: 1 instrument has frequency x, 2 instruments has frequency 10, 3 instruments has frequency 5, 4 instruments has frequency y, and 5 instruments has frequency 1. Given that the total number of people in the band is 30, use this information to form an equation in terms of x and y.

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Question 2802

[2 marks]Statistics & Probability
The table shows the frequency distribution of the number of instruments each member of a band could play: 1 instrument has frequency x, 2 instruments has frequency 10, 3 instruments has frequency 5, 4 instruments has frequency y, and 5 instruments has frequency 1, with a total of 30 people. Given further that the mean of the distribution is 2,1, form another equation in terms of x and y.

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Question 2803

[3 marks]Statistics & Probability
Solve the two simultaneous equations x+y=14x+y=14 and x+4y=23x+4y=23, formed from a band's instrument-frequency data, to find the values of x and y.

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