ZIMSEC O Level Mathematics Paper 2 November 2016 (topical set)

Question 5

[10 marks]Constructions & Loci

Use ruler and compasses only for all constructions and show clearly all the construction lines and arcs. (a) On a single diagram, construct (i) triangle PQR in which PR = 9 cm, PQ = 7 cm and angle QPR = 45 degrees, [3] (ii) the locus of points which are equidistant from PQ and PR, [2] (iii) the locus of points which are equidistant from P and Q, [2] (iv) mark and label clearly, the point X which is equidistant from PQ and PR and is also equidistant from P and R. [1] (b) Measure and write down (i) the length of XR, [1] (ii) angle PRQ. [1]

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Question 7

[12 marks]Measures & Mensuration

The diagram shows a trough in the form of a prism whose cross section ABCD is a trapezium with AD parallel to BC and the measurements are in centimetres. AD = 40, BC = 21, AB = 18, the perpendicular height from BC to AD is 14 and the trough is 90 long. (a)(i) Calculate the area of the cross-section ABCD of the trough. (ii) Calculate the capacity of the trough when full. (b) The inside of the trough is to be painted. One litre of the paint covers an area of 1 496 cm^2. (i) Calculate the area of the trough to be painted. (ii) Calculate the number of litres of paint needed to paint the inside of the trough to the nearest litre. (iii) Calculate the cost of the paint if one litre of the paint costs $6,30.

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Question 101

[2 marks]Algebraic Expressions

Remove the brackets and simplify (a - b)(2a - b).

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Question 102

[3 marks]Fractions, Decimals & Percentages

Simplify 2 1/4 ÷ (1 1/4 + 3 1/3).

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Question 103

[4 marks]Algebraic Fractions

Express as a single fraction in its simplest form (2x + 9)/7 - (x + 1)/28.

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Question 104

[2 marks]Consumer Arithmetic

A trader sold a bicycle for $84 and made a profit of 40% on the cost price. Calculate the cost price of the bicycle. [2]

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Question 201

[5 marks]Matrices

It is given that M = (3 9; 2 7) and N = (5 -1; 4 -6). (i) Find M^-1, the inverse of matrix M. (ii) Find matrix P such that 2P + N = (7 3; 4 -4).

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Question 202

[3 marks]Change of Subject of Formula

Given that x = y + sqrt(m + x^2), make m the subject of the formula.

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Question 203

[3 marks]Ratios, Rates & Proportions

If Mrs. Pindo pays with a R100 note for an item worth US$2.20, she gets US$10.40 change. Calculate the exchange rate in the form R n : US$ where n is correct to 2 decimal places.

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Question 301

[4 marks]Points, Lines & Angles

In the diagram, MNC is a triangle in which angle MNC = 64°. A is a point inside the triangle such that AM = AC, angle AMN = 42°, angle ACN = 26°, angle AMC = x° and angle CAM = y°. (i) Find the value of y, [2] (ii) Find the value of x. [2]

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Question 302

[6 marks]Vector Geometry

Points P(-3 ; 1), Q(3 ; 4) and R are on a Cartesian plane. (i) Find PQ. [1] (ii) If PR = (2; -6), find the coordinates of R. [2] (iii) Find the equation of the line PQ. [3]

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Question 401

[3 marks]Linear Equations

Solve the equation 3/(x + 7) - 1/(x + 2) = 0.

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Question 601

[2 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ADP is right-angled at P. AP = (x - 7) cm, AD = (x + 2) cm and DP = x cm. Form an equation in x and show that it reduces to x^2 - 18x + 45 = 0.

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Question 602

[3 marks]Trigonometry, Bearing & Distances

Solve the equation x^2 - 18x + 45 = 0.

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Question 603

[1 marks]Trigonometry, Bearing & Distances

In the diagram, triangle ADP is right-angled at P. AP = (x - 7) cm, AD = (x + 2) cm and DP = x cm, where x satisfies x^2 - 18x + 45 = 0. Hence write down the length of AP.

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Question 802

[1 marks]Statistics & Probability

The table shows the cumulative frequency of the results of a Physics examination taken by 40 candidates.
mark (%): x < 40, x < 45, x < 50, x < 55, x < 60, x < 65, x < 70, x < 75, x < 80
cumulative frequency: 0, 3, 10, n, 31, 36, 38, 39, 40
Find the value of n.

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Question 803

[4 marks]Statistics & Probability

The cumulative frequency of the results of a Physics examination taken by 40 candidates is:
mark (%): x < 40, x < 45, x < 50, x < 55, x < 60, x < 65, x < 70, x < 75, x < 80
cumulative frequency: 0, 3, 10, 22, 31, 36, 38, 39, 40
Find the number of candidates who scored 60 marks or more.

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Question 901

[7 marks]Measures & Mensuration

In the diagram, VABCD is a right pyramid on a rectangular base ABCD. O is the centre of the rectangle ABCD with AB = 7 cm, BC = 24 cm and VO = 30 cm. (i) Calculate the length of the diagonal AC. (ii) Calculate the length of the edge VA. (iii) Calculate the angle which the edge VA makes with the horizontal plane ABCD.

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Question 902

[5 marks]Variation

A workman's weekly income is made up of a fixed weekly wage and overtime wage which varies directly as the number of hours of overtime that he works. If he works 6 hours overtime, his weekly income is $96. If he works 8 hours overtime, his weekly income is $103. Find the workman's fixed weekly wage. [5]

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Question 1001

[1 marks]Functional Graphs

The table of values is for the function y = 5 - 3x - 2x^2, with x = -3, -2, -1, 0, 1, 2, 3 giving y = p, 3, 6, 5, 0, -9, -22. Find the value of p.

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Question 1101

[5 marks]Trigonometry, Bearing & Distances

In the diagram, C is 8,3 km on a bearing of 142 degrees from V. D is 6,2 km on a bearing of 264 degrees from V. Calculate the length of CD.

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Question 1102

[5 marks]Trigonometry, Bearing & Distances

In the diagram, C is 8,3 km on a bearing of 142 degrees from V. D is 6,2 km on a bearing of 264 degrees from V. Calculate the bearing of D from C, correct to the nearest degree.

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Question 1103

[2 marks]Trigonometry, Bearing & Distances

In the diagram, C is 8,3 km on a bearing of 142 degrees from V. D is 6,2 km on a bearing of 264 degrees from V. Calculate the distance that D is to the west of C.

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Question 1202

[2 marks]Geometrical Transformation

Triangle P has vertices at (1; 2), (3; 2) and (5; 4) and triangle V has vertices at (-1; -2), (-3; -2) and (-5; -4). Describe fully the single transformation which maps triangle P onto triangle V.

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Question 40201

[1 marks]Circle Geometry

In the diagram, A, B, C and D are points on the circumference of a circle centre O. P is a point on BD such that OP is parallel to AB and APC is a straight line. TA is a tangent to the circle at A where angle BAT = 28 and angle APB = 46. Calculate angle ADB.

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Question 40202

[2 marks]Circle Geometry

In the diagram, A, B, C and D are points on the circumference of a circle centre O, and AOD is a straight line. P is a point on BD such that OP is parallel to AB and APC is a straight line. TA is a tangent to the circle at A where angle BAT = 28 and angle APB = 46. Calculate angle BAP.

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Question 40203

[2 marks]Circle Geometry

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Question 40204

[2 marks]Circle Geometry

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Question 60201

[2 marks]Inequalities & Linear Programming

The unshaded region R of a graph is bounded by four straight lines:

x=1

y=3

, the line through

(0; 15)

and

(5; 0)

, and the line through

(2; 2)

and

(5; 10)

. The point

(2; 5)

lies inside R. Write down the inequality that the line through

(0; 15)

and

(5; 0)

contributes, in the form

3x+y\ldots

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Question 60202

[2 marks]Inequalities & Linear Programming

A region R is defined by

x\geq1

y\geq3

3x+y\leq15

and

3y\geq8x-10

. Find the greatest possible value of

x+y

, given that

x

and

y

are integers.

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Question 80101

[1 marks]Statistics & Probability

The table shows the results of 40 candidates' marks in a Physics examination.
mark (%): 35-40, 40-45, 45-50, 50-55, 55-60, 60-65, 65-70, 70-75, 75-80
frequency: 0, 3, 7, 12, 9, 5, m, 1, 1
Find the value of m.

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Question 80102

[3 marks]Statistics & Probability

The table shows the results of 40 candidates' marks in a Physics examination.
mark (%): 35-40, 40-45, 45-50, 50-55, 55-60, 60-65, 65-70, 70-75, 75-80
frequency: 0, 3, 7, 12, 9, 5, 2, 1, 1
Calculate the approximate mean mark for these candidates correct to the nearest whole number.

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Question 80401

[2 marks]Statistics & Probability

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Question 80402

[2 marks]Statistics & Probability

The cumulative frequency of the results of a Physics examination taken by 40 candidates is:
mark (%): x < 40, x < 45, x < 50, x < 55, x < 60, x < 65, x < 70, x < 75, x < 80
cumulative frequency: 0, 3, 10, 22, 31, 36, 38, 39, 40
Use the graph to find the number of candidates who passed the examination if the pass mark was 49%.

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Question 100201

[4 marks]Functional Graphs

State the coordinates of the point where the graph of y = 5 - 3x - 2x^2 crosses the y axis.

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Question 100202

[1 marks]Functional Graphs

State the coordinates of the point where the line y = 2x - 3 crosses the x axis.

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Question 100301

[2 marks]Functional Graphs

Use the graph to find the gradient of the curve y = 5 - 3x - 2x^2 when x = -2.

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Question 100302

[2 marks]Functional Graphs

Use the graph to solve the equation 5 - 3x - 2x^2 = 0.

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Question 100303

[2 marks]Functional Graphs

Use the graph to solve the equation 5 - 3x - 2x^2 = 2x - 3.

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Question 120101

[1 marks]Geometrical Transformation

Using a scale of 2 cm to represent 2 units on both axes for -8 <= x <= 10 and -8 <= y <= 8, triangle P has vertices at (1; 2), (3; 2) and (5; 4). Draw and label clearly the triangle P.

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Question 120102

[2 marks]Geometrical Transformation

Triangle P has vertices at (1; 2), (3; 2) and (5; 4). Triangle Q is the image of triangle P under a shear of factor -2 with the x-axis invariant. Draw and label clearly the triangle Q.

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Question 120103

[1 marks]Geometrical Transformation

Triangle V has vertices at (-1; -2), (-3; -2) and (-5; -4). Draw and label clearly the triangle V.

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Question 120104

[3 marks]Geometrical Transformation

Triangle P has vertices at (1; 2), (3; 2) and (5; 4). Triangle W is the image of triangle P under a reflection in the line y = x - 2. Draw and label clearly the line y = x - 2 and triangle W.

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Question 120105

[3 marks]Geometrical Transformation

Triangle P has vertices at (1; 2), (3; 2) and (5; 4). Draw and label clearly, the triangle U, the image of triangle P under an enlargement of scale factor -2 with (4; 0) as centre.

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Mathematics Paper 2 November 2016 (topical set)

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The questions

Question 5

Question 7

Question 101

Question 102

Question 103

Question 104

Question 201

Question 202

Question 203

Question 301

Question 302

Question 401

Question 601

Question 602

Question 603

Question 802

Question 803

Question 901

Question 902

Question 1001

Question 1101

Question 1102

Question 1103

Question 1202

Question 40201

Question 40202

Question 40203

Question 40204

Question 60201

Question 60202

Question 80101

Question 80102

Question 80401

Question 80402

Question 100201

Question 100202

Question 100301

Question 100302

Question 100303

Question 120101

Question 120102

Question 120103

Question 120104

Question 120105

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