ZIMSEC O Level Mathematics Paper 2 November 2014 resit (topical set)

Question 6

[12 marks]Constructions & Loci

Answer the whole of this question on a sheet of plain paper. Use ruler and compasses only for all constructions and show clearly all construction lines and arcs. All constructions should be done on a single diagram. (a) Construct a quadrilateral ABCD in which AB = 8,5 cm, AD = 7 cm, DC = 5 cm, angle ADC = 90 degrees and angle BAD = 60 degrees. [6] (b) Measure and write down the length of BC. [1] (c) Construct the locus of a point (i) that is 4,5 cm from B, (ii) X, on the same side of AD as C, such that the area of triangle ACD = area of triangle AXD. [3] (d) Mark and label X1 and X2, the points that are 4,5 cm from B and are such that the area of triangle AX1D = the area of triangle AX2D. [2]

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Question 11

[4 marks]Polygons, Symmetry & Circles

(b) The sum of the interior angles of an n-sided polygon is 6 120°. Find the value of n. [2] (c) If three of the angles of a heptagon are 162°, 150° and 132° and the rest of the angles are equal, calculate the size of each of the equal angles. [2]

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Question 102

[2 marks]Measures & Mensuration

A car tank holds 22 1/2 litres of fuel when it is 3/8 full. Calculate the amount of fuel when it is full.

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Question 103

[1 marks]Factorisation, H.C.F & L.C.M

Find the H.C.F (Highest Common Factor) of 3 x 5^2 x 7^2 and 3^2 x 5^2 x 7^2 x 11, leaving the answer in index form.

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Question 104

[3 marks]Ordinary & Standard Form

Given that x = 2.25 x 10^6 and y = 4 x 10^-20, find the numerical value of sqrt(x/y), giving the answer in standard form.

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Question 201

[4 marks]Factorisation, H.C.F & L.C.M

Factorise completely (i) 9m^2 - 3m - 6, (ii) (y + x)^2 - 4.

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Question 301

[2 marks]Consumer Arithmetic

Jane sells airtime every day. During weekdays (Monday to Friday) her sales average is $22 per day and during weekends (Saturday and Sunday) her sales average is $29 per day. Calculate her average daily sales for a week. [2]

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Question 303

[4 marks]Points, Lines & Angles

In the diagram, ABC is an isosceles triangle with AB = AC and angle ABC = 68°. ACD is parallel to PBQ. Calculate (i) angle BCD, (ii) angle PBA.

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Question 401

[2 marks]Sets

Write down, in set notation and in terms of P, Q and R, the set that is represented by the shaded part in the Venn diagram. The shading is the part of the large outer set that lies outside the other large set; the small set lies wholly inside the unshaded region.

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Question 403

[5 marks]Quadratic Equations

Solve the equation 2x^2 + 3x - 84 = 0, giving the answers correct to 2 decimal places.

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Question 501

[4 marks]Change of Subject of Formula

Given that A = P + PRT/100, (i) calculate A when P = 350, T = 1 1/2 and R = 5. (ii) make P the subject of the formula.

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Question 701

[6 marks]Matrices

It is given that P = (3 5; 4 x) and Q = (-2; 3). (a) Find PQ in terms of x. (b) Find the value of x that makes |P| = 7. (c) Hence write down P^-1.

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Question 702

[6 marks]Vector Geometry

In the diagram, BT and AS produced meet at O. OA = a, AB = b - a and OS/OA = 1/4. (i) Express 1. OB in terms of a and/or b in its simplest form, 2. OS in terms of a and/or b in its simplest form. (ii) It is also given that ST = k AB. 1. Express OT in terms of a, b and k in its simplest form, 2. Given that OT = h OB, use the results in (b)(ii)1 to find the numerical value of k. (iii) Hence, express ST in terms of a and b. [6]

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Question 801

[1 marks]Functional Graphs

The following is an incomplete table of values for y = 2x^2 + 5x - 3, with x = -3 1/2, -3, -2, -1, 0, 1/2, 1 giving y = 4, 0, P, -6, -3, 0, 4. Find the value of P.

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Question 802

[4 marks]Functional Graphs

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

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Question 901

[2 marks]Measures & Mensuration

The trapezium PQRS, in which QR is parallel to PS, is such that PS = 11 cm, PQ = 5 cm and angle QPS = 90 degrees. If the area of the trapezium is 45 cm^2, find the length of QR.

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Question 902

[4 marks]Variation

It is given that d varies jointly as e^2 and f. If d = 5 when e = 3 and f = 2, find (i) the formula for d in terms of e and f, (ii) the value of d when e = 2 and f = 3. [4]

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Question 1001

[4 marks]Measures & Mensuration

Use 22/7 for pi. The diagram shows two semi-circles with diameters 7 cm and 14 cm, the smaller one drawn on the left half of the diameter of the larger one and the region between them shaded. Calculate (i) the area of the shaded part, (ii) the perimeter of the shaded part.

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Question 1101

[3 marks]Prime Numbers, Sequences & Types of Numbers

Study the number pattern below: 2 ; 3 ; 5 ; 9 ; 17 ; ... Write down (i) the next two numbers, (ii) the formula that is used to get the next number, (r th term) in terms of r.

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Question 1104

[5 marks]Probability

John had four $1 notes and five $2 notes in his pocket. He wanted to buy an item costing $2. He just pulled out two notes, one after another, without first checking. Find the probability that he pulled out notes that (i) were worth the same value, (ii) added up to more than the price of the item.

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Question 1202

[2 marks]Trigonometry, Bearing & Distances

From P, the angle of elevation of the top of a vertical mast at Q is 31 degrees, where PQ = 100 m. Calculate the height of the mast to the nearest 10 m.

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Question 10101

[2 marks]Measures & Mensuration

Simplify: 10 hrs 25 min 42 sec + 8 hrs 41 min 30 sec.

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Question 10102

[3 marks]Fractions, Decimals & Percentages

2 1/4 ÷ (2 1/16 - 3/4), giving the answer as a mixed number in its simplest form.

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Question 20201

[3 marks]Algebraic Fractions

Express 2/(x + 2) - 1/3 as a single fraction in its simplest form.

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Question 20202

[5 marks]Linear Equations

(a) Express 2/(x + 2) - 1/3 as a single fraction in its simplest form. (b) Hence or otherwise solve the equation 2/(x + 2) - 1/3 = -1/5.

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Question 30201

[2 marks]Trigonometry, Bearing & Distances

Triangle ABC is right-angled at B. AB = 2,5 cm, BC = 6 cm and the perpendicular from B meets AC at D. Find the length of AC.

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Question 30202

[2 marks]Trigonometry, Bearing & Distances

Triangle ABC is right-angled at B. AB = 2,5 cm, BC = 6 cm and the perpendicular from B meets AC at D. Find the length of BD.

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Question 40201

[3 marks]Inequalities

Solve the inequality x - 3 < 4 - 2x <= x + 13.

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Question 40202

[2 marks]Inequalities

Illustrate your solution of x - 3 < 4 - 2x <= x + 13 on a number line.

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Question 50201

Circle Geometry

In the diagram, ABCD is a circle with centre O and diameter AOC. Line AOC meets BD at T, making angle ATB = 70 and angle BDC = 43. Calculate angle BAC.

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Question 50202

Circle Geometry

In the diagram, ABCD is a circle with centre O and diameter AOC. Line AOC meets BD at T, making angle ATB = 70 and angle BDC = 43. Calculate angle DBC.

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Question 50203

Circle Geometry

In the diagram, ABCD is a circle with centre O and diameter AOC. Line AOC meets BD at T, making angle ATB = 70 and angle BDC = 43. Calculate angle BAD.

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Question 50204

Circle Geometry

In the diagram, ABCD is a circle with centre O and diameter AOC. Line AOC meets BD at T, making angle ATB = 70 and angle BDC = 43. Write down the triangle that is similar to triangle ATB.

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Question 50205

Circle Geometry

In the diagram, ABCD is a circle with centre O and diameter AOC. Line AOC meets BD at T, making angle ATB = 70 and angle BDC = 43. If AT/DT = 3/2, find the ratio (area of triangle BAT)/(area of triangle DCT).

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Question 80301

[2 marks]Functional Graphs

Use your graph of y = 2x^2 + 5x - 3 to find the equation of the line of symmetry.

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Question 80302

[2 marks]Functional Graphs

Use your graph of y = 2x^2 + 5x - 3 to find the gradient of the curve when x = 0.

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Question 80303

[2 marks]Functional Graphs

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

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Question 80304

[1 marks]Functional Graphs

Use your graph to estimate the area bounded by the curve y = 2x^2 + 5x - 3, the axes and the line x = -1.

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Question 90301

[3 marks]Inequalities & Linear Programming

A region R is defined by four inequalities. One of them is

y<x+1

. The other three boundaries are the line

x=-1

, the line

y=-1

and the line through

(0; 2)

and

(2; 0)

. The point

(0; 0)

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

(0; 2)

and

(2; 0)

contributes.

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Question 90302

[3 marks]Inequalities & Linear Programming

The region R is defined by

x\geq-1

y\geq-1

y<x+1

and

x+y\leq2

. Find the maximum value of

3x+2y

, where

x

and

y

are integers.

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Question 100201

[2 marks]Geometrical Transformation

Triangle ABC has vertices A(4; 1), B(6; 1) and C(6; 2). Calculate the area of triangle ABC.

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Question 100202

[2 marks]Geometrical Transformation

Triangle ABC has vertices A(4; 1), B(6; 1) and C(6; 2). Transformation T represents a translation vector (-2; -6). Draw and label A1B1C1, the image of triangle ABC under T.

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Question 100203

[2 marks]Geometrical Transformation

Triangle ABC has vertices A(4; 1), B(6; 1) and C(6; 2). Transformation R represents a clockwise rotation of 90 degrees about (4; 4). Draw and label triangle A2B2C2, the image of triangle ABC under R.

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Question 100204

[1 marks]Geometrical Transformation

Triangle A3B3C3 has vertices at A3(8; 2), B3(12; 2) and C3(12; 4). State the coordinates of the midpoint of A3B3.

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Question 120101

[2 marks]Trigonometry, Bearing & Distances

In the diagram are three points P, Q and R on level ground. Q is 100 m away from P on a bearing of N68 degrees E. R is on a bearing of N40 degrees W from P and the distance between R and Q is 150 m. Calculate the distance that Q is to the east of P.

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Question 120102

[3 marks]Trigonometry, Bearing & Distances

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Question 120103

[3 marks]Trigonometry, Bearing & Distances

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Question 120104

[2 marks]Trigonometry, Bearing & Distances

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Mathematics Paper 2 November 2014 resit (topical set)

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The questions

Question 6

Question 11

Question 102

Question 103

Question 104

Question 201

Question 301

Question 303

Question 401

Question 403

Question 501

Question 701

Question 702

Question 801

Question 802

Question 901

Question 902

Question 1001

Question 1101

Question 1104

Question 1202

Question 10101

Question 10102

Question 20201

Question 20202

Question 30201

Question 30202

Question 40201

Question 40202

Question 50201

Question 50202

Question 50203

Question 50204

Question 50205

Question 80301

Question 80302

Question 80303

Question 80304

Question 90301

Question 90302

Question 100201

Question 100202

Question 100203

Question 100204

Question 120101

Question 120102

Question 120103

Question 120104

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The answers, and why they are the answers

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