SUCCESS IN MATHS PAPER 1 & 2 GRADE 8 - 9 THE ONLY REMEDY FOR EXAMINOPHOBIA COMPILED BY MR MUSONDA LAURENT PRICE: K65 WHATSAPP: 0965038377 CONTACT: 0965038377 / 0974794056 EMAIL: laurentmsnd@gmail.com TABLE OF CONTENTS 1. Integers ………………….……………………………………………………..…….………1-2 2. Sets……………………………………………………………………………………………2-6 3. Approximation ……………………………………………………………………………….6-7 4. Ratio and proportion………………………………………………………………………….7-8 5. Index notation……………………………………………………...……………….………...8-9 6. Algebraic expressions…………………………………………….…………………..……..9-10 7. Equations and inequations……………………………………..………………………..…10-12 8. Polygons and angles………………………………………...……………………………..12-16 9. Directions and bearings………………………………………………….………………...17-18 10. Matrices ……………………………………………………………….…………………19-20 11. Similarity and congruency………………………………………………………………..20-22 12. Cartesian plane…………………………………………………………….……………..23-27 13. Relations and Functions………………………………………….…………………….....27-30 14. Mensuration…………………………………………………….………………………...30-34 15. Pythagoras theorem……………………………………………….……………………...34-36 16. Number bases …………………………………………………….……………………...36-39 17. Geometrical construction…………………………………………………………………39-41 18. Social and commercial arithmetic………………………………………………………..41-42 19. Probability……………………………………………………………..…………………43-44 20. Computer…………………………………………………………….…………………...44-47 21. Statistics…………………………………………………………………………………..47-52 22. Additional questions……………………………………………………………………...52-53 1 TOPIC 1: INTEGERS Worked examples 1. Evaluate the following (a) (-5) +(-3) 2. Solve (a) 12× (3) (b) 10+(-4) (b) -16×4 (f) -72÷ (-8) 3. Find the value of (a) 0.06+5 (c) (-14) - (-9) (c) -9× (-8) (d) 3+(-11) (d) 4× -3 (e) 10-(-4) (e) (g) -48÷6 (b) 2.46-1.524 4. Evaluate 20-6×3+8÷2. 5. Evaluate (a) , (b) Answers 1. (a) (-5) +(-3) (b) 2. (a) 12× (3) 36 (f) -72÷ (-8) 9 3. (a) 0.06+5 5.06 (b) -16×4 -64 (g) -48÷6 -8 (b) 2.46-1.524 2.46 1.524 0.936 4. 20-6×3+8÷2 (c) 5. (a) 20-18+4 20-14 6 Compiled and solved by MR. Mununga J (d) (c) -9× (-8) 72 (d) 4× -3 -12 (b) (e) (e) -9 2 Activity Evaluate the following (a) -7+(-6) (b) 8-(-3) (c) -4-(-9) (d) 11+(-17) TOPIC 2: SETS Worked examples 1. given that E= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A= {2, 3, 4, 5}, B= {0, 2, 4, 6, 8, 10} and C= {factors of 10}. (i) Illustrate this information in the Venn diagram below. (ii) List the sets 2. (a) using set notation describe the shaded region shown in the Venn diagram shown in the Venn diagram below. (b) The Venn diagram below shows sets x and y. List the elements of Compiled and solved by MR. Mununga J . 3 3. Given that E= {1, 2, 3, 4, 5, 6, 7, 8, 9}, A= {1, 2, 4, 5}, B= {2, 4, 6, 7} and C= {2, 3, 5, 7, 8} (i) Illustrate this information in the Venn diagram below. (ii) List the elements of the set Answers 1. (i) C= {1, 2, 5, 10} (ii) {0, 3, 4, 6, 8} 2. (a) (b) {a, b, k} 3. (i) (ii) {3, 8} The foundation is the determiner. Justin Mununga Compiled and solved by MR. Mununga J 4 Activity 1. The diagram below shows sets A and B List the sets (a) 2. Given that { and (b) { (c) }, { } }. (i) Illustrate this information in the Venn diagram below. (ii) List the elements of Compiled and solved by MR. Mununga J { } 5 3. In a group of 30 pupils, all play either netball or volleyball. 23 pupils play Netball and 19 play volleyball. (i) Complete the Venn diagram below to illustrate this information. (ii) How many pupils play one game only? 4. (a) In the diagram below shade the region (b) The Venn diagram below shows the number of elements in each region. Find n(A) The activity you are avoiding contains your biggest opportunity. Robin Sharma Compiled and solved by MR. Mununga J 6 }, X { }, Y 5. Given that E={ } Z { (i) Illustrate this information in the Venn diagram below. E X { } and Y Z (ii) List the elements of the set TOPIC 3: APPROXIMATION AND ESTIMATION Worked examples 1. (a) Express 18468.5 in standard form correct to 3 significant figures. (b) Round off 37.86 to the nearest tenth. 2. (a) Express 0.0005426 in standard form correct to 2 decimal places. (b) Write 58.234 correct to one significant figure. (c) How many significant figures has the number 0.4220? (d) Write 74648 to the nearest 1000. 3. write 2736.4 in standard form correct to 3 significant figures. Answers 1. (a) 18468.5 1.85 ×104 2. (a) 0.0005426 5.43×10-4 (b) 37.86 37.9 (b) 58.234 60 Compiled and solved by MR. Mununga J (c) 0.4220 4 (d) 74648 75000 7 Activity 1. (a) Express 2543800 in standard form correct to 3 significant figures. (b) Round off 607.25 correct to 2 significant figures 2. (a) Express 0.0004573 in standard form correct to 1 decimal place. (b) How many significant figures has the number 56700200? (c) Round off 84.46 to the nearest unit. (d) Round off 47.951 to one decimal place. TOPIC 4: RATIO AND PROPORTION Worked examples 1. (a) The exchange rate between the American dollar and the Zambian kwacha was $1=k9.96 on a particular day. How many dollars could be exchanged for k19920.00? (b) Sepo and thabo shared sweets in the ratio 5:3. If Thabo had 15 sweets, how many sweets did Sepo receive? 2. (a) Chiti is preparing to go to London. He has k19600.00 to convert to British pounds. How much will he get if the exchange rate is €1=k9.80? (b) A boarding house had enough food to feed 30 boys for 5 days. If only 25 boys reported, how many days did the food last if consumption per day was the same? Answers 1. (a) Compiled and solved by MR. Mununga J (b) 8 2. (a) (b) Activity 1. (a) on a particular day, the exchange rate between the Zambian kwacha and American dollar was $1=k9.50. How many dollars could be exchanged for k28500.00? (b) Two learners shared k72.00 in the ratio 3:5. How much did each learner get? 2. (a) The ratio of female teachers at a Basic school in Zambezi is 4:5. There are 24 female teachers. How many male teachers are there? (b) The scale of a map is 1:20000. What is the actual distance represented by a distance of 2m on the map? (c) In an election 80,000 people voted. The votes that candidates A, B and C got were in the ratio 9:5:2 respectively. How many votes did candidate B receive? 3. A car in Japan is valued at . What is its cost in kwacha if the rate of exchange is TOPIC 5: INDEX NOTATION Worked examples 1. (a) find the value of (b) find the value of √ 2. (a) find the value of (b) evaluate Answers 1. (a) (b) √ 24 Compiled and solved by MR. Mununga J 5 √ . √ 9 2. (a) (b) 85-4 Activity 1. Evaluate the following (a) , (b) 42×50. 2. Find the value of (a) , √ 3) Find the value of 2 (a) √ , +√ (b) TOPIC 6: ALGEBRAIC EXPRESSIONS Worked examples 1. (a) simplify (b) Given that and , find the value of . (c) Factorise completely 2. (a) simplify . (b) Simplify Answers 1. (a) (b) 2. (a) Compiled and solved by MR. Mununga J (b) (c) 10 Activity 1. Simplify the following expressions (a) (b) (c) 2. Evaluate the following given that (a) 3. , and (b) (c) (d) . . , (d) Simplify 4. (a) Find the value of , if (c) Factorise completely and . (b) Simplify (d) Factorise completely 5. (a) Simplify (b) simplify (c) Find the value of 6. simplify , when and . TOPIC 7: EQUATIONS AND INEQUATIONS Worked examples 1. (a) solve the equation , make q the subject of the formula. (b) Given that (c) Solve the simultaneous equations. 2. (a) Solve the inequation (b) Solve the equation (c) Given that . , make w the subject of the formula. Answers 1. (a) (b) Compiled and solved by MR. Mununga J . 11 (c) 2. (a) (b) (c) Activity 1. (a) solve the equation b) Solve the inequation (c) Given that , make m the subject of the formula. (d) Solve the equation 2. (a) Solve the equation (b) Solve the simultaneous equations (c) Solve the equation (d) Solve the inequation (i) (ii) 3. (a) Solve the equation (b) Given that , make x the subject of the formula. (c) Solve the simultaneous equations (i) (ii) (d) Solve the inequation 4. (a) solve the equation (b) given that make r the subject of the formula. 5. (a) solve the inequation Compiled and solved by MR. Mununga J . 12 (b) Solve the simultaneous equations TOPIC 8: ANGLES AND POLYGONS Worked examples 1. (a) In triangle ABC below, AC=BC and angle BAC=4y° Express the size of angle ACB in terms of y in its simplest form. (b) In the diagram below, AB is parallel to CD and EF is a transversal, angle APQ=130 Find angle (i) PQC, (ii) CQF. (c) in the diagram below, the lines AB and PQ intersect at O. Angle AOP=60 and angle BOQ=5w . Find the value of w. Compiled and solved by MR. Mununga J 13 2. (a) the diagram below shows a regular polygon with an exterior angle marked e. Find the size of angle . (b) The interior angle of a regular polygon is 108. How many sides does this polygon have? (c) In the diagram below, AOB is a straight line, <BOD=143°, <AOC=57° and <BOE is a right angle. Find the sum of a and b. Answer ̂ 1. (a) ̂ A 4y ̂ (b) (i) angle PQC 4y =180 ̂ 2. (a) (b) = (c) Compiled and solved by MR. Mununga J (ii) angle CQF (c) 14 Activity 1. (a) In the diagram below, AB is parallel to CD, angle HEB=50° and angle EGD=110° Find angle FEG. (b) The angles of a triangle ABC are shown in the diagram below Calculate the value of x. (c) In the diagram below, lines AB and CD are parallel. The line XY crosses AB and CD at P and Q respectively. R is on AB such that QR=RP=PQ Find angle DQY. (d) Find the sum of the interior angles of a polygon with eight sides. 2. (a) Two angles x and y are complementary. If x=35°, what is the value of y? Compiled and solved by MR. Mununga J 15 (b) In the diagram above, angle ABC=121°, angle BCD=39° and ABDE is a straight line. Find the value of x. (c) Find the value of x in the diagram below 3. (a) in the diagram below, AB is parallel to DE, angle DCE=40° and angle CDE=80° Find the size of angle ABC. (b) Triangle ABC below is an isosceles triangle in which AB=AC angle BAC=3x angle ABC=x°. Find the value of x Compiled and solved by MR. Mununga J 16 (c) Given that an acute angle XOY in the diagram below is 45°. What is the size of the reflex angle XOY? (d) Find the size of each exterior angle of a regular hexagon 4. (a) In the diagram below, ABC is a straight line, BD is parallel to CE, angle ABD=75° and angle BDC=45°. Find angle (i) DCE, (ii) BCD. (b) The sum of interior angles of a regular polygon is 1080°. Calculate the size of each interior size. 5. in the diagram below, KM=ML, angle M K L Find the value of . Compiled and solved by MR. Mununga J and angle . 17 TOPIC 9: DIRECTIONS AND BEARINGS Worked examples 1. In the diagram below, F is due of H and Calculate the bearing of G from F. 2. (a) The diagram below shows the bearing of Q from P which is 077°. Find the bearing of Q from P. (b) An aircraft flies from A to B on a bearing of 120°. What bearing should it take to fly from B to A. 3. In the diagram below, the bearing of B from A is 130° Find the bearing of A from B. Compiled and solved by MR. Mununga J 18 1. Answer s 2. (a) (b) or 3. Activity 1. (a) State the bearing of P from O. (b) State the bearing of M from J. 2. Given that the bearing of A from B is 290°. Find the bearing of B from A. Look forward with hope not backwards with regret. Compiled and solved by MR. Mununga J 19 TOPIC 10: MATRICES Worked examples ) and 1. (a) Given that P=( ( (b) Matrix 2. (a) Given that A ( ), find the matrix PQ. ) and matrix ( ( ). Find ) (i) State the order of matrix A, ( 3. (a) Given that A . (b) Express ( (ii) Find 3A. ), Find ) ( ) as a single matrix. Answers 1. (a) ( ( )( ) ) ) ( 2. (a) (i) (ii) 3. (a) ( ( ( (b) ) ) ) ( ) ( ) (b) ( ) ( ( ( ) ) Activity 1. Given that matrix N= (a) State the order of matrix N, 2. (a) Express ( (b) Given that A )( ( (b) Find 3N. ) as a single matrix. ) and ( Compiled and solved by MR. Mununga J ), find AB. ) 20 3. If ( ) and B ( ) , find (a) (b) 4. Find the unknowns in each of the following (i) ( ) 5. Given that (ii) ( ( ) and )( ) ( ( ) (iii) ( )( ) ( ) ), find MN. TOPIC11: SIMILARITY AND CONGRUENCY Worked examples 1. (a) In the diagram below, PQT is a straight line, angle OPT= angle QRS=90°, angle PQT= angle RQS, PQ =3cm, QR=9cm and QS= 15cm Calculate the length of QT. (b) In the triangle below, BE is parallel to CD, AB=2cm and BC=3cm. Write the ratio BE: CD. Compiled and solved by MR. Mununga J 21 2. (a) The diagram below shows a triangle ABC in which DE is parallel to BC Name one pair of corresponding sides? (b) In the diagram below, AB is parallel to PQ. AB=12cm, AP=6cm and CP=3cm Write the ratio CQ to CB in its lowest terms. Answers 1. (a) 2. (a) AE and AC (b) (b) Activity 1. (a) The diagram below shows two similar right-angled triangles ORS and OAB. OR= 8cm, OA=16cm and OS=10cm Calculate, in its lowest terms the ratio (i) OR: AR, Compiled and solved by MR. Mununga J (ii) RS: AB. 22 (b) In the diagram below, triangles LMN and LPQ are similar Given that LP=6cm, PM=3cm, PQ=4cm and NQ=2cm, Calculate the length of LQ. 2. (a) In the diagram below, YZ is parallel to PQ, XY=3cm YP=2cm and YZ=5cm Find the ratio of YZ: PQ. (b) The triangles below are similar Given that PQ=18cm, QR=20cm And XY=30cm. calculate the length of WY. 3. In the diagram below, triangle ABE and ACD are similar. D E 9cm 6cm A B 5cm Given that Compiled and solved by MR. Mununga J C , calculate the length of AB. 23 TOPIC 12: CARTESIAN PLANE Worked examples 1. On the XOY-plane below (i) Plot the points L (-4, 3), M (4, 1) and N (1, -1). (ii) Draw the graph of y=-3 y 4 3 2 1 -4 -3 -2 -1 0 -1 1 2 3 4 x -2 -3 -4 2. On the XOY-plane below (i) Give the x-values of points C, D, E and F (ii) Give the Y values of points C, D, E and F (iii) Give full coordinates of points A, B, G and H Compiled and solved by MR. Mununga J 24 Answers 1. 2. (i) 2, 3, 5 and -1 (iii) A(-3, 2) (ii) 0, 3, 1 and -2 B(-1, 1) Activity 1. On the XOY plane below, (i) Plot the points R(1, 1), Q(3, 4) and R(5, 1), (ii) Join the points to form triangle PQR, (iii) Draw the graph of 6 5 4 3 2 1 -2 -1 0 -1 1 2 3 4 5 -2 Compiled and solved by MR. Mununga J 6 x G(0,4) H(3, -2) 25 2. on the XOY- plane below (i) Plot the points M(2, 4), J(4, 3) and P(-3, 1), (ii) Draw the graph of . 3. (a) A rectangular has three of its four points as (0, 1), (0,3) and (4, 3). Find the coordinates of the fourth point. (b) Draw the straight line graph of (i) (ii) Compiled and solved by MR. Mununga J (iii) 26 (c) Find the function that describe the relationship between x and y in the following set of ordered pairs. (-2, -3), (-1, -1), (0, 1), (1, 3), (2, 5) 4. On the grid provided below (i) Plot the points N (-5, -5), W (-5, 1), X (-2, 3), Y (1, 1) and Z (1, -5), (ii) Join the points to form a polygon VWXYZ. (iii) Draw the line . 5. Given the following set of ordered pairs (22, 11), (20, 10), (18, 9), (16, 8) and (14, 7). (i) Find the function representing this mapping, (ii) Find the value of x when 6. Illustrate the solution of x+ y wanted region for the domain . on the XOY-plane shown below, by shading the Compiled and solved by MR. Mununga J 27 7. Illustrate the solution of region, for the domain on the XOY plane below by shading the wanted TOPIC 13: RELATIONS AND FUNCTIONS Worked examples 1. A relationship is given by the rule (a) Express the relationship between x and y in a mapping diagram. (b) What type of relation is this? (c) Why is this relation a function? (d) Write down the ordered pairs for this relation. 2. Given that y=x2-1 (a) Use a mapping diagram to illustrate the relationship between x and y, (b) Describe the type of relation and state whether it is a function or not. 3. (a) The table shows the corresponding values of x and y (i) Find the function that describes the relationship between x and y, (ii) Find the value of a. Compiled and solved by MR. Mununga J 28 (b) Given that , find f(3). (c) Given that , find f(-8). Answers 1. (a) (b) The relationship is one to one. (c) It is a function because only one value of x maps to only one value of y. there is only one value of y for each value of x. (d) (-2,-8), (-1, -4), (0, 0),(1, 4), (2,8), (3,12),(4, 16) 2. (a) (b) The relationship is many to one (more than one input value maps to one output value) therefore it is a function. 3. (a) (i) 0-(-3) y=mx +c (ii) m=3 3=3(1) +C (b) (c) Failure is the opportunity to begin again more intelligently.-Henry Ford Compiled and solved by MR. Mununga J 29 Activity 1. Given the rule y=x2+2 (a) Draw a mapping diagram of the relationship between x and y for the values { }. of (b) What type of relationship is this? (c) Is this relationship a function? 2. Given f(x) =5-3x and , find (a) f(4), (b) g(-3). 3. Given the arrow diagram below represents a relation from set A to set B (i) if , write the formula for the relation. (ii) Find the value of x when 4. A mapping from A to B is such that x 2x Find the values of p, q and t. 5. The diagram below shows a mapping from set D to set R Find the value of x. Compiled and solved by MR. Mununga J 30 6. The arrow diagram below represents a relation from set A to set B. (i) (ii) A B -1 5 0 4 1 3 2 2 If and , write the formula for the relation. Find the value of y when TOPIC 14: MENSURATION Worked examples 1. (a) The diagram below shows a triangular prism UVWXYZ Given that angle VUZ=angle WXY=90°, UV=12cm VW=20cm, VZ=15cm and UZ=9cm, calculate the Volume of the prism (b) A tomato sauce container is in the form of a cylinder of base radius 3.5cm and height 10cm (Take ) Calculate the total surface area of the container. Compiled and solved by MR. Mununga J 31 2. (a) The area of the base of a cylindrical block is154cm2 and its height is 10cm as shown below Given that the mass of the block is 385g, find its Density. (b) The diagram below shows a wooden triangular prism PQRSTU Given that P R= STU=90 PR=10cm P =6cm QR=8cm and RU=12cm, calculate the total surface Area of the prism PQRSTU Answers 1. (a) (b) = =77+220 =297cm2 2. (a) Density=0.25g/cm3 (b) = =60+72+120+96 =348cm2 Compiled and solved by MR. Mununga J 32 Activity 1. (a) A woodwork practical, Jessica cut a wooden block of length 15cm, breadth 10cm and height 6cm as shown below Given that the density of the wooden block is 0.05g/cm3, find its mass. (b) A cylinder whose radius is 21cm has a curved surface area of 528cm2. Calculate the height of the cylinder. (Take ). (c) In the triangular prism ABCDEF below, AC=4cm, AB=3cm, BC=5cm and BF=11cm Find its total surface area. 2. (a) The diagram below shows a cylinder of radius 3.5cm and length 22cm (Take Calculate its volume. (b) A window frame is made up of a square of side70cm and a sector with center A joined together as shown in the diagram below. Given that angle EAD=90°. Find the area of the window frame (Take ) Compiled and solved by MR. Mununga J 33 3. (a) Mr. Mununga’s garden is in the form of a trapezium shown below. A =22m DC=18m and EC=10m Calculate the area of Mr. Mununga’s garden. (b) The diagram below shows a tin for storing seeds the diameter of the tin is 7cm and height 6cm. Calculate the volume of the tin. (c) The diagram below shows a solid cylinder of diameter 10cm and height 20cm. Taking , calculate its curved surface area. 4. (a) The figure ABCDEF below is a triangular prism, AC=10cm, CF=15cm and the height of triangle ABC is 6cm Find the volume of the prism. ABCDEF. Compiled and solved by MR. Mununga J 34 (b) The figure below is the net of a 5. The diagram below shows a cylinder with diameter 7cm and height 10cm. . 7cm Calculate its volume. 10cm 6. The figure below shows a triangular prism PQRSTU. S 17cm 20cm U T R 15cm P 8cm Q Given that US=17cm, PQ=8cm, QR=15cm and SR=20cm, calculate its total surface area. TOPIC 15: PYTHAGORA’S THEOREM Worked examples 1. (a) The diagonal of a flat rectangular television (TV) screen is 50cm. if the screen is 30cm broad. Find its length Compiled and solved by MR. Mununga J 35 (b) The diagram below shows two straight roads AB and BC which join the main road at A and C. The road AB meets the road BC at right angles. Given that AB=8km and AC=10km, find the length of The road BC. 2. The diagram below shows a rectangular field ABCD with a straight path from A to C. if BC=9m and CD=12m, calculate the length of the path AC. Answers 1. (a) (b) 2. Activity 1. In the figure below, AB=3cm, BC=4cm, CD=12cm and angle ABC=angle=90° Calculate the length of AD. Compiled and solved by MR. Mununga J 36 2. In the figure below. VWYZ is a square which is joined to a triangle XWY. XY=15cm, VZ=9cm and angle XWY=90° Calculate the length of VX. 3. (a) The figure below is a trapezium PQRS, in which angle PQR=angle QPS=90°, PQ=6cm, QR=8cm and PS=12cm. calculate the length of the diagonal PR (b) Calculate the length of a diagonal of a rectangle whose sides are 12cm by 5cm. TOPIC 16: NUMBER BASES Worked examples 1. (a) Convert 143five to base 10. (b) Convert 1325eight to base10. 2. (a) Convert 91ten to a binary number (base 2). (b) Express 152ten to base 5. 3. calculate 213four +144five. Give your answer in base five. 4. (a) Convert 0.125 to bicimal. (b) Write 12.375 as a base 2 number. 5. (a) Convert 10101.12 to base 10. (b) Convert 1101.1012 to a decimal number 6. Evaluate the following (a) ( Compiled and solved by MR. Mununga J (c) 37 (d) 7. (i) Calculate the following in base 2 (a) (b) (ii) Calculate in base 5. Answers 1. (a) ( (b) 25+20+3 48ten 143five = 48ten 2. (a) 512+192+16+5 725ten 1325eight=725ten (b) 152ten = 1102five 91ten= 1011011two 3. 213four = =( =32+4+3 =39ten 213four=124 five 124five + 144five=323five 4. (a) . . . Compiled and solved by MR. Mununga J (b) . . . 38 5. (a) 0.12 = 0.510 (b) 16s 8s 4s 2s 1s 1 8 1 4 0 0 1 1 . 1 0.5 0 0 1 0.125 8+4+0+1+0.5+0+0.125 =13.625 6. (a) (b) (c) (d) 7. (i) (a) (ii) Compiled and solved by MR. Mununga J (b) 39 Activity 1. (a) Evaluate (b) Evaluate giving your answer in base two. giving your answer in base five. 2. (a) Convert 34.5 to a number in base 2. (b) Convert 10.1112 to base 10. 3. (a) Find the product of 432five and 23five, giving your answer in base five (b) Find the value of 4. Divide , giving your answer in base two , giving your answer in base two. TOPIC 17: GEOMETRICAL CONSTRUCTION Worked examples 1. (i) Use geometrical instruments to construct triangle DEF in which DE=8cm, angle DEF=60° and angle EDF=70°. (ii) Bisect angle EDF and angle DEF and let the angle bisectors meet at O. (iii) Draw a perpendicular from O to the side DE. Label the point where the perpendicular meets DE as G. (iv) With centre O, draw a circle which touches the three sides of triangle DEF. 2. (i) Construct triangle ABCD in which AB=4cm, BC=5cm and AC=6cm. (ii) Bisect the sides AB and AC and let them meet at O. (iii) With centre O and radius OA, draw a circle. The strongest factor for success is self-esteem. Compiled and solved by MR. Mununga J 40 Answers 1. 2. Activity 1. (i) Construct triangle LMN in which LM=7cm, MN=5cm and LN=6cm. (ii) Bisect angle LNM and angle LMN and label the point of intersection of the angle bisectors as O. (iii) Draw a perpendicular from O to the side LM. Label the point where the perpendicular meets LM as P. (iv) With O as the centre, draw a circle which touches all the three sides of the triangle LMN 2. Using Geometrical instruments (i) Construct triangle CDE in which CD=7cm, angle CDE=100° and angle DCE=45°. (ii) Measure and write the length of DE. (iii) Bisect angle CED and let the bisector meet CD at F. (iv) Construct a perpendicular from D to meet CE at G. 3. (i) Using geometrical instruments to construct triangle PQR in which PQ=11cm, angle PQR=117° and QR=6.5cm (ii) Measure and write the length of PR. (iii) Construct the perpendicular bisector of PQ. (iv) Bisect angle PRQ. Compiled and solved by MR. Mununga J 41 4 (i) Use geometrical instruments to construct triangle XYZ in which XY=8cm, angle XYZ=60° and angle YXZ=40°. (ii) Measure and write the length of XZ. (iii) Bisect the sides XY and XZ and let them meet at O. (iv) With centre O and radius OX draw a circle. 5. (i) Construct triangle PQR in which PQ=6cm, angle PQR=60° and angle QPR=90°. (ii) Construct a perpendicular bisector of PQ and let it meet PQ at X. (iii) Construct the bisector of angle PQR to meet the perpendicular bisector of PQ at Y. (iv) Measure and write the length of XY. TOPIC 18: SOCIAL AND COMMENCIAL ARITHMETICAL Worked examples 1. (a) Calculate the simple interest on k360 000.00 invested at 12% per annum for 3 years. (b) Francis was given K150.00 to buy the following items 2kg sugar at k24.00 1 loaf of bread at k9.00 6 books at k35.00 2.5 litres of cooking oil at k39.00 (i) How much did he spend? (ii) How much change did he receive? 2. (a) Mr Mununga invested k860.00 at a rate of 7% simple interest per annum. After how many years is the interest going to be k301.00? (b) Zambezi primary school budgeted for k16200.00 to renovate the school. The school raised 25% and applied for the rest of the amount from a bank. How much did the school apply from the bank? 3. (a) A car dealer receives a commission of 3% of the selling price of the car. Find the selling price of a car, if he was given a commission of k1500.00. (b) Justin needs k130.00 to buy a shirt. He has k45.00, if he saves k17.00 each week, how many weeks will it take him to save the remaining amount? (c) After the bus fare from Zambezi to Kabompo was increased by 15%, passengers paid k46.00. What was the bus fare before the increase? Compiled and solved by MR. Mununga J 42 Answers 1. (a) k129,600.00 (b) (i) 2. (a) (ii) (b) T =5 years 3. (a) (b) (c) Activity 1. (a) Matamu land , which is valued at k80 000.00, appreciates by straight line method at 10% per year, what is its book value after 2 years? (b) A stove costs k3 000.00 exclusive of value added Tax (VAT). Calculate the cost of the stove if 16% VAT is included 2. (a) Emmanuel is paid k20.00 per hour for a 30 hour week and the rate of over-time is double rate. Calculate his total wage in a week in which he worked for 40 hours. (b) A sofa can be bought for k8400.00 cash. It can also be bought on hire purchase by paying a deposit of k3000.00 plus 10 equal monthly installments of k800.00. Raphael wants to buy this sofa on hire purchase. How much more will he pay on hire purchase. 3. Angela bought a car at k40 000.00. if it depreciated using the straight line method at 20% per year, calculate its value after 3 years. 4. Francis is paid at the rate of k32.00 per hour for a 40-hour week. If overtime is paid at the rate of “time and a half” calculate his total wage in a week in which he works for 45 hours. Compiled and solved by MR. Mununga J 43 TOPIC 19: PROBABILITY Worked examples 1. (a) A coin was tossed 40 times . The number of times when a head and a tail were obtained were 28 and 12 respectively. Find the probability of getting a (i) Head (H), (ii) Tail (T). (b) In 20 fights, a boxer won 15 times, drew 2 and lost 3 times. What is the probability that (i) He won? (ii) He does not win the next fight. 2. (a) The probability of passing a mathematics test is 60%. Find the probability of failing the same mathematic test. (b) A die and a coin are tossed together at the same time. Draw a two way table to show the possible outcomes. 3. Numbers 1 to 12 are written on small cards of the same size and place in an opaque bag. A card is picked at random. What is the probability that the number drawn will be (a) Even, (b) prime, (c) Even prime. 4. A woman has 6 green and 8 red marbles in a box. Find the probability of randomly picking a red marble from the box. Activity 1. (a) (i) (ii) (b) (i) (ii) 2. (a) (b) 3. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 (a) P (Even) = (b) 4. Compiled and solved by MR. Mununga J 44 1. A bag contains 15 white and 9 green balls. If a ball is picked at random from the bag, find the probability that it is green. 2. A bag contains 6 red marbles and 3 blue marbles. A marble is picked at random from the bag, find the probability that it is blue. 3. A Box contains 6 blue pencils and 5 red pencils. If one pencil is picked at random from the box, find the probability that it is blue. 4. Grace has 4 red pens and 6 black pens in her bag. She picks a pen at random from the bag. Find the probability that it is black. TOPIC 20: COMPUTER Worked examples 1. The distance (D) covered by a car and the time (T) the car takes to cover this distance, complete the flow chart below for calculating and displaying its average speed(S). Start Stop 2. (a) Which symbol in the flow chart represents a decision stage? (b) Name one output device Compiled and solved by MR. Mununga J 45 3. Given that the base of a triangle is b and its perpendicular height is h, complete the flow chart below, which is for calculating and displaying its area. Start Stop 4. Given the length l and breadth b of a rectangle, write a simple program to calculate and output the area A of a rectangle. Answers 1. 2. (a) (b) speaker Start Enter D, T S=D/T Display avrg speed Stop 3. Start Enter b, h Output area Stop Compiled and solved by MR. Mununga J 4. Start Enter l, b Area=l * b Display Area Stop 46 Activity 1. Study the program below and answer the question that follows Start Enter radius If radius < 0 Then display “error message” and re-enter positive radius Else enter height If height <0 Then display “error message” and re-enter positive height Else volume End if End if Display volume Stop Use the program to complete the table below (Take Input Radius 7 Height 10 ) Output Volume 2. (a) Name two input devices. (b) Given that the radius of a circle is r, complete the flow chart below for calculating and displaying its area. The first and best victory is to conquer self.-Plato Compiled and solved by MR. Mununga J 47 3. given the density (D) of a stone and its mass (M), complete the flow chart below for calculating and displaying its volume (V). TOPIC 21: STATISTICS Worked examples 1. The table below shows the quality of fuel sold by a filling station on a particular day Type of fuel Number of litres sold Petro 6000 Diesel 4000 Kerosene 2000 Illustrate this information on the pie chart below. Work hard stay consistent and be patient. Compiled and solved by MR. Mununga J 48 2. The table below shows the amount of money spent by 40 learners in a school tuck-shop in a particular week. Amount(kwacha) 10 Number of learners 8 20 12 30 9 40 6 50 5 Use this information to complete the bar chart 3. The marks scored in an English test by learners in a grade 9 class are distributed as shown in the bar chart below. How many learners scored more than five marks? Success is the sum of small repeated efforts efforts every day. Compiled and solved by MR. Mununga J 49 4. The pie chart below shows colors that grade 9 learners at Zambezi day secondary school like If 40 learners like blue, find the total number of grade 9 9 learners at this school. Answers 1. 2. 3. 4. Activity 1. A marketer made k200.00 profit from kalembula, k150.00 profit from chibwabwa and k250.00 profit from tomatoes. Illustrate this information on the pie chart below. Compiled and solved by MR. Mununga J 50 2. The bar chart below shows the number of goals scored by a football team (i) How many games did the team play? (ii) Complete the frequency table below Number of goals Number of games 3. (a) The bar chart below shows the distribution of the pupils shoe sizes in a grade 9 class Find the number of pupils who wear Size 5 and above? Compiled and solved by MR. Mununga J 51 (b) The frequency table below shows the marks obtained by pupils in a mathematics test Mark 0-4 No. of pupils 7 (i) What was the model class? 5-9 8 10-14 3 15-19 2 (ii) Calculate the mean mark. (c) A netball team scored the following goals in seven games 6, 3, 7, 2, 3, 5 and 10. What was the mean score? 4. The compound bar chart below shows the number of bags of maize produced by Mr. Mununga and Mr Musumali from 2010 to 2014. KEY Find the difference in the total number of bags produced by the two farmers from 2010 to 2014. 5. The frequency table below shows the number of questions answered by grade 9 class in mathematics test. Number of questioned answered Number of pupils 1 10 2 8 3 12 (i) Use the information in the table to complete the bar chart Compiled and solved by MR. Mununga J 4 4 5 6 52 (ii) How many pupils are in this class? ADDITIONAL QUESTIONS 1. (a) Convert 1110two to base ten number. (b) Evaluate giving your answer in base ten. (c) Subtract 34eight from 421eight giving your answer in base eight. (d) Divide 10010two by 11two giving your answer in base two. (e) Find the sum of 101five and 124five, giving your answer in base ten. 2. The figure below is a net of a 3. (a) How many faces has a triangular pyramid? (b) Dorothy walked around a square garden of area 49m2. Find the total distance she walked. (c) Name the figure that can be formed by the net below. 4. (a) How many faces does the solid below have? Compiled and solved by MR. Mununga J 53 (b) Given that is equivalent to , find the value of x. 5. (a) In a mathematics club, of the members are boys and the rest are girls. Calculate the number of girls, given that the club has 45 members. (b) How many lines of symmetry does the shape below have? With God nothing is impossible The end, answers to the activities next Compiled and solved by MR. Mununga J