Term revision test sheets

Term revision test sheets Teacher s name: Class name: Student s name: Date: Term Revision Test 1 (Chapters 1, 2, 8) Circle the correct answer in Questions 1 5. 1 The next term in the sequence 2, 3, 5, 8, 12, 17, is: a 18 b 19 c 22 d 23 e 24 2 Which of these statements is/are true? i 1 089 is divisible by 6. ii 1 089 is divisible by 9. iii 1 089 is a perfect square. a i only b ii only c iii only d i and ii only e ii and iii only 3 The square root of 12 _ 1 4 a 1 1_ 3 b 1 1_ 2 c 3 3_ d 6 1_ 4 4 4 What is 0.000263 in standard form? e 6 1_ 8 a 2.63 10 6 b 2.63 10 5 c 2.63 10 4 d 2.63 10 4 e 2.63 10 5 5 What is 0.003867 to 3 significant figures? a 0.004 b 0.00386 c 0.00387 d 386 e 387 6 If 1 2 = 2 2 2 2 3 = 3 2 3 3 4 = 4 2 4 4 5 = 5 2 5 = a Complete: n (n + 1) =. b Use this to calculate 1 001 2 1 001. 7 Write 1 296 as a product of its prime factors. Hence find 1 296. 8 These numbers are in standard form. Change them to ordinary form. a 9 10 2 b 3.6 10 5 c 6.1 10 7 d 8 10 4 e 6 10 1 f 3.4 10 3 9 A student writes 78 words in 8 lines of writing. a Find, to the nearest whole number, the average number of words per line. b Estimate how many lines of writing it will take to write a 1 500-word essay. 140 Term revision test sheets

10 Draw graphs to show: a The first six multiples of 3. b The factors of 42. Term revision test sheets 141

Teacher s name: Class name: Student s name: Date: Term Revision Test 2 (Chapters 3, 6) Circle the correct answer in Questions 1 5. 1 In Figure R8, PQRT and TQRS are parallelograms, QR = 3 cm and TQ = 4 cm. How long is PS? Figure R8 a b c d e 3 cm 4 cm 5 cm 6 cm 7 cm 2 Which one of these statements is false? a All rhombuses are parallelograms. b All trapeziums are parallelograms. c All squares are kites. d All squares are rectangles. e All rectangles are trapeziums. 3 In Figure R10, POQ and SOR are straight lines. If P Ô S = 40 and T Ô Q = 65, calculate T Ô R. a 105 b 35 c 30 d 25 e 15 Figure R10 4 In Figure R11, the size of angle x is: Figure R11 a 29 b 32 c 58 d 61 e 64 142 Term revision test sheets

5 A quadrilateral has angles of 128, 91, a and 2a. Find the value of a. 6 The sum of the angles of a polygon is 1 620. Calculate the number of sides that the polygon has. 7 a Find the sum of the angles of a pentagon. b Hence calculate the value of y in Figure R12. Figure R12 8 The sum of four of the angles of a heptagon (seven sides) is 600. The other three angles are of sizes 4x, 5x and 6x. Find the value of x and hence find the sizes of the three angles. 9 Sketch a quadrilateral that has only one line of symmetry. Term revision test sheets 143

Teacher s name: Class name: Student s name: Date: Term Revision Test 3 (Chapters 4, 5, 7) Circle the correct answer in Questions 1 5. 1 If ( 3) ( 24) = y, then y =. a +72 b +8 c +8 d 8 e 8 2 Look at the data in Table R1. If Grades C and above are pass marks for the test, how many students passed? Grade A B C D E Frequency 2 4 3 2 1 Table R1 a 1 b 2 c 3 d 6 e 9 3 Simplify 5a 2. 15a a 5a 3 b 2_ 3 c 2 d a_ 3 e a_ b 4 Find the value of, when a = 5 and b = 2. (2a + b) a 1_ 3 b 1_ c 1_ 4 9 d 1_ 6 e 1 10 5 Simplify (a + ( a)) + b. a 2b b b c 2a d 2a b e 2a + b 6 Simplify these expressions: a ( 6) 8 b ( 2 1_ 2 ) ( 2 2_ 5 c 7_ 8 of ( 5 1_ 3 ) d 38 ( 2) e ( 3.6) ( 9) f ( 3 2_ 3 ) 6 3_ 5 5 144 Term revision test sheets

7 Solve these expressions: a 3x = 18 b 1_ a = 7 5 15 c n_ 2 = 5 27 d d = 42 2 7m e 10 = 2 4_ 5 f 5_ 8 y = 1 1_ 4 8 I think of a number. 19 subtracted from the number gives 2. What number am I thinking of? 9 Find the value of the following when x = 2, y = 5, z = 1: a x 2 + y 2 b (x + y) 2 (x + y) c (y + z) d x_ y + _ y z 10 Expand these expressions: a (v 4)(v 9) b (b + 4)(3b + 2) c (5x + 2)(2x 3) d (4m n)(3m 2n) Term revision test sheets 145

Teacher s name: Class name: Student s name: Date: General Revision Test A (Chapters 1 8) Circle the correct answer in Questions 1 10. 1 What is the next term in the sequence 1, 3, 7, 15, 31,? a 33 b 47 c 51 d 59 e 63 2 Find the least number by which 112 must be multiplied to give a perfect square. a 2 b 3 c 5 d 7 e 11 3 Express 526 000 in standard form. a 5.26 10 5 b 5.26 10 4 c 5.26 10 3 d 5.26 10 4 e 5.26 10 5 4 a length of wire is given as 6.8 cm, correct to 2 significant figures. What is the least possible length of the wire? a 6.7 cm b 6.74 cm c 6.75 cm d 6.8 cm e 6.85 cm 5 In Figure R13, ABCD is a kite. B Â C = 26 and A ˆD C = 105. A Ĉ D =. Figure R13 a 26 b 41 c 49 d 62 e 64 6 Simplify (y + z) 2 2yz: a y 2 + z 2 + 4yz b y 2 z 2 c y 2 + z 2 d y 2 + z 2 2yz e y 2 + z 2 4yz 7 If m ( 2) = 12, then m =. a +24 b +14 c +6 d 6 e 24 8 If 5_ of a certain number is 6 _ 2, the number is: 6 3 a 1_ 8 b 5 1_ 3 c 5 5_ 9 d 7 1_ 2 e 8 146 Term revision test sheets

9 In Figure R14, ABCDE is a pentagon such that ABD is equilateral. Figure R14 If x = 35, then y =. a 95 b 110 c 120 d 130 e 145 10 What is the value of p 2 q q 2 p, if p = 3 and q = 1? a 12 b 6 c 0 d 6 e 12 11 Express these numbers as products of their prime factors. a 800 b 126 c 198 12 If 1 = 1 2 1 + 3 = 2 2 1 + 3 + 5 = 3 2 1 + 3 + 5 + 7 = 4 2 = What will be the value of y, if 1 + 3 + 5 + + 99 = y 2? 13 Express 1.56 10 4 as a whole number correct to 2 significant figures. 14 Express 0.5046 correct to: a 3 decimal places. b 2 significant figures. Term revision test sheets 147

c The nearest 1 10. 15 Simplify these expressions: a ( 6) (+5) b (+7) ( 0.9) c ( 10) 2 d ( 5) ( 40) e ( 5.4) (+0.6) +34 f 17 16 Solve these expressions: a 3_ m = 15 4 44 b 1 2_ 3 x = 5 _ 5 6 c x_ = 5_ 5 8 d 1 3_ 7 = 3 1_ 3 y 17 Find the value of k in Figure R15. Figure R15 148 Term revision test sheets

18 Expand these expressions: a (x 5)(x 6) b (2p 3q)(2p 5q) c (m + 4)(m 4) d (t 8) 2 19 Figure R16 shows part of a pattern. Figure 16 Sketch the basic shape that makes the pattern. 20 10 nails have a mass of about 63 g. Estimate the number of nails in 1 kg to the nearest 10 nails. Term revision test sheets 149

Teacher s name: Class name: Student s name: Date: Term Revision Test 4 (Chapters 9, 10) Circle the correct answer in Questions 1 5. 1 In 2010, a watch cost N2 800. In 2014, the same watch cost N5 200. Give the 2010 cost to the 2014 cost as a ratio in its simplest terms. a 1 : 2 b 7 : 13 c 28 : 52 d 26 : 14 e 199 : 200 2 I travelled at 60 km/h and took 2 h for a journey. How long would it have taken me, if I had travelled at 50 km/h? a 1 1_ h b 1 1_ 5 3 h c 1 2_ 3 h d 2 2_ h e 2 2_ 5 3 h 3 In an exam 154 out of 175 candidates passed. What percentage failed? a 6 2_ 7 b 12% c 13 7 % d 15% e 88% 11 4 How much interest does N40 000 make in 5 years at 7% per annum? a N700 b N2 000 c N2 800 d N3 500 e N1 400 Taxable income/month Tax charged First N200 000 10% Next N200 000 15% Next N200 000 20% Above N600 000 25% Allowances to be deducted before income is taxed: For self Allowance of N60 000 For each child under 16 Allowance of N35 000 Table R1 5 Daudu has two children under 16. Use Table R1 to calculate his allowances before tax. a N25 000 b N50 000 c N60 000 d N85 000 e N130 000 6 Daudu (in Question 5) has a monthly salary of N380 000. Use Table R1 to help calculate: a His taxable salary. b How much tax he pays. c His income after tax is deducted. 150 Term revision test sheets

7 The hire purchase price of a motor bike is N680 000. There is a deposit of 12.5%. The remainder is spread over 12 equal monthly instalments. a Calculate the amount of the deposit. b Calculate the remainder to be paid. c Find the amount of each monthly instalment to the nearest naira. 8 By selling a house for N69 million, an agent makes a profit of 15%. How much did the house cost? 9 In one afternoon, a street vendor sells air-time cards of value N150, N200, N200, N500, N750 and N1 500. He also sells a SIM starter pack costing N1 600. If he gets 5% commission on his sales, how much does he earn? 10 A salesman gets a commission of 8 _ 1 % of the value of the things he sells. Find his commission for 2 selling two guitars at N35 400 each, five tennis rackets at N9 900 each and 14 electric kettles at N2 550 each. Term revision test sheets 151

Teacher s name: Class name: Student s name: Date: Term Revision Test 5 (Chapters 11, 13) Circle the correct answer in Questions 1 5. 1 Express 2_ a + _ 7 as a single fraction. b a 2b + 7a b 9ab c 9 d 9 e 2b + 7a ab a + b ab a + b a + b 2 A teacher asks a class to write x + 8 in another way. Three of the answers are: i 1_ (x + 8) ii x + 2 iii 1_ x + 2 4 4 Which of the answers are correct? a i only b ii only c iii only d i and ii only e none of these 3 Simplify x 2 x 7. 6 4 a 8 5x b (12 5x) c 17 x 6 6 12 d (25 x) e x 17 6 12 12 4 Express this statement as an algebraic equation: The result of taking 2 from n and multiplying the answer by 4, is the same as multiplying n by 3 and taking away 5. a 4(n 2) = 5(n 3) b 4(n 2) = 3n 5 c 4(n 2) = 5 3n d 4(2 n) = 2n e 4(2 n) = 3(n 5) 5 Solve the equation x + 2 + 2x = 10. 3 a x = 9 1 b x = 5 c x = 4 _ 2 36 3 d x = 4 e x = 1 _ 1 7 6 a Factorise the numerator and denominator of 2x 6. Hence simplify the expression. b 3x + 9 Simplify and factorise 2a(b + c) b(c + 2a). c Solve 3x + 2 = 5 x. 7 Solve these equations: a 9 4x = 11 7x b 6a 3 = 25 + 5a c 9 5x = 3 2x d 13x + 15 = 7x + 17 152 Term revision test sheets

8 A mother is 10 times as old as her son. In 6 years time, she will be four times as old as her son. Find their present ages. (Hint: Let the son s present age be x years.) 9 Solve these equations: a 4(x + 2) = 2(3x 1) b 17y 2(6y + 1) = 8 7z c 2 18 = _ z 2 d a + _ 3 3 3a 7 = 10 5 10 The height of a boy is x cm. His father is 1 1 10 times his height. His sister is _ 7 his height. 8 a Express the heights of the father and sister in terms of x. b If the difference in height between his father and sister is 36 cm, find the height of the boy. Term revision test sheets 153

Teacher s name: Class name: Student s name: Date: Term Revision Test 6 (Chapters 12, 14) Circle the correct answer in Questions 1 5. 1 The position of a point X is given by X( 0.9). Which of the points A, B, C, D, E in Figure R22 is in the same position as point X? A B C D E 2 1 0 1 Figure R22 2 Which of the points A, B, C, D, E in Figure R23 has these co-ordinates ( 2; 3)? Figure R23 3 A straight line PO joins the point P(5; 3) to the origin, O. PO is extended to Q so that PO = OQ. What are the co-ordinates of Q? a ( 5; 3) b ( 3; 5) c ( 5;3) d ( 3;5) e (3; 5) Figure R24 is a graph giving the cost (in N) of cloth (in metres). Use the graph to answer Questions 4 and 5. 4 What is the cost of 3 m of cloth? a N180 b N360 c N2 100 d N2 200 e N3 000 5 Approximately what length of cloth can I buy for N900? a 1.3 m b 2.5 m c 4 m d 15.75 m e 17.5 m Figure R24 Cost and length of cloth 154 Term revision test sheets

6 Choose a suitable scale and plot the points A(1;3), B(6;3), C(3; 1) and D( 2; 1). a AC and BD cross at P. Find the co-ordinates of P. b c What is the size of A ˆP D? What kind of quadrilateral is ABCD? 7 Figure R25 is a graph showing the cost of hiring a car. The cost is made up of a basic charge and an additional charge for the distance that the car is driven. a How much does it cost to hire the car for a journey of: i 100 km ii 460 km? b What is the basic charge (that is, the charge if no distance is travelled)? c Find the additional charge as a rate in naira/km. Figure R25 Cost of car hire Term revision test sheets 155

8 Saratu walks at a speed of 6 km/h. a Make a table of values showing how far Saratu walks in _ 1, 1_ 4 2, 3_, 1, 1 1_, 1 1_ 4 4 2, 1 3_, 2 hours. 4 b Using scales of 1 cm to _ 1 hour and 1 cm to 1 km, draw a graph of the information. 4 c Use the graph to find: i How far Saratu walks in 69 min. ii How long it takes Saratu to walk 10 km. 156 Term revision test sheets

9 Figure R26 is a distance time graph of a walker (A) and a cyclist (B). A walks steadily from the Post Office to the bank. B cycles from the bank to the Post Office but stops to talk to a friend on the way. a How long does the journey take both A and B? b How far is it from the bank to the Post Office? c How long does B stop to talk to his friend? Figure R26 Travel graph of A and B d How far is B from the bank when he stops? e How far are A and B from the Post Office when they meet on the road? 10 Given that R1 = N12, draw a graph for converting naira to rands for amounts up to R10. Read off the equivalent amounts in the other currency of: a N80 b N24 c R8.50 d R5 Term revision test sheets 157

Teacher s name: Class name: Student s name: Date: Term Revision Test 7 (Chapters 15, 16) Circle the correct answer in Questions 1 5. 1 On a scale drawing a straight railway track measures 12.5 cm. What is the actual length of the track, if the scale is 1 cm to 5 km? a 6 km b 12.5 km c 25 km d 62.5 km e 625 km 2 In XYZ, XY = 4 cm, ˆX = 100, Ŷ = 50. Which sketch shows this information? Figure R28 a b c d Neither A, B nor C. e All of A, B and C. 3 From the information in Question 2, what is the longest side of XYZ? a XY b YZ c XZ d They are all the same length. e Impossible to say. 4 a map is drawn to a scale of 2 cm to 100 km. If the actual distance between two towns is 374 km, what is this distance as measured on the map? a 1.97 cm b 3.74 cm c 7.48 cm d 19.7 cm e 74.8 cm 5 Refer to the map in Figure 16.14. Which one of these buildings is on Banjul Crescent? a Bank b Church c Dispensary d Mosque e Station Figure 16.14 158 Term revision test sheets

6 In XYZ, YZ = 10 cm, Ŷ = 45 and Ẑ = 35. Use a ruler and protractor to construct XYZ. Measure the shortest side of the triangle. 7 a Construct an isosceles triangle PQR such that PQ = PR = 7 cm and QR = 5 cm. b Construct the bisectors of angles Q and R to cross at X. Term revision test sheets 159

c Draw a straight line from P through X to meet OR at Y. What can you say about point Y? 8 A photograph measures 8 cm by 10 cm. It is enlarged so that the shorter side becomes 12 cm and the longer side x cm. Find x. 9 A plan of a compound is drawn on a scale of 1 cm to 5 m. a If a wall is 24 m long, find its length on the drawing. b If the scale drawing of a round house is a circle of diameter 0.7 cm, find the actual diameter of the round house. 10 A rectangular sheet of paper measures 60 cm by 40 cm. Use a scale of 1 cm to 10 cm and make a scale drawing of the sheet of paper. Hence find the length of a diagonal of the sheet of paper. 160 Term revision test sheets

Teacher s name: Class name: Student s name: Date: General Revision Test B (Chapters 9 16) Circle the correct answer in Questions 1 10. 1 If 5 people can do a piece of work in 6 days, how many days, to the nearest whole number, should 8 people take to do it? Assume that the rate of work is the same. a 4 b 5 c 7 d 8 e 9 2 What percentage of 4 is 5? a 125% b 120% c 80% d 25% e 20% 3 A trader gains N4 000 on a sale which was equivalent to 8% profit. What was the cost price? a N54 000 b N50 000 c N32 000 d N500 e N320 4 Which of these are factors of 4x 2 y? i 2x ii xy iii 4y a i only b ii only c iii only d None of them e All of them 5 The LCM of 5ab 2 and 3a 2 b is: a ab b 3a c 5b 5b 3a d 15a2 b 2 e 15a 3 b 3 6 In Figure R29, what are the co-ordinates of the point where the diagonals of kite PQRS cross? a ( 1 1_ 2 ; 1_ 2 ) b ( 1 1_ 2 ; 1_ 2 ) c ( 1_ 2 ; 1 1_ 2 ) d ( 1_ 2 ; 1 1_ 2 ) e (1 1_ 2 ; 1_ 2 ) 7 If 5 2x 3 = 1, a x = 1 b x = 4 c x = 6 d x = 7 e x = 9 8 Figure R30 is a distance time graph for a car. What does the value of QR represent? PQ a The time taken by the car. b c d The distance the car travels. The average speed of the car. The time the car was not moving. e The distance between P and R. Figure R29 Figure R30 Term revision test sheets 161

9 Which of these triangles can you construct using only ruler and compasses? a Any triangle, given two sides and their included angle. b Any triangle, given two angles and their common side. c Any triangle, given all three sides. d None of the above. e All of the above. 10 A map is drawn to a scale of 1 : 40 000. What distance, in km, will a line on the map 2.8 cm long represent? a 11.2 km b 7 km c 1.12 km d 0.7 km e 0.112 km 11 In one month, a man spent N650 on newspapers and N240 on soap. In the following month, he reduced his newspaper spending by 40% and increased his spending on soap in the ratio 5 : 3. How much did he save? 12 A 500 g bag of sugar costs N195. A 25 kg sack of sugar costs N8 750. Calculate the saving per kg by buying the 25 kg sack. 13 Use Table 10.1 to answer this question. Tax bands on taxable income (N) Rate of tax First N200 000 10% Over N200 000 and up to N400 00 15% Over N400 000 and up to N600 000 20% Over N600 000 25% Table 10.1 Tax bands for PAYE system If a woman's income is N260 000 per month, calculate her taxable income and the amount of tax she pays. 14 a Complete the brackets: 5x 2 10x = 5x( ) b Factorise 18ax + 12ay. 162 Term revision test sheets

c Simplify 5 t 4 t. 5 4 3(2x 3) d Simplify 1_ 5 3. 15 a Choose a suitable scale and plot these points: A(11; 15), B( 4;0), C( 7; 3), D( 10;0), E( 4;6), F(5;6), G( 2;2), and H(13; 13). b Join the points in alphabetical order and join H to A. c What picture have you drawn? 16 a Solve 3(x 6) = 4(1 2x). b Solve c 5 6 c 4 8 = 1 c Six times a number added to seven times 4 less than the number comes to 11. Find the number. Term revision test sheets 163

17 A man leaves home and cycles to his office 12 km away. His journey is shown on the graph in Figure R31. Figure R31 Travel graph of cyclist a What time did he arrive at his office? b How long did the journey take altogether? c Find his average speed for the whole journey. d During the journey he stopped to replace the chain. How long did this take? e How far was he from home when the chain came off? 18 a Construct PQR such that ˆQ = 90, PQ = 10 cm and QR = 6 cm. b Measure the length of the hypotenuse of PQR. 19 Figure R32 is a scale drawing of the plan of a round house. Figure R32 a If the actual diameter of the house is 6 m, use measurement to find the scale of the drawing. 164 Term revision test sheets

b Hence find the actual width of the door. 20 Figure R33 is a sketch of a simple bridge. M is the mid-point of the bridge. Figure R33 a Use a scale of 1 cm to 1 m to draw an accurate scale drawing of the bridge. b Hence find the length of the support AM. Term revision test sheets 165

Teacher s name: Class name: Student s name: Date: Term Revision Test 8 (Chapters 17, 19) Circle the correct answer in Questions 1 5. 1 Which of these are Pythagorean triples? i (3, 4, 5) ii (5, 12, 13) iii (8, 13, 17) a i only b i and ii only c ii only d ii and iii only e iii only 2 PQRS is a rectangle with sides 3 cm and 4 cm. If its diagonals cross at O, calculate the length of PO. a 2.5 cm b 3.0 cm c 3.5 cm d 4.0 cm e 5.0 cm 3 The diagonals of a rhombus measure 8 cm by 6 cm. What is the length of a side of the rhombus? a 5 cm b 6 cm c 7 cm d 8 cm e 10 cm 4 The volume of a cone of height h and base radius r is given by: a 1_ 3 πrh b 1_ 3 πr2 h c πrh d πr 2 h e 2πrh 5 A cone is 8 cm high and has a base diameter of 12 cm. Its slant height is: a 6 cm b 8 cm c 10 cm d 12 cm e 20 cm 6 In Figure R35, PQR is right-angled at Q and QR = 5 cm. Figure R35 a b If the area of PQR is 30 cm 2, find the length of PQ. Hence find the length of PR. 166 Term revision test sheets

7 Figure R36 shows the net of an open cylinder. 7 cm 10 cm Figure R35 If the net is folded to make the cylinder: a What is the radius of the cylinder? b What is the height of the cylinder? Use the value 22 for π to find: c d 7 The surface area of the open cylinder. The volume of the cylinder. 8 A mound of rice is roughly in the shape of a cone of height 12 cm and base diameter 40 cm. Use the value 3 for π to find the approximate volume of rice. 9 A cylinder of diameter 40 cm contains 62 l of water. Use the value 3.1 for π to find how deep the water is in the cylinder. 10 Estimate the capacity in litres of a cylindrical drum that is 45 cm in diameter and 66 cm high. Term revision test sheets 167

Teacher s name: Class name: Student s name: Date: Term Revision Test 9 (Chapters 18, 21, 22) Circle the correct answer in Questions 1 5. 1 In the last 20 years, it has rained on 6 January twice. Estimate the probability that it will rain on 6 January next year. 1 a 0 b 10 c 3 10 d 1_ 3 e 1_ 9 2 A card is picked at random from a pack of 52 playing cards. The probability that it is a 6 is: a 1 52 b 1 13 c 3 26 d 1 26 e 1_ 4 3 A boy has more than N900. He spends N300 and has Nm left. Which one of these inequalities gives m? a m > 500 b m < 600 c m > 600 d m < 1 200 e m > 1 200 Figure R38 is an old railway timetable for train services between Makurdi, Kafanchan and Jos. Use Figure R38 to answer Questions 4, 5 and 6. MAKURDI KAFANCHAN JOS 401 UP 402 DN Makurdi D 6.40 a.m. A 6.15 p.m. Kafanchan A 5.05 p.m. D 9.20 a.m. D 5.35 p.m. A 8.50 a.m. Jos A 9.50 p.m. D 5.00 a.m. Figure R38 4 What time does the 402 DN train depart from Kafanchan? a 5.05 p.m. b 5.35 p.m. c 6.40 a.m. d 8.50 a.m. e 9.20 a.m. 5 How long does the journey from Makurdi to Jos take? a 1 h 15 min b 3 h 10 min c 8 h 50 min d 15 h 10 min e 20 h 50 min 6 Find these times: a The time taken between Kafanchan and Jos on the UP journey. b The time taken between Jos and Kafanchan on the DOWN journey. c The difference between these two times. 168 Term revision test sheets

7 A book contains pages numbered from 1 to 48. A student picks a page at random. What is the probability that the page number contains a 3? 8 A letter is chosen at random from the word trapezium. Find the probability that it is: a A vowel. b One of the letters of the word permit. c One of the letters of the word hollow. 9 Find the range of values of x for which: a x + 9 > 14 b 6 x > 7 c 7 28 3x d 3_ x 1 1 _ 1 4 2 1_ 2 x 10 Three times a whole number, n, is subtracted from 38. The result is less than 20. a Make an inequality in n. b Find the four lowest values of n. Term revision test sheets 169

Teacher s name: Class name: Student s name: Date: Term Revision Test 10 (Chapters 20, 24) Circle the correct answer in Questions 1 5. 1 Figure R43 shows a right square-based pyramid resting so that its base is horizontal. Figure R43 Which of the points A, B, C, D, E is vertically below V? A B C D E 2 If the angle of elevation of P from Q is 38, then the angle of depression of Q from P is: a 19 b 38 c 52 d 128 e 142 3 A vertical fence post has a shadow 1 m long when the angle of elevation of the sun is 45. The height of the fence post is: a 0.5 m b 0.7 m c 1 m d 1.4 m e 2 m 4 Which of the points A, B, C, D, E in Figure R44 is on a bearing 230 from O? Figure R44 5 The bearing of P from Q is 063. The bearing of Q from P is: a 027 b 063 c 117 d 153 e 243 6 From a point P the bearing of a radio mast is 060. From a point Q 100 m due east of P, the bearing is 330. 170 Term revision test sheets

Draw a labelled sketch to show the positions of P, Q and the mast. 7 The angle of elevation of the top of a tower from a point 23 m from its base on level ground is 50. Make a scale drawing to find the height of the tower to the nearest metre. Term revision test sheets 171

8 Two posts are 1 800 m apart on a road running east and west. A tree is north of one post and on a bearing 304 from the other. Make a scale drawing and find the distance of the tree from each post. 9 A woman walks 2 km N, 3 km NE and finally 2 km E. Make a scale drawing of her journey. Find how far... she is from her starting point. a North b East 172 Term revision test sheets

10 From the top of a tree, the angle of depression of a stone on horizontal ground is 55. If the stone is 8 m from the foot of the tree, make a scale drawing to find the height of the tree. Term revision test sheets 173

Teacher s name: Class name: Student s name: Date: General Revision Test C (Chapters 17 24) Circle the correct answer in Questions 1 10. 1 In Figure R45, which one of these equations gives the value of a 2? Figure R45 a a 2 = b 2 c 2 b a 2 = (b c) 2 c a 2 = b 2 + c 2 d a 2 = c 2 b 2 e a 2 = (c b) 2 2 What is the length of the longest rod that can lie flat in a rectangular box that is 2 m long and 1 1_ 2 m wide? a 7 m b 5 1_ 2 m c 5 m d 3 1_ 2 m e 2 1_ 2 m 3 Table R6 shows the numbers of students getting Grades A, B, C, D, E in an essay. Grade A B C D E Number 5 11 24 10 6 Table R6 Which grade did the least number of students get? A B C D E 4 Which one of these curved surfaces is Figure R46 the net of? a Open cylinder b Sphere c Open cone d Half cylinder e Open hemisphere Figure R46 174 Term revision test sheets

5 A cylinder is of height 5 cm and base radius 2 cm. Use the value 3.14 for π to calculate the area of its curved surface to the nearest cm 2. a 13 cm 2 b 25 cm 2 c 31 cm 2 d 63 cm 2 e 126 cm 2 6 The height of a tree is equal to the length of its shadow. The angle of elevation of the sun is: a 0 b 30 c 45 d 60 e 90 7 A teacher picks a student at random from a class containing 17 boys and 13 girls. What is the probability that the student is a girl? a 1 30 b 1 13 c 13 30 d 17 30 e 13 17 8 The range of values of a for which 11 2a 1 is: a a 5 b a 5 c a = 5 d a 5 e a 5 9 Figure R47 is the graph of which one of these inequalities? x Figure R47 5 a x > 5 b x 5 c x < 5 d x 5 e x < 5 10 The bearing of X from Y is 196. The bearing of Y from X is: a 016 b 074 c 106 d 164 e 196 11 In Figure R48: C 14 cm A Figure R48 50 cm B a b Find the length of AC. Hence find the area of ABC. Term revision test sheets 175

12 Table R7 shows the number of students in each form of a JSS for the years 2010 to 2014. Year 2010 2011 2012 2013 2014 Form 1 90 90 118 121 119 Form 2 87 88 90 118 120 Form 3 60 87 88 89 120 Table R7 a How many students were in the school in 2013? b A girl entered Form 1 in 2010. She is one of the 90 circled in the table. If she is promoted at the end of each year: i In what year is she in Form 3? ii How many students were in Form 3 in that year? c At the beginning of which year in the table did the school increase its Form 1 intake? d In which previous year (not in the table) did the school probably increase its Form 1 intake? 13 A cone and a cylinder have equal volumes and radii. The height of the cone is 12 cm. Find the height of the cylinder. 176 Term revision test sheets

14 a Draw the graph of y = 5x 2 for values of x from 3 to +3. b At what point does the graph cut the x-axis? c What are the co-ordinates of the point where the graph meets the line y = 8? Term revision test sheets 177

15 Figure R49 shows sketch notes that a student made of a survey of a tree. Figure R49 Make a scale drawing and hence find the height of the tree to the nearest 1 _ 2 m. 16 Find the probability of selecting a shape that is a parallelogram from one square, one rectangle, one rhombus, one kite and one trapezium. 17 Find the range of values of x for which: a 4x + 4 > 7 b 28 5x < 2x + 9 c 3_ 2 x _ 7 5_ 6 2 1_ 3 x 178 Term revision test sheets

18 Use number lines to draw graphs of the solutions of these expressions: a x + _ 5 2 > 0 b 9 1 2x 19 Freetown is approximately 1 820 km on a bearing 275 from Lagos. Use a scale of 1 cm to 200 km to make a scale drawing of the positions of Freetown and Lagos. Hence find: a How far Freetown is north of Lagos. b How far Lagos is east of Freetown. 20 A student has a hand-span of about 21 cm. The diameter of a bicycle wheel is approximately three hand-spans. Estimate, to the nearest 100, the number of times the wheel turns in travelling 1 km. Term revision test sheets 179