Term revision test sheets

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1 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 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 is divisible by 6. ii is divisible by 9. iii 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_ What is in standard form? e 6 1_ 8 a b c d e What is to 3 significant figures? a b c d 386 e If 1 2 = = = = = a Complete: n (n + 1) =. b Use this to calculate Write as a product of its prime factors. Hence find These numbers are in standard form. Change them to ordinary form. a b c d e f 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 word essay. 140 Term revision test sheets

2 10 Draw graphs to show: a The first six multiples of 3. b The factors of 42. Term revision test sheets 141

3 Teacher s name: Class name: Student s name: Date: Term Revision Test 2 (Chapters 3, 6) Circle the correct answer in Questions 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 Term revision test sheets

4 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 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

5 Teacher s name: Class name: Student s name: Date: Term Revision Test 3 (Chapters 4, 5, 7) Circle the correct answer in Questions 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 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 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_ Term revision test sheets

6 7 Solve these expressions: a 3x = 18 b 1_ a = c n_ 2 = 5 27 d d = m 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

7 Teacher s name: Class name: Student s name: Date: General Revision Test A (Chapters 1 8) Circle the correct answer in Questions 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 in standard form. a b c d e 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 Term revision test sheets

8 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 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 Express these numbers as products of their prime factors. a 800 b 126 c If 1 = = = = 4 2 = What will be the value of y, if = y 2? 13 Express as a whole number correct to 2 significant figures. 14 Express correct to: a 3 decimal places. b 2 significant figures. Term revision test sheets 147

9 c The nearest Simplify these expressions: a ( 6) (+5) b (+7) ( 0.9) c ( 10) 2 d ( 5) ( 40) e ( 5.4) (+0.6) +34 f Solve these expressions: a 3_ m = 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 R Term revision test sheets

10 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 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

11 Teacher s name: Class name: Student s name: Date: Term Revision Test 4 (Chapters 9, 10) Circle the correct answer in Questions In 2010, a watch cost N In 2014, the same watch cost N 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 : 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 N 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 N % Next N % Next N % Above N % Allowances to be deducted before income is taxed: For self Allowance of N For each child under 16 Allowance of N Table R1 5 Daudu has two children under 16. Use Table R1 to calculate his allowances before tax. a N b N c N d N e N Daudu (in Question 5) has a monthly salary of N 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

12 7 The hire purchase price of a motor bike is N 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 N He also sells a SIM starter pack costing N 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 N each, five tennis rackets at N9 900 each and 14 electric kettles at N2 550 each. Term revision test sheets 151

13 Teacher s name: Class name: Student s name: Date: Term Revision Test 5 (Chapters 11, 13) Circle the correct answer in Questions 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 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 a 8 5x b (12 5x) c 17 x d (25 x) e x 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 x = a x = 9 1 b x = 5 c x = 4 _ d x = 4 e x = 1 _ 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 = a c 9 5x = 3 2x d 13x + 15 = 7x Term revision test sheets

14 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 = The height of a boy is x cm. His father is 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

15 Teacher s name: Class name: Student s name: Date: Term Revision Test 6 (Chapters 12, 14) Circle the correct answer in Questions 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 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 N Approximately what length of cloth can I buy for N900? a 1.3 m b 2.5 m c 4 m d m e 17.5 m Figure R24 Cost and length of cloth 154 Term revision test sheets

16 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

17 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

18 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

19 Teacher s name: Class name: Student s name: Date: Term Revision Test 7 (Chapters 15, 16) Circle the correct answer in Questions 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 Which one of these buildings is on Banjul Crescent? a Bank b Church c Dispensary d Mosque e Station Figure Term revision test sheets

20 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

21 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

22 Teacher s name: Class name: Student s name: Date: General Revision Test B (Chapters 9 16) Circle the correct answer in Questions 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 N b N c N 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

23 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 : 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 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 N 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 N % Over N and up to N % Over N and up to N % Over N % Table 10.1 Tax bands for PAYE system If a woman's income is N 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

24 c Simplify 5 t 4 t (2x 3) d Simplify 1_ 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

25 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

26 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

27 Teacher s name: Class name: Student s name: Date: Term Revision Test 8 (Chapters 17, 19) Circle the correct answer in Questions 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

28 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

29 Teacher s name: Class name: Student s name: Date: Term Revision Test 9 (Chapters 18, 21, 22) Circle the correct answer in Questions 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 < e m > 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

30 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 x d 3_ x 1 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

31 Teacher s name: Class name: Student s name: Date: Term Revision Test 10 (Chapters 20, 24) Circle the correct answer in Questions 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 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 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 Term revision test sheets

32 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

33 8 Two posts are 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

34 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

35 Teacher s name: Class name: Student s name: Date: General Revision Test C (Chapters 17 24) Circle the correct answer in Questions 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 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 R Term revision test sheets

36 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 d e 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 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

37 12 Table R7 shows the number of students in each form of a JSS for the years 2010 to Year Form Form Form Table R7 a How many students were in the school in 2013? b A girl entered Form 1 in 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

38 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

39 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

40 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 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