QUESTION 1 50 FOR JSS 3

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1 QUESTION 1 5 FOR JSS 3 1. The knowledge of probability is necessary for the following reasons except A. In predicting B. In deciding C. In selecting D. In drawing table E. In forecasting. Factorise 7a b 9ab A. 9ab(3a + b) B. 9ab(b-3a) C. 9ab(3a-b) D. 9a b(3a b) E. 9b (a b ) 3. The table shows the sales made by a trader who sells articles A, B, C and D. Product A B C D Sales (N) Using the probability of D, Find the expected sale from D, if total sales is N1,. A. N B. N333.3 C. N D. N E. N In the diagram below, which one of the following expressions for h in terms of d and α is correct? h d α A. sin α = h/d B. h = d sinα D. h = d sin α E. h = d tan α C. h = d cos α 5. Which of the following is not a quadrilateral? A. Rhombus B. Parallelogram C. Rectangle D. Square E. Triangle

2 6. Which of the following number lines is a solution of 5x 8 > 1 A. X B C x D x E x 7. Write the number , correct to decimal places? A B C D E Find the LCM of 1ab, 14b and 18a b A. 63a 3 b B. 63ab C. 63a b D. 1a b E. 1ab 9. Which of the following is not a pair of equivalent fractions? A. ½, 8 / 16 B. 3 / 1 5, / C. / 1 3, / 18 D. 3 / 4, 7 / 36 E. 3 / 5, 8 / 1 1. Express two as a number in base 1. A ten B ten C ten D ten E ten

3 11. What number must be multiplied by 5 to make ¾? A..1 B. 1 / 5 C..5 D..3 E. 1 / 8 1. Work out 1 1 X X 1 5 A. 3 1 / B. 7 1 / C. 5 1 / 3 D. 7¼ E. 6 1 / cm 3 of a metal weights 17.5g. What is the weight of 35cm 3 of the same metal, if the mass of the metal is directly proportional to the volume? A. 98.6g B. 1.g C. 13.g D. 56.1g E. 97.5g 14. The simple interest on a certain sum of money invested for 6 years at 5½% per annum is N39 6. Calculate the amount invested. A. N98 B. N1 C. N1 D. N15 E. N 15. Estimate the answer to 47.9 x ( ) by rounding each number to 1 s.f. A. 1 B. 95 C. 9 D. 85 E Which of these numbers is an irrational number? A. 41 B..81 C. (.3) D. 16 / 5 E. 9 / Evaluate (4.1 x 1 7 ) (3. x 1 6 ) and leave your answer in standard form. A. 3.7 x 1 7 B x 1 7 C x 1 6 D x 1 5 E. 1.5 x Factorise this expression; 4xyz 1ayz 4x +1a A. (yz + 1) (x + 5a) B. (yz + 1) (5a x) C. 3(yz +1) (x 5) D. (yz -1) (x + 5a) E. (yz -1) (x -5a) 19. Find the sum of the 6 th and 7 th term of the sequence 3,7,11,15,19.. A. 5 B. 4 C. 39 D. 37 E. 5

. Solve the equation: 3 y+ y 1 A. y = -13 B. y = -1 C. y = 1 D. y = 13 E. y = 15 1.

4 . Solve the equation: 3 y+ y 1 A. y = -13 B. y = -1 C. y = 1 D. y = 13 E. y = The solution of the simultaneous equations: x + y = 1, 4x y = 4 graph is y x + y = 1 4x y = x A. x = -1, y = -3 B. x = 1, y =3 C. x = +1, y = + D. x = 3, y = E. x = 3, y = 4. <POR in the construction below is P O A. 9 o B. 6 o C. 3 o D. 15 o E. 7½ o R

5 3. In the diagram below, ABC is similar to ADE AB = 9cm, BE = 1cm, AC = 15cm, find CD? A 1cm B 9cm Z 15 cm C E A. 7cm B. 5cm C. 3cm D. cm E. 1cm Z D 4. How many edges has a triangular prism? A. 3 B. 4 C. 5 D. 8 E Find the area of parallelogram with base 1cm and height 7cm. A. 74cm B. 8cm C. 84cm D. 88cm E. 9cm 6. A simple way of representing data using identical drawing or pictures is called. A. Pictogram B. Bar chart C. Pie chart D. Histogram E. Cumulative frequency curve 7. Find the square root of 111 two? A. 11 two B. 111 two C. 1 two D. 11 two E. 11 two 8. The sum of the angles of a polygon is right angles. How many sides has the polygon? A. 8 sides B. 1 sides C. 13 sides D. 15 sides E. 16 sides 9. How many vertices has a square based pyramid? A. 4 B. 5 C. 6 D. 7 E. 8

6 3. Solve the equation: 3 (x + 3) 7 (x + ) = A. x = B. x = 5 C. x = -5 D. x = -6 E. x = A trader gains N4, on a sale which was equivalent to 8% profit. What was the cost price? A. N3. B. N5. C. N3. D. N5. E. N Calculate the length of the third side of the triangle. a cm 5cm A. a = 6cm B. a = 1cm C. a = 13cm D. a = 15cm E. a = 17cm 33. Calculate the total surface area of a solid cone of vertical height 4cm and base diameter 14cm. [use the value / 7 for π] A. 51cm B. 61cm C. 85cm D. 85cm E. 74cm 34. If the bearing of X from Y is 47 o, find the bearing of Y from X. A. 1 o B. 18 o C. 9 o D. 8 o E. 67 o 35. The electric resistance R ohms of a wire of a given length varies inversely as the square of the diameter of the wire, d mm. If R = 7 ohms when d = 5mm, find the equation connecting R and d. A. R = 17 ohms B. R = 196 ohms C. R = 675 ohms d d d D. R = 1 k ohms E. R = 167 ohms d d [Note: k is constant] 13cm

7 36. Solve simultaneously: x -y = 4, x + 5y = 17 A. x = 1, y = 6 B. x = 1, y = 4 C. x = 8, y = 3 D. x = 7, y = E. x = 6, y = Solve the equation: cos Ɵ = Sin 3Ɵ for o < Ɵ < 9 o A. Ɵ = 1 o B. Ɵ = 18 o C. Ɵ = 15 o D. Ɵ = 1 o E. Ɵ = o 38. Approximate correct to 1 significant figure A. 7 B. 7 C. 6 D. 6 E Approximate 148 to the nearest ten. A. 143 B. 148 C. 14 D. 15 E An arc subtends an angle of 15 o at the centre of a circle of radius 6cm. find the length of the arc, if π is 7 A. 8.cm B. 9cm C. 1cm D. 11cm E. 1cm 41. Factorise a + 7a + 6 A. (a 6) (a + 1) B. (a + 6) (a 1) C. (a + 6) (a + 1) D. (a 6) (a -1) E. (a + 7) (a + 1) 4. What is the size of <PAB in the construction shown below: P A A. 9 o B. 75 o C. 6 o D. 3 o E. 45 o 43. The quantity y is partly constant and partly varies inversely as the square of x. write down the relationship between x and y. [use a & b as constant] A. y = ax + b/x B. y = a b/x C. y = ax + b/x D. y = a +b/x E. y = a + b/x B

8 44. Triangle ABC and XYZ are equiangular. Calculate XY A X B 17 cm 8.5cm. 4c m A. 5cm B. 6cm C. 7cm D. 9cm E. 1cm C Y.5cm Z 45. Each face of a cuboid is in the shape of a A. Square B. Rectangle C. Triangle D. Pentagon E. Kite The diagram below shows the speed-time graph of a car. Use the diagram to answer question 46 & 47. Sp ee d (m 15 Time(s) Calculate the acceleration of the car during the first seconds. A. 1 / 3 m/s B. 6 / 7 m/s C. / 5 m/s D. 3 / 4 m/s E. 1 / m/s 47. Calculate the distance the car travels from rest before it begins to decelerate? A. 9m B. 6m C. 5m D. 35m E. m 48. A circle of radius r, has chord 4cm long. Calculate the radius of the circle, if the chord is 9cm from the centre of the circle. A. 31.cm B. 1cm C. 16cm D. 15cm E. 6.8cm

9 49. The surface area of a sphere of radius r is S, where terms of s and π S 4 r. Express r in A. 4π S B. S 4π C. π S D. S π E. S 4π 5. The scale on a map is 1:. The length of a bridge is 1.5km. Calculate its length in cm on the map. A. 9.cm B. 8.3cm C. 7.5cm D. 6.5cm E. 5.5cm

10 JSS3 WORKED SOLUTIONS FOR 17 MATHSCHAMP 1. The knowledge of probability is not necessary in drawing table but necessary in all the other options. Option D is the correct answer.. 7a b 9ab 9 ab(3 a b). Option C is the correct answer. 3. From the table, the probability of D 4 4. The expected sale from D is 1,. 15 N Option A is the correct answer. h 4. Using the trigonometrical ratio of sine, sin and h dsin. Option D is the correct d answer. 5. A quadrilateral is a plane shape with 4 sides. A triangle is not a quadrilateral because it has 3 sides. Option E is the correct answer. 6. 5x 8 1, 5x 1 8, 5x and x 4. Option B is the correct answer to decimal places. Option C is the correct answer. 8. 1ab 5 a b, 14b 7 b b, 18a b 3 3 a a b. L.C.M a a b b 63a b. Option C is the correct answer and 8 1 the correct answer. are not equivalent because 8 1 in the lowest terms is 4 5 and not 3 5. Option E is two ten Option A is the correct answer Let the number be x. correct answer. 3 x 5, x 5.3 Option D is the Applying the rule of BODMAS, Option B is the correct answer

11 cm the correct answer. weighs 17.5g, therefore 3 35cm will weigh g. Option E is answer. PRT I 1, 1I P RT 1 39,6 3,96, 1,. Option C is the correct By rounding each number to 1 significant figure, 47.9 ( ) 5 (1 7) Option D is the correct answer. 16. Option A is the correct answer because 41 is a prime number and its square root cannot be expressed as a fraction of two integers while each of the other options can be expressed as a fraction of two integers. (4.1 1 ) (3. 1 ) Option B is the correct answer xyz 1ayz 4x 1a 4xyz 4x 1ayz 1a (xyz x 5ayz 5 a) x( yz 1) 5 a( yz 1) ( yz 1)( x 5 a). Option E is the correct answer. 19. Each term of the sequence is formed by adding 4 to the previous term. Therefore, the 6 th term is 3 while the 7 th term is 7. Hence, the sum of 6 th and 7 th terms is 3+7=5. Option A is the correct answer y y 1, 3 y 1 5 y, 6y 3 5y 1, 6y 5y 1 3, y 13. Option D is the correct answer. 1. The solutions to the simultaneous linear equations is the intersection of the two linear graphs. At the point of intersection, x 3and y 4. Option E is the correct answer.. POR 6. Option B is the correct answer. 3. From the diagram, ABC and ADE are equiangular hence they are similar. AB AC BC 9 15 BC 9 15 Therefore,,, AD AE DE 15 CD 9 1 DE 15 CD 9 1, 3 15 CD 15 CD 9, 15 CD 18 CD cm. Option C is the correct answer. 4. A triangular prism has 9 edges, 6 vertices and 5 plane faces ( triangular faces and 3 rectangular faces). Option E is the correct answer.

12 5. Area of parallelogram = base height = cm. Option C is the correct answer. 6. Option A is the correct answer two ten. Therefore, the square root of 111 two square root of 81 ten is equal to the. Hence, 81ten 9ten 11two. Option D is the correct answer. 8. n 18 9, answer. 9 n 11 and n 13. Option C is the correct A square based pyramid has 5 vertices. Option B is the correct answer , 6x 9 7x 14, x 14 9 and 3. x x the correct answer. x 5 Option C is profit 31. Let the cost price be N x. Percentage profit 1%. cos tprice 8x 4 1 and 3. Using Pythagora s theorem, 4 1 x 5. Option D is the correct answer. 8 a 5 13, a Option B is the correct answer. 33. Total surface area of a cone = r l , % 1%, x a and rl, but l h r, l. Therefore, total surface area Option E is the correct answer. 7 l 4 7, 34. If the bearing of X from Y is 47, then the bearing of Y from X is = 67. Option E is the correct answer. 1 k 35. R, R where k is a constant. By cross multiplying, k Rd d d Therefore, R. Option C is the correct answer. d 36. x y 4 (1) x 5y 17 () (1) : x 4y 8 (3)

13 () (3) :9y 9 in Option E is the correct answer. y 1, substituting for y (1) : x (1) 4, x 4 and x 6 x 6, y If cos sin 3 and B is the correct answer. 9, then 3 9, 5 9 and 18. Option correct to 1 significant figure. Option A is the correct answer correct to the nearest ten. Option A is the correct answer. 4. Length of arc r cm. Option D is the correct answer In order to factorise the quadratic expression, we find two numbers whose product is 6 and whose sum is 7. The two numbers are 6 and 1, hence a 7a 6 ( a 1)( a 6). Option C is the correct answer. 4. Angle 9 is first constructed and then bisected. Option E is the correct answer. b 43. y a. Option D is the correct answer. x 44. ABC is similar to XYZ, therefore, Option A is the correct answer. AB XY, BC YZ 17 XY, XY cm Each face of a cuboid is in the shape of a rectangle. Option B is the correct answer. 46. Acceleration speed time ms. Option D is the correct answer. 47. The distance is given by the sum of the areas of the first triangle and the middle rectangle 1 in the graph. Therefore, distance m. Option A is the correct answer. 48. A r 1cm O 9cm M 1cm B

14 Let the length of the chord be AB 4cm and AM 1cm. Therefore, using Pythagora s theorem, answer. r and r 5 15cm. Option D is the correct 49. S 4 r, r S 4 and r S 4. Option E is the correct answer. 5.,cm on land is represented by 1cm on the map. 1.5km = 1.5 1, = 15,cm. Therefore, 15,cm long bridge will be represented by 15, 7.5cm on, the map. Option C is the correct answer.

Preliminary chapter: Review of previous coursework. Objectives

Preliminary chapter: Review of previous coursework Objectives By the end of this chapter the student should be able to recall, from Books 1 and 2 of New General Mathematics, the facts and methods that