# Cambridge International Examinations Cambridge International General Certificate of Secondary Education

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2 2 Formula List For the equation ax 2 + bx + c = 0 x b! b 4ac = - - 2a 2 Curved surface area, A, of cylinder of radius r, height h. A = 2rrh Curved surface area, A, of cone of radius r, sloping edge l. A = rrl Curved surface area, A, of sphere of radius r. A = 4rr 2 1 Volume, V, of pyramid, base area A, height h. V = Ah 3 Volume, V, of cylinder of radius r, height h. 2 V = rr h Volume, V, of cone of radius r, height h. 1 2 V = rr h 3 Volume, V, of sphere of radius r. A 4 3 V = rr 3 a b c = = sin A sin B sin C c b a = b + c - 2bc cos A 1 Area = bc sin A 2 B a C

3 3 Answer all the questions. 1 The table shows the marks that 80 students scored in an examination. Mark Number of students (a) Write down the mode. Answer(a)... [1] (b) Write down the range. Answer(b)... [1] (c) Find the median. Answer(c)... [1] (d) Find the interquartile range. Answer(d)... [2] (e) Calculate the mean. Answer(e)... [1] [Turn over

4 4 2 Solve the simultaneous equations. You must show all your working. 5x 2y = x + 3y = 0 Answer x =... y =... [4] 3 A car of length 4.5 metres is travelling at 72 km/h. The car approaches a tunnel of length 260 metres. (a) Change 72 km/h into m/s. (b) Find the time it will take for the car to pass completely through the tunnel. Give your answer in seconds. Answer(a)... m/s [1] Answer(b)... s [2]

5 5 4 y 10 9 A B x (a) Describe fully the single transformation that maps triangle A onto triangle B. Answer(a) [2] (b) Rotate triangle B through 90 clockwise, centre ( 1, 6). Draw this triangle and label it C. [3] (c) Describe fully the single transformation that maps triangle C onto triangle A. Answer(c) [2] [Turn over

6 6 5 (a) y varies inversely as the square root of x. y = 5 when x = 9. (i) Find the value of y when x = 25. (ii) Find the value of x when y = 25. Answer(a)(i) y =... [2] (iii) Find x in terms of y. Answer(a)(ii) x =... [2] Answer(a)(iii) x =... [2] (b) y x Find the equation of this quadratic curve. Answer(b)... [3]

7 7 6 The Venn diagram shows the sets A, B and C. U A C B U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} A = {factors of 12} B = {factors of 6} C = {11, 12, 13, 14} (a) List the elements of sets A and B. Answer(a) A = {...} B = {... } [2] (b) Write all the elements of U in the correct regions of the Venn diagram above. [3] (c) List the elements of (i) A + B, (ii) Al + C, (iii) B, Cl. (d) Find (i) n( A, B, C) l, (ii) n( A + B + C) l. Answer(c)(i) {... } [1] Answer(c)(ii) {... } [1] Answer(c)(iii) {... } [1] Answer(d)(i)... [1] Answer(d)(ii)... [1] [Turn over

8 7 Squash balls have radius 1.5 cm. They are sold in boxes. Each box is a cuboid. Each box has length 15 cm, width 12 cm and height 3 cm. (a) Show that the maximum number of balls in a box is [1] (b) Calculate the volume of one ball. Answer(b)... cm 3 [2] (c) Calculate the total volume of 20 balls. Answer(c)... cm 3 [1] (d) Write your answer to part (c) in standard form. Answer(d)... cm 3 [1] (e) Calculate the percentage of the volume of the box that the 20 balls fill. Answer(e)... % [2]

9 9 8 C A NOT TO SCALE O X 26 P B A, B and C lie on a circle, centre O. AP and BP are tangents to the circle. AB intersects OP at the point X and angle OPB = 26. (a) Find the size of (i) angle ABP, Answer(a)(i)... [1] (ii) angle OBA, Answer(a)(ii)... [1] (iii) angle ACB. Answer(a)(iii)... [1] (b) Write down the mathematical name of quadrilateral AOBP. Answer(b)... [1] (c) Complete these statements. (i) Triangle OBP is congruent to triangle.... [1] (ii) Triangle OBP is similar, but not congruent to, triangle.... [1] [Turn over

10 10 9 The table shows the amount in dollars, y, that 10 families of different size, x, spend in one week. Number in family, (x) Amount in dollars, (y) (a) (i) Complete the scatter diagram. The first four points have been plotted for you. y Amount in dollars Number in family x [2] (ii) What type of correlation is shown by the scatter diagram? Answer(a)(ii)... [1]

11 11 (b) Find (i) the mean family size, Answer(b)(i)... [1] (ii) the mean amount spent in one week. (c) (i) Find the equation of the regression line in the form y = mx + c. Answer(b)(ii) \$... [1] Answer(c)(i) y =... [2] (ii) Use your answer to part (c)(i) to estimate the amount spent in one week by a family of 4. Answer(c)(ii) \$... [1] [Turn over

12 12 10 B 72 NOT TO SCALE 65 m 80 m A C 64 m 58 D (a) Find AC. Answer(a)... m [2]

14 14 11 Paula invests \$3000 in Bank A and \$3000 in Bank B. (a) Bank A pays compound interest at a rate of 4% each year. (i) Find the total amount that Paula has in Bank A at the end of 3 years. Answer(a)(i) \$... [2] (ii) After how many complete years is the total amount that Paula has in Bank A greater than \$4000? (b) Bank B pays simple interest at a rate of 5% each year. Answer(a)(ii)... [3] (i) Find the total amount that Paula has in Bank B at the end of 3 years. Answer(b)(i) \$... [1] (ii) After how many complete years is the total amount that Paula has in Bank B greater than \$4000? Answer(b)(ii)... [1] (c) After how many complete years will the total amount that Paula has in Bank A be greater than the total amount that Paula has in Bank B? Answer(c)... [3]

15 12 Bag 1 only contains 6 blue balls and 4 red balls. Bag 2 only contains 8 blue balls and 2 red balls. Marco chooses a ball at random from Bag 1 and puts it in Bag 2. He then chooses a ball at random from Bag 2 and puts it in Bag 1. (a) Complete the tree diagram. 15 Bag 1 Bag 2... blue 6 10 blue... red blue red (b) Find the probability that the two balls chosen are... red [2] (i) both blue, Answer(b)(i)... [2] (ii) one red and one blue. Answer(b)(ii)... [3] (c) Find the probability that, after Marco chooses the two balls, there are exactly 6 blue balls in Bag 1. Answer(c)... [3] [Turn over

16 16 13 In this question all lengths are in centimetres. 2x 1 6x + 1 NOT TO SCALE 5x + 4 (a) Write down a quadratic equation, in terms of x, and show that it simplifies to 7x 2-24x - 16 = 0. [3] (b) Factorise 7x 2-24x Answer(b)... [2]

17 17 (c) Show that the area of the triangle is 84 cm 2. (d) The area of this rectangle is equal to the area of the triangle. Find the value of y. y y + 2 [2] NOT TO SCALE Answer(d) y =... [4] [Turn over

18 18 14 In this question all measurements are in metres. A rectangular garden has length p and width q. The garden is divided into 3 sections as shown in the diagram. 2 3 p 1 4 q Vegetables x Flowers NOT TO SCALE q Grass p (a) Write down an expression, in terms of p and q, for the area for flowers. Answer(a)...m 2 [1] 3 (b) Show that x = p. 4 [2]

19 19 (c) Find an expression, in terms of p and q, for the area for grass. Give your answer in its simplest form. (d) Find the ratio area for vegetables : area for grass. Answer(c)...m 2 [2] Answer(d)... :... [2] Question 15 is printed on the next page. [Turn over

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