DULWICH COLLEGE -13+ Paper 4 by smoothmaths | Sep 19, 2020 | 0 comments Welcome to your DULWICH COLLEGE -13+ YEAR 9 ENTRANCE AND SCHOLARSHIP EXAMINATION Mathematics Specimen Paper D 1. Below is a sequence of numbers: 0.5, 3, 5.5, 8, … Calculate: (a) the 8th term,1814162022 (b) the 100th term,248198250298None of the Above (c) which term has a value of 148.6055506570 2. A train was scheduled to leave at 17.40. It departed 30 minutes late and the journeytook 3 hours and 45 minutes. Find the time that it arrived at its destination.21 : 5517 : 7521 : 2511 : 553 : 75 3. (a) Simplify the ratio 25 : 15.5 : 34 : 53 : 55 : 5None of the Above (b) Divide £400 in the ratio 25 : 15.£250 , £150£160 , £240£100 , £300£150 , £250None of the Above (c) A recipe for a large cake uses 600 grams of flour and 450 grams of butter. A recipe for a smaller cake uses 400 grams of flour. Calculate how much butter is needed for the smaller cake if the ratio of flour to butter is to be the same in both cakes.300400246731450 4. The value of a painting in 2010 was £12000. Its value rose by 40% in 2011, but thenfell by 20% in 2012 and fell again by 20% in 2013. (a) Calculate the value of the painting in 2011.£16800£14400£7200£12800£12300 (b) Calculate the value of the painting in 2013.£10752£13440£14112£8192None of the Above 5. Write a simplified expression for the perimeter of the shape drawn below. a+6b+109a+6b+10-a+6b-10a+5b+8None of the Above 6. Expand and simplify the following: (a) –5(2 – 3y)-10 + 15y-10 - 15y10 - 15y10 + 15yNone of the Above (b) 2x(3x – y) – y(2y + x)6\[x^{2}\]- 3xy -2\[y^{2}\]6\[x^{2}\]- 3xy -2\[y^{2}\]6x- 3xy -2y6\[x^{2}\]+ 3xy -2\[y^{2}\]6\[x^{2}\]+ 3xy +2\[y^{2}\] (c) (4x – 5)(2 – 3x)23x-12\[y^{2}\]-1023x -12x-107x-12\[y^{2}\]+1023x+12\[y^{2}\]+10None of the Above 7. Simplify: \[\frac{6b^{2}}{12b}\]\[\frac{b}{2b}\]1/22\[b^{2}\]2\[b^{-2}\]None of the Above 8. On the grid above draw the result of: (a) reflecting triangle T in the x-axis. Label your answer A. (b) enlarging triangle T by a scale factor of 2 with centre of enlargement (–5, 5). Label your answer B. (c) translating triangle T by the vector \[\left(\frac{3}{-7}\right)\] . Label your answer C . (d) reflecting triangle T in the line y = x. Label your answer D. 9. A baseball bat and some wax for the bat together cost £50. The bat costs £48 more than the wax. Find the cost of the bat.£49£48£47£46£50 10. Calculate the total surface area of a cube whose volume is 27 cubic centimetres.54\[cm^{2}\]36\[cm^{2}\]18\[cm^{2}\]27\[cm^{2}\]81\[cm^{2}\] 11. Factorise the following expressions fully:(a) 18\[y^{2}\]– 6y6y(3y-1)3y(6y-2)6(3y-1)6(3y-y)18y(y-1) (b) 4\[a^{3}\]\[b^{2}\] - 12\[a^{2}\]b4\[a^{2}\]b(ab-3)4\[a^{2}\](ab-3)4\[a^{2}\](a\[b^{2}\]+3)4\[a^{2}\]b(b-3)4\[a^{2}\]b(a-3) 12. Solve the following equations for x: (a) 2(7 – x) = 11\[\frac{3}{2}\] or 1.5\[\frac{1}{2}\] or 0.5\[\frac{2}{3}\] or 0.6\[\frac{3}{4}\] or 0.7None of the Above (b) 3\[x^{2}\] + 2(2x – 3) = 3x( x – 2)\[\frac{3}{5}\] or 0.6\[\frac{5}{3}\] or 1.63\[\frac{1}{2}\] or 0.5\[\frac{2}{3}\] or 0.6 (c)\[\frac{x}{3}\] - 2 = 4x-\[\frac{6}{11}\]-65-\[\frac{11}{6}\]11 13. (a) Complete the table for y = 1 – 2x x -2 0 2 Y 1 (b) On the grid below, plot the lines: y = x x = –2 y =1 – 2x 14. Find the perimeter of the trapezium below. 219cm189cm154.5cm187.5cmNone of the Above 15. Two triangles ABC and BDE are drawn on a square grid as shown. Calculate what fraction of the area of triangle ABC is covered by the triangle BDE. \[\frac{1}{6}\]\[\frac{1}{3}\]\[\frac{1}{4}\]\[\frac{1}{2}\]\[\frac{3}{4}\] 16. 90% of the students at a school went on to go to university, and of these 30% stayed on to study a Master’s degree. Calculate the percentage of the students at the school who went on to study a Master’s degree.27%60%30%25%20% 17. The diagram shows a semicircle of radius 2 cm containing a smaller circle which touches the circumference and midpoint of the diameter of the semicircle as shown. Calculate the fraction of the semicircle that is shaded. \[\frac{1}{2}\]\[\frac{3}{4}\]\[\frac{1}{4}\]\[\frac{2}{3}\]\[\frac{3}{2}\] 18. In the diagram PQ = PR = RS and angle QPR = 40˚. Find the size of angle x. 105°70°40°110°75° 19. The average height of 10 trees is 2.6 metres. One of the trees grows from 1.7 metres to 2.2 metres. Calculate the new average height of the 10 trees, giving your answer to two decimal places.2.65cm2.66m2.55m2.95m3.05m 20. Find two whole numbers, neither of which has a zero for any of its digits, whose product is: (a) 100,4 & 256 & 154 & 205 & 203 & 35 (b) 1000000.64 & 1562546 & 1652556 & 1256272 & 25621None of the Above 21. Sarah’s bottom drawer contains many pieces of underwear, each coloured red, white, blue or black. There are more than two pieces of underwear of each colour. Sarah draws pieces of underwear randomly from the drawer, one at a time, and does not replace them. Write down how many pieces of underwear she must draw from the drawer in order to ensure that at least three pieces of underwear of the same colour have been drawn.9 pieces12 pieces8 pieces4 pieces16 pieces 22. Find the smallest possible value of 20a + 10b + c where a, b and c are different positive whole numbers.4313234045 23. In the diagram shown, triangle ABC is isosceles with AC = BC. Find the size of angle r in terms of p and q. \[\frac{p+q}{2}\]p+q\[\frac{p-q}{2}\]\[\frac{p-q}{3}\]None of the Above 24. I went to a store and picked up four items. The cost of three of them was £1.50, £3 and £4. I was a bit bored whilst I was waiting at the checkout and happened to notice that the sum of the prices of all four items was the same as the product of the prices of all four items. Calculate how much the fourth item cost.£0.5£0.4£1.5£0.7£0.8 25. Sixty 20p coins are lined up side by side. Every second 20p coin is then replaced by a 10p coin. Then every third coin in the resulting row is replaced by a 5p coin. Finally every fourth coin in the row is replaced by a 2p coin. Calculate the total value of the coins in the final line of coins.£6.05£4.84£5.45£7.50£5.05 Time is Up!