FOREST SCHOOL 13+ Paper 1 by smoothmaths | Sep 24, 2020 | 3 comments Welcome to your Forest School 13+Entrance Examination Sample Paper 1 1. Calculate the following: (a) 9784 + 83671815117151180411805117141 (b) 576 × 181036893681026810328None of the Above (c) 121815 ÷ 913535133551358013545None of the Above (d)\[0.14^{2}\]0.01960.1960.0280.281.096 (e) The number halfway between 3.4 and 4.13.753.253.503.653.55 2. Calculate the following: (a)\[(-2)^{3}\]-84812-4 (b) -5 × -525-25125225None of the Above (c) -15 + 6-9219-21None of the Above (d) -18 ÷ 3-6-7-5-46 3. If x = -2, y = 3 and z = -6 calculate the following: (a) x – y × z1630182420 (b) \[2y^{2}\]1836162432 4. (i) Expand and simplify (a) 3(2x + 4y) + 5(6x – y)36x + 8y2(18x + 4y)30x - 8yBoth a & b24x + 8y (b) 3x\[y^{2}\] (2x + 5y)6\[x^{2}y^{2}\] + 15x\[y^{3}\]6x\[y^{2}\] + 15x\[y^{3}\]6\[x^{20]}y + 15x\[y^{2}\]6\[x^{2}y^{2}\] + 15\[x^{2}\]yNone of the Above (ii) Factorise these expressions as far as possible(a) 2x + 10y2(x + 5y)2x(1 + 5y)12(x + y)12(x - y)None of the Above (b) 10\[x^{3}\]\[y^{2}\] + 4\[x^{2}\]y2\[x^{2}\]y(5xy+2)2xy(5xy+2xy)2\[x^{2}\]y(5xy+2y)2xy(5\[x^{2}\]y+2xy)None of the Above 5. When my father was 31, I was 8. Now he is twice as old as me. How old am I now?23 years13 years33 years25 years20 years 6. Calculate, giving your answer in simplest form: (i) \[\frac{5}{7}\] + \[\frac{3}{4}\]1 \[\frac{13}{28}\]\[\frac{8}{11}\]\[\frac{19}{28}\]\[\frac{29}{11}\]None of the Above (ii) \[\frac{5}{7}\] ÷ \[\frac{10}{21}\] \[\frac{3}{2}\]1 \[\frac{1}{2}\]\[\frac{1}{2}\]\[\frac{2}{3}\]1 \[\frac{1}{3}\] (iii) 16\[\frac{2}{3}\] - 12\[\frac{3}{4}\]3 \[\frac{11}{12}\]1 \[\frac{1}{2}\]\[\frac{2}{3}\]\[\frac{11}{12}\]2 \[\frac{11}{12}\] (iv) 1\[\frac{2}{3}\] × 2\[\frac{3}{4}\]4 \[\frac{7}{12}\]2 \[\frac{6}{12}\]3 \[\frac{1}{2}\]2 \[\frac{8}{9}\]3\[\frac{5}{12}\] 7. (a) Karthegan scores14 out of 40 in a test. What % is this?35%33%45%25%55% (b) Increase £42 by 10%.£46.20£41.80£45.80£47.20£48.20 (c) What is the percentage increase from £56 to £63?12.5%11.1%5.2%10.5%14.5% 8. (i) What are the mean, median, mode and range of these numbers? 2,3,3,4,2,1,2,7mode=2, median =2.5, range=6,mean=3mode=3, median =1.5, range=5,mean=5mode=4, median =3.5, range=4,mean=3mode=1, median =5, range=6,mean=2.5mode=1.5, median =4.5, range=3,mean=4 (ii) Three different prime numbers have a mean of 10 and a median greater than 10. What are the numbers?2,11,175,13,197,11,133,11,177,13,19 (iii) Class A and Class B both took the same maths test. The mean of Class A was 50% and the mean of Class B was 80%. Sophia said: “Everyone in Class B did better than everyone in Class A in the test.” Do you agree? Explain your reasoning clearly. 9. The probability that it rains on a day in April in Nodnol is 0.2 (i) What is the probability it doesn’t rain?0.81.20.21.8None of the Above (ii) How many days in April would you expect it to rain? (There are 30 days in April)6 Days15 days5 days3 days24 days (iii) In 3 consecutive days in April it could rain, not rain, rain. We can write this RNR. List all the different possibilities for 3 days in this way and so find the probability it rains on exactly one of the days.0.3752.60.4280.330.275 10. In a group of children the ratio of boys to girls is 3:5. (i) If there are 72 children in all, how many boys are there?279241420 (ii) On a fruit stall the ratio of apples to bananas is 4:5 and the ratio of bananas to plums is 2:7. What is the ratio of apples to plums?8:358:1010:3514:35None of the Above 11. In this question use the following exchange rates. £1 = $ 1.20 1 Euro = 85p (a) Is £1 worth more or less than 1.1 Euros? You must justify your answer clearly.1.1Euro<£11.1Euro>£11.1Euro=£11.1Euro=$1None of the Above (b) What is £1.70 in dollars?$2.04$2.40$1.40$1.04None of the Above 12. S is the sum of all the even numbers from 2 to 1000 inclusive . T is the sum of all the odd numbers from 1 to 999 inclusive. What is S – T? Show your working clearly.500400800300700 13. Alex throws 2 ordinary dice and adds the scores. Grace throws 1 dice and doubles the score on the dice. Who is more likely to score 10 or more? Explain your reasoning clearly.Grace is more likely to score more than10 or moreAlex is more likely to score more than10 or moreBoth may score more than10 or moreNo one is more likely to score more than10 or moreNone of the Above 14. You are given that 24 × 36 = 864. Use this to write down the answers to these: (i) 12 × 72864684860486846 (ii) 2.4 × 360008640068400860004860084600 (iii) 864 ÷ 0.362400311140025002800 15. In this regular octagon calculate the angles x, y and z x=45 y=67.5 z=135x=60 y=60 z=154x=51.4 y=64.3 z=120x=45 y=72.5 z=180None of the Above 16. If 3 chickens lay 3 eggs in 3 minutes, how many eggs would 9 chickens lay in 9 minutes, laying eggs at the same rate?27 Eggs9 Eggs18 Eggs12 Eggs15 Eggs 17. On these axes mark clearly the points A (2,3), B (2,-4) and C (-3,-2) (i) What is the equation of the line AB?x = 2x = -3x = -2x = 3None of the Above (ii) What is the area of the triangle ABC?17.5 squnits12.5 squnits10.5 squnits16.5 squnitsNone of the Above (iii) The point D fits on the diagram above and ABCD is a parallelogram. What are the coordinates of D?(-3,-5)(4,5)(2,3)(-3,5)(1,2) 18. The middle section of a magazine has been removed to reveal pages 34 and 87. (i) If the above sheet containing pages 34 and 87 was removed, which pages would you then see?Page 32 & Page 89Page 36 & Page 85Page 32 & Page 85Page 34 & Page 87None of the Above (ii) How many pages does the magazine have in total?120 Pages121 Pages119 Pages110 Pages112 Pages Time is Up!