User:Fangz/KS2 Answers

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KS2 Exam answers
1. a+b = 21, a-b = 5. So 2a = 26. Ans: 13, 8

2.

OOX

OOO

XOX

and

XOOX

OOOO

3. Arton in the middle, Boxham in the left, Carby outside both circles, but in the box

4. a+b = 18, b + c = 16, 2a = 14. Ans: a = 7, b = 11, c = 5

5. 95 + 4x = 155, so x = 60/4 = 15 Ans: 110, 125, 140

6. x > 30, x < 33.333.. Ans: 31, 32, 33

7. 41. (Check multiples of 5 + 1)

8. 1/3 = 5/15, 2/5 = 6/15, so 2/5 is larger.

9. The remaining area is 3/4 + 3/4. So the total area is 7/4. So the fraction is 1/4 * 4/7 = 1/7.

By the same argument, the total area is 5/3, so the fraction is 1/3 * 3/5 = 1/5

10. Angle of an equilateral triangle is 60 deg, so a = 360 - 90 - 90 - 60 = 120 deg

11. The 'end' edges are 8 cm, and the 'inner' edges are (18 - 8)/2 = 5 cm. So straightforward counting exercise gives 8 x 5 + 4 x 8 = 72cm

12. Length = 14 cm. Width = (22 - 14)/2 = 4 cm. So area is 56 cm^2. (Man, in my day, we had to put in the units ourselves. Kids these days.)

13. The largest area has P and Q as corners of the same (diagonal) edge. The direct distance between the two pts is by Pythagoras, sqrt(3^2 + 3^2). So the area is 3^2 + 3^2 = 18.

KS3 Answers
1. Tons of different solutions, but the positive integer answers are 1x50, 2x25, 5x10

2. B. With the other two, the outer numbers sum to equal the middle number.

3. This is fiddly. Try and add and subtract areas in pairs to get a rectangle. See

4. Left is 5. For rest, tick off the ones used and experiment at making 15. Or employ other sudoku-esque magic. Ans: Clockwise 8, 3, 1, 9, 5

5. Hey, check it out, it's the same broken question that was in the paper. I guess maybe any possible answer will do, as long as it's consistent. So feel free to throw in random numbers at the bottom (adding up to 8.2, and continue. Maybe there was an errata that year.

6. Similar to the previous. This time, start in the middle tier and work down.

7. Surface area is 80 + 160 + 100 = 340cm^2. The sheet is easily big enough, at 750cm^2. Though you might need to use scissors, depending on how you are wrapping.

8. Total messages then are 80, and 52 for boys and girls respectively. Note that this is ALL the info the means give us. So (a) is false, since it's possible for the girls to have an even spread whilst the boys have all of their messages received by one boy. For (b), mean is (52+80)/6 = 132/6 = 22, so also false.

9. No. The square of an even number is always even, and the square of an odd number is always odd. So, the square root of this number must be even, and the only even prime number is 2. But obviously, the square root of this number isn't 2.

10. Focus on the cross in the middle. Equilateral triangles have angle 60. So each rhombus has acute angle (360 - 4 * 60)/4 = 30 deg. Since the two angles in a rhombus add to 180, the obtuse angles must be 180 - 30 = 150 deg.

11. The two operations are 5x + 8, 5x + 5 * 8. So the smaller number is always the first one. So x = (73 - 8)/5 = 13. For the second part, deduct the two expressions, getting 4*8 = 32

12. The total area is 9a. The shaded area is 4a - a (think about moving halves around). So, the fraction is 3/9 = 1/3.

13. About the top 1100/45000 = 2.44... % of pupils got into the finals. Looking at the first chart on the next page, clearly this means that we need x to be between 21 and 25, and probably closer to 25. Something like 24 or 25 would probably be a good guess. The second graph is a red herring, since we have no idea how the marks are awarded in the finals, compared to the main competition.