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1. A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
2. Toma spent 4 euros, then spent half of what was left, and now has 6 euros. How much did she start with?[3]
3. In the number 4073, what is the value of the digit 7?[3]
4. Three quarters of a class of 28 travelled by bus. How many did not travel by bus?[3]
5. Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
6. A bag of flour holds 2.5 kg. 1750 g are used. How many grams are left?[3]
7. Which of these fractions lies between one third and one half?[3]
8. A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?[3]
A (1, 3)B (1, 7)C (5, 3)D (7, 7)E (7, 3)9. What is the remainder when 7 to the power 100 is divided by 5?[3]
10. A sequence is defined by a(1) = 2 and a(n+1) = 2 a(n) - 1 for every n. What is a(6)?[3]
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1. E — 60 KA-0026 Percentages and simple discounts
A I worked out the size of the discount and gave that as the new price instead of subtracting it.B I treated a quarter off as half off and took the price down to 40.C I applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.D I subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.2. C — 16 KA-0050 Working backwards
A I added the 4 and the 6 and stopped, forgetting to undo the halving.B I doubled the 6 first and then added the 4, reversing the steps in the wrong order.D I doubled the total at the end rather than doubling only the amount left after the first spend.E I doubled twice because spending half felt like it needed undoing more than once.3. C — 70 KA-0055 Place value and digit positions
A I gave the last digit of the number instead of looking at the 7 at all.B I gave the digit itself rather than what it is worth in the position it sits in.D I counted the positions from the left, so I read the 7 as being in the hundreds place.E I gave the value of the largest digit instead of the value of the 7.4. B — 7 KA-0064 Fractions of a quantity
A I divided 28 by 7 instead of taking a quarter of it.C I found three quarters of 16 by mistake, mixing up the class size.D I found how many did travel by bus and gave that instead of how many did not.E I subtracted the 4 quarters as if they were 4 students.5. B — 75 KA-0088 Angles on lines, in triangles, in polygons
A I added the three angles wrongly, getting 295 instead of 285.C I used an angle sum of 370, mis-remembering the total for a quadrilateral.D I repeated one of the given angles instead of computing the missing one.E I used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.6. C — 750 KA-0113 Unit conversion
A I worked in kilograms and gave the answer in kilograms when grams were asked for.B I converted 2.5 kg to 250 g rather than 2500 g.D I subtracted 1750 from 3000, mis-converting 2.5 kg as three thousand grams.E I subtracted without converting at all, taking 2.5 away from 1750.7. C — 2/5 KA-0141 Number lines and betweenness
A I compared the bottom numbers and assumed a bigger denominator means a bigger fraction.B I saw that 4 lies between 3 and 2 and assumed one quarter therefore lies between the two fractions.D I checked that it is bigger than one third but never checked it against one half.E I compared the top numbers only and ignored what the bottoms do to the size.8. E — (7, 3) KA-0145 Grid coordinates and lattice reasoning
A I moved left instead of right, subtracting the 4 rather than adding it.B I moved left and up, reversing both directions.C I swapped the two coordinates round before moving.D I moved up instead of down, adding the 2 rather than subtracting it.9. A — 1 KA-0169 Remainders and modular cycles
B I reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.C I read the cycle backwards and landed on the entry before the right one.D I used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.E I assumed a power that large must be divisible by 5.10. A — 33 KA-0171 Recursive rules
B I used the rule 2a(n) - 1 but started the sequence at 1 instead of 2.C I doubled six times and ignored the minus one entirely.D I stopped at a(5), one term early.E I computed 2^6 - 1, applying the minus one only once at the very end.