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1. In a triangle, one angle is 90 degrees and another is 35 degrees. What is the third angle?[3]
A 35 degreesB 45 degreesC 55 degreesD 65 degreesE 145 degrees2. Which of these is true of every rectangle?[3]
A all four sides are the same lengthB the diagonals cross at right anglesC it has four lines of symmetryD the angles add to 180 degreesE the two diagonals are the same length3. A rectangle has a perimeter of 20 cm. One of its sides is 6 cm. What is its area in square centimetres?[3]
4. A floor measuring 6 by 4 units is covered exactly with tiles measuring 2 by 1, with no gaps and no overlaps. How many tiles are needed?[3]
5. Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
6. Which capital letter, printed plainly, has both a horizontal and a vertical line of symmetry?[3]
7. 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)8. In a triangle, one angle measures 30 degrees. Of the other two angles, one is exactly twice the other. What is the largest angle in the triangle?[3]
A 50 degreesB 75 degreesC 100 degreesD 150 degreesE 90 degrees9. What is the size of one interior angle of a regular twelve-sided polygon?[3]
A 150 degreesB 30 degreesC 165 degreesD 1800 degreesE 144 degreesKangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 1 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
1. C — 55 degrees KA-0022 Angles on lines, in triangles, in polygons
A I assumed the triangle was isosceles because it had a right angle, so I repeated the 35.B I assumed a right-angled triangle always has two 45 degree angles.D I subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.E I subtracted only the 35 from 180 and forgot to take off the right angle as well.2. E — the two diagonals are the same length KA-0079 Properties of triangles and quadrilaterals
A I confused a rectangle with a square, which is only one special kind of rectangle.B I remembered a fact about squares and rhombuses and applied it to every rectangle.C I counted the two diagonals as lines of symmetry, which only works for a square.D I used the angle sum of a triangle on a four-sided shape.3. B — 24 KA-0083 Perimeter and area of rectilinear shapes
A I subtracted 6 from 20 and gave that, which is neither a side nor an area.C I took the other side to be 20 minus 6 divided by 2, forgetting there are two sides of each length.D I multiplied the perimeter by half the known side instead of finding the missing side first.E I used 16 as the other side, taking 20 minus 6 plus 2 rather than working from the perimeter properly.4. C — 12 KA-0086 Tiling and tessellation
A I divided the floor area by 3 instead of by the tile area of 2.B I laid tiles along the edges only and never filled the middle.D I gave the area of the floor rather than the number of tiles that cover it.E I multiplied the floor area by the tile area instead of dividing.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 — H KA-0142 Line and rotational symmetry
A I found the vertical fold and assumed a horizontal one must work too.B I found the horizontal fold and stopped without testing the vertical one.D I counted the vertical fold twice rather than testing a horizontal one.E I mistook turning the letter upside down for folding it, which is rotation rather than symmetry about a line.7. 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.8. C — 100 degrees KA-0152 Angles on lines, in triangles, in polygons
A I found the smaller of the two unknown angles and stopped before doubling it.B I split the remaining 150 degrees into two equal halves instead of a one-to-two split.D I split the remainder evenly into 75 and 75, then doubled one of them.E I assumed that the largest angle in a triangle like this must be a right angle.9. A — 150 degrees KA-0170 Angles on lines, in triangles, in polygons
B I found the exterior angle and answered with that instead of the interior one.C I used 360 divided by 12 subtracted from 195, or otherwise slipped a step in the arithmetic.D I gave the total of all twelve interior angles rather than one of them.E I used a ten-sided polygon by mistake.