Key Stage 2 Mathematics Paper 2: Reasoning (2017)

What does this graph tell us?

The y-axis goes up in steps of 20 (0, 20, 40…). There is one line between each major mark, representing 10.

• Year 2 Walk (dark): Between 60 and 80 = 70
• Year 2 Don’t Walk (light): Between 100 and 120 = 110
• Year 6 Walk (dark): On the line 120
• Year 6 Don’t Walk (light): Between 80 and 100 = 90

Why we do this: We need to add the “don’t walk” (light grey) bars for both years.

Why we do this: We compare the “walk” (dark grey) bars. “How many more” means subtraction.

Why we do this: “10 times greater” means we multiply the number by 10.

Why we do this: We know that \( 9 \times \text{something} = 63 \) and \( 9 \times \text{something else} = 54 \).

Why we do this: Now we look at the bottom row. \( \text{Something} \times 7 = 56 \).

Why we do this: First, we need to find the total height of Mount Kilimanjaro and Ben Nevis.

Why we do this: Now subtract this combined height from the height of Mount Everest to find “how much higher” it is.

Why we do this: For the first missing box, we need to find “1,000 more” than 85.

Why we do this: For the bottom two rows, we are given the “1,000 more” column and need to find the original number. We must subtract 1,000.

Why we do this: To compare decimals easily, look at the units column first, then tenths, then hundredths.

Let’s line them up:

• 1.900 (1 unit)
• 0.960 (0 units, 9 tenths)
• 1.253 (1 unit)
• 0.328 (0 units, 3 tenths)

Fact: There are 12 months in 1 year.

Fact: There are 24 hours in 1 day.

Fact: There are 7 days in 1 week.

Why we do this: First, add the new cars to the starting amount.

Why we do this: Now take away the cars that were sold from the total.

Why we do this: We need to find the shapes where the shaded fraction equals \( \frac{3}{4} \). Note that \( \frac{3}{4} \) is equivalent to \( \frac{6}{8} \) or \( \frac{12}{16} \).

• Top Left: 8 total rectangles. 6 are shaded. \( \frac{6}{8} = \frac{3}{4} \). YES.
• Top Right: 8 total rectangles. 4 are shaded. \( \frac{4}{8} = \frac{1}{2} \). NO.
• Bottom Left: 9 total squares. 8 are shaded. \( \frac{8}{9} \). NO.
• Bottom Right: 16 total squares. 12 are shaded (4+4+2+2). \( \frac{12}{16} = \frac{3}{4} \). YES.

Why we do this: The rule says we need 40 minutes for each kilogram, plus 20 minutes extra.

Why we do this: We need to work backwards. First, remove the “extra 20 minutes”, then divide by 40 to find the kilograms.

Why we do this: We need to check the properties of each shape individually.

• Cube: 6 Faces, 8 Vertices (Corners). No match.
• Square-based pyramid: 5 Faces (1 base + 4 sides), 5 Vertices (4 base + 1 top). Match!
• Triangular prism: 5 Faces (2 ends + 3 sides), 6 Vertices. No match.
• Triangular-based pyramid (Tetrahedron): 4 Faces (1 base + 3 sides), 4 Vertices (3 base + 1 top). Match!

Why we do this: Jack buys 12 stickers at 99p each. We need to find his total cost.

Strategy: \( 12 \times 99p \). It is easier to do \( 12 \times £1 \) and subtract \( 12 \times 1p \).

Why we do this: Compare Jack’s cost (£11.88) with Ally’s cost (£10.49).

Why we do this: We know 2 seeds grew out of every small group. We need to find how many groups of 2 fit into the total 12 seeds.

Why we do this: In each of those 6 groups, she planted 3 seeds.

Why we do this: Convert each part of the Roman numeral into numbers.

• M = 1000
• M = 1000
• V = 5
• I = 1

Fact: A full circle (one somersault) is 360 degrees.

Why we do this: We need to find the locations of the remaining two coordinates on the grid.

• (1, -3): Go Right 1, Down 3.
• (-3, 4): Go Left 3, Up 4.

Why we do this: There are 24 hours in a full day. The koala sleeps for 18 of them.

Why we do this: Simplify the fraction to make it easier to see the percentage.

Why we do this: Find out how much she actually spent by subtracting the change from the money given.

Why we do this: Divide the total cost by 3 to find the cost of a single letter.

Why we do this: To compare them, both need to be decimals or fractions.

Why we do this: Every 20km in real life corresponds to 1cm on the map. We need to find how many “20kms” are in 250km.

Why we do this: Since the triangles are on a grid and “similar”, we can compare their corresponding lengths.

• Triangle A: The base is 3 squares wide. The height is 2 squares high.
• Triangle B: The base is 6 squares wide. The height is 4 squares high.

Why we do this: Compare the dimensions.

Why we do this: Find the total amount shaded first. We need a common denominator for 4 and 6, which is 12.

Why we do this: The whole circle is 1 (or \( \frac{12}{12} \)). We subtract the shaded part to find the unshaded part.