MATHS FOR KIDS

Year 6 Mathematics Homework

Equations, Volume, Similar Shapes & Powers of 2

A. Equations and Independent Information

1. Solve the simultaneous equations: x + y = 18 and y − x = 6.

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2. Consider x + y = 12 and 2x + 2y = 24. Can x and y be determined uniquely? Explain why or why not.

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3. Given P + Q = 21, P + R = 17, and Q + R = 14, find P, Q and R.

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4. Given A + B = 6, B + C = 9, C + D = 12, and D + A = 9:

a) Show that one equation can be derived from the others.

b) Explain why the four variables cannot be determined uniquely.

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5. For Question 4, suppose A = 2. Find B, C and D.

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B. Similar 2D and 3D Shapes

6. A small sphere has radius 1 cm and a similar larger sphere has radius 5 cm.

A> Find the ratio of their volumes.

B> How about the ratio of their surface areas?

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C. Powers of 2 and Computer Sizes

7. Complete the following:

a) 1 K = 2¹⁰ ≈ ________

b) 1 M = 2²⁰ ≈ ________

c) 1 G = 2³⁰ ≈ ________

8. Under a simplified Moore’s Law model, computer capacity doubles every 2 years.

a) By what factor does it increase in 10 years?

b) By what factor does it increase in 20 years?

c) Explain why 20 years is roughly one jump from K to M, or M to G.

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