Polygons / angle problems / transformations / indices ...



Polygons / angle problems / transformations / indices / surds / irrational numbers

You MUST NOT use a calculator for any part of this homework. Show ALL working out.

Year 11 – Weekly revision homework (5) [pic]Score [pic] = %

Topics to revise: (1)

(2)

1.

[pic]

(a) Describe fully the single transformation that will transform the shape labelled A to the shaded shape.

(2)

(b) On the grid draw the shape labelled A after it has been rotated 90° clockwise about the origin. Label it B.

(2)

(c) On the grid enlarge the shape labelled A by a scale factor of 2 from the centre of enlargement P (6, 1).

P (6, 1) is marked on the grid.

Label the enlargement C.

(2)

2. (a) x is a number which is greater than 1.

List the following four terms in order of size, smallest first.

[pic]

Answer ………………………………. (2)

(b) If 0 < x < 1, how should your list in part (a) be re-arranged, if at all?

(1)

3. Using (a + b)2 = a2 + 2ab +b2, or otherwise, show that

(√2 + √8)2 = 18

(2)

4. The diagram shows a regular hexagon drawn inside a circle with diameter AD.

[pic]

(a) Name a triangle which is congruent to triangle ACD.

Answer ...........................................

(1)

(b) Calculate the size of angle DFE.

Answer ...........................................degrees

(3)

(c) The circle has an area of 50.3 cm2.

Calculate AD.

Answer ........................................... cm

(3)

7. (a) Simplify [pic]

Answer ………………….. (2)

(b) Evaluate

(i) 4–2

Answer …….……………. (1)

(ii) [pic]

Answer …………………… (1)

5. (a) Simplify[pic].

Answer …………………………… (2)

(b) A curve has the equation y = x2 – 6x + 7.

(i) Find the value of y when x = [pic].

(2)

(ii) Explain what your answer tells you about the graph of y = x2 – 6x + 7.

(1)

6. (a) Explain why equilateral triangles tessellate.

(2)

(b) On the grid draw at least five regular hexagons in the form of a tessellation.

[pic]

(2)

(c) This tessellation is formed from regular octagons and squares.

[pic]

Calculate the size of angle x°.

Show all your working.

(2)

8. Do not use a calculator to answer this question

(a) Show that [pic] = [pic]

(1)

(b) Solve the equation

x2 + 4x + 2 = 0

Express your answers in the form p ± q[pic] where p and q are integers.

Answer …………………………… (3)

9.

[pic]

BCD is a straight line.

CE bisects angle ACD.

AB = AC.

(a) Calculate the value of x.

Answer …………………. (3)

(b) Is EC parallel to AB?

Give a reason for your answer.

(1)

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