S G C T IO r fEssential Maths Book

You need squared paper. Calculators may be used

1. Look at the sequence 1 1 , , ...

Write down () the 1 oth term ^ (b) the nth term

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(1 mark) (2 marks)

z . (a) Sketch a pentagon in which four of the exterior angles are 70, 50, 65and 90. : o

(b) Work out the size of the other exterior angle.

3. The value of a new car is 15000. I 000 }The value of the car depreciates by 20% per year. ^ I X 0 '6 ^Work out the value of the car after 2 years. ' ^ ( )0\ > ?Show your working.

I ' I f(1 mark)

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1.9cm

4.3cm

H M I i ; / 1

/o , A cupboard weighs 58kg to the nearest kg. 1 7 ^ >Write down the lower bound for the weight of the cupboard. (1 mark)

11. After an increase of 15%, the price of a golf bag is 74.75. Find the price of the bag before the increase. 7 1 . -J . 1 ^ 7 ^ 7 ) 7 / -' f j K 7 (2 marks)

12. Three cylinders of radius 2cm and thickness *

1.5cm are melted down to form acube of side X cm. N < 'LFind X1 correct to 2 decimal places. (4 marks)

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13. The numbers are written in a repeating pattern. The first base number is 11 the second base number is 6, the third base number is 11 and so on.

(a) What is the 100th base number?(b) What is the nth base number?

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1 16

11 base number

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2nd base I, b , ^ ' / t bnumber

(2 marks) (2 marks)

14. Find the largest angle in this triangle. Show your working

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1 , ^ 11

^ 'K c >3

(2 marks)

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15. The dimensions of this rectangle have been measured correct to the nearest cm. Work out the least possible length of a diagonal of this rectangle.

^ Y - ? (3 marks)

16. A tank in the form of a cylinder is filled to a depth of 30cm.This takes 18 litres of water. i&oov v Find the diameter of the tank. ' ^ \y' f^11 c'' (3 marks)

Draw a pair of axes for X and y from -8 to +8 Plot and label the following triangles:A1: (4 ,-3 ) (7 ,-3 ) (7 ,-5 ).Shade this triangle.A2: (-4 ,3 ) (5 ,3) (5 ,-3 )A3: (4 ,5) (7 ,5) (7,7)A4: ( -5 ,-3 ) ( 2 ,-3 ) ( -2 ,-5 )Describe fully the following transformations: (a) A1 A2 (b) A1 - A3 (c) A1 -> A4

18. Here is a shape made from squares of side 1cm.(not to scale)

- ___ 3 V '' I'D /V- A(a) Write down the perimeter and the area of this shape. (1 mark)(b) Design a shape, using the same size squares, which has a perimeter of

18cm and an area of 18cm2. 1- r ~ V (2 marks)