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Mathematics Department Clyde Valley High School 1. Find the equation of the straight line shown in the diagram. y (6,2) 0 x (0,-2) 2. Write 6 in its simplest form as a surd with a rational 18 denominator. 3. The diagram shows a set of stacked circles. The circles are all identical and have a diameter of 2cm. Find the height of the point P above the ground. P ● Ground Mathematics Department Clyde Valley High School 4. Solve the equation 2x + 5 1 − x 2 = − 3 2 5 5. The number of eagles breeding in Scotland is estimated at 5600. The numbers are expected to rise by 5% in each of the next 3 years. Find the number of eagles expected to be breeding in each of the next three years. 6. Simplify the expression 6x(x – 2) – 6(x - 1)2. 7. Solve the trigonometric equation 12cosx – 7 = 0, where, 0 ≤ x ≤ 360°. 8. Write as a single fraction 9. Calculate the area of the shape ABCD. x − 2 1− x − . 5 6 C D A 4cm 8cm 10. Solve the simultaneous equations 4x – 3y = 11 y=x-2 B Mathematics Department Clyde Valley High School 11. The diagram shows a washer with an internal radius r and a width w. a) Prove that the area of the washer is A = πw(2r + w) b) w A new washer with the same internal radius but with double the width is to be made. Find the area of the new washer. c) Prove that the increase in the area over the original washer is h r πw(2r + 3w) 12. A ship leaves Dundee and sails 60km east. It then turns and sails 96km on a bearing of 046°. Find the distance and the bearing of the ship from Dundee. N N ●Ship Dundee 13. The diagram shows two similar urns. The volume of the larger urn is 400cm3. Find the volume of the smaller urn. 9cm 12cm Mathematics Department Clyde Valley High School 14. Solve the inequation 5(1 – x) -2x > 5 15. The annual profit (₤) of a company was 3.8 × 108 for the year 2006. What profit did the company make per minute? Give your answer in scientific notation correct to 3 significant figures. 16. Calculate the shaded area. 12cm 17. In the triangle shown, x and y are whole numbers and x > y. Use the converse of Pythagoras to Prove that the triangle is right angled. x2 + y2 x2 - y2 2xy 18. Solve the quadratic equation 2x2 – x – 2 = 0 , giving your answers correct to 2 decimal places. Mathematics Department Clyde Valley High School 19. The diagram shows a lake. Two towers A and B are on opposite sides of the lake. Lake A● The distances from an observation point to each of the towers is shown. The angle made by the towers 143m at the observation point is 34°. How far apart are the towers? ●B 154m 34° ● Observation Point 20. The triangular array shown is called Pascal’s Triangle. Row 1 Row 2 Row 3 Row 4 Row 5 1 1 1 1 1 1 2 3 4 1 3 6 1 4 1 a) Write down the next two rows. b) Pascal’s Triangle can be used to expand expressions like (1 + x)n where n is a whole number. Eg. (1+x)0 = 1 (1+x)1 = 1 + x (1+x)2 = 1 + 2x + x2 (1+x)3 = 1 + 3x + 3x2 + x3 etc. Use Pascal’s Triangle to expand (i) (1+x)4 (ii) (1+x)5 (iii) (1+x)6