Paper 3 Unseen Topics

Transcription

1 Paper 3 Unseen Topics This is a collection of questions based on the topics that are so far UNSEEN or are usually more prominent Make sure you revise all topics as it is very likely topics from Paper 1 and 2 will appear in Paper 3. Guidance 1. Read each question carefully before you begin answering it. 2. Don t spend too long on one question. 3. Attempt every question. 4. Check your answers seem right. 5. Always show your workings Revision for this test

2 Question Topic Video number 1 Scatter Graphs 165, Currency 214a 3 Conversion Graphs 151, Standard Form (operations) Percentages of Amounts 234, Percentage Change Ratio 270, Two-way Tables Pie Charts 163, Frequency Polygons 155, Parallel Lines Estimated Mean Box Plots Collecting like Terms 9 15 Expanding 2 Brackets Factorising Factorising Two Brackets 118, 119, Changing the Subject 7, 8 19 Substitution Equation (forming and solving) 114, Solving Inequalities 177, 178, Inequalities (Regions) Drawing Linear Graphs Reverse Percentages Compound Interest Solving Quadratics Angles in Parallel Lines 25, Bearings 26, Angles in Polygons 32

3 Question Topic Video number 30 Constructions/Loci 72 to Area of a Trapezium Circumference Conditional Probability Arc Length Volume of a Cylinder Trigonometry Volume of a Prism Surface Area of a Prism Translations Quadratic nth term Perpendicular Lines Circle Theorems 64, Equation of a Circle Density Pressure Limits of Accuracy 183, Congruent Triangles Drawing Histograms Error Intervals Inverse Proportion Algebraic Proof Hard Simultaneous Equations Trigonometric Graphs 338, Quadratic Inequalities Completing the Square 10, Transformations of Graphs Iteration Circle Theorems Proofs Exponential Graphs 345

4 Question Topic Video number 60 3D Trigonometry and Pythagoras 259, The value of cars in a used car garage are recorded below. The scatter graph shows this information. Another car arrives at the garage. It is 4 years old and worth (a) Show this information on the scatter graph. (1) (b) Describe the correlation between the value of the car and the age of the car. The next car that arrives is 6 years old.... (1) (c) Estimate the value of the car....

5 2. Terry goes to the Post Office to exchange money. Terry changes $651 and into pounds sterling. The Post Office deducts their commission and gives Terry 528. What is the percentage commission?...% (4)

6 3. (a) Use the fact 5 miles = 8 kilometres to draw a conversion graph on the grid. Use your graph to convert (b) 8 miles to kilometres (c) 6 kilometres to miles...km (1)...miles (1)

7 4. The distance of the moon to the Earth is 384,400 km. The speed of light is x 10 8 m/s. Work out how long it will take light to travel from the moon to the Earth. Include suitable units The table gives information about the number of people voting for each party at an election. There are people who can vote The target was that 88% of people would vote. Was the target met?

8 6. A clothes shop normally sells their goods at 80% above cost price. In a sale, the shop reduces the prices by 25%. What percentage profit does the shop make on clothes sold in the sale? 7. A piece of carpet is 240cm long. Mr Jones cuts it into three pieces in the ratio 1 : 2 : 5...% Work out the length of the longest piece of carpet people study one language at a college. Some people study French. Some people study Spanish. The rest of the people study German. 54 of the people are male. 20 of the 29 people who study Spanish are female. 31 people study German. 15 females study French. Work out the number of males who study German.... (4)

9 9. The table gives information about the number of students in years 7 to 10. Draw an accurate pie chart to show this information. (4)

10 10. The frequency table gives information about the weight of some rugby players. (a) Draw a frequency polygon to represent this data. (b) Write down the modal class interval.... (1) One player is chosen at random. (c) Work out the probability that this player is more than 90kg.... (1)

11 11. Write down the equation of the line that is parallel to x + 2y = 4 and passes through the point (0, 5) 12. Sally is raising money for charity for a fun run. The table below has been given to her from the website.... Sally says the average donation is 10. By calculating the estimated mean, decide if you agree with Sally. (4)

12 13. Mrs Davis sets her class a quiz, which has a maximum score of 50. The distribution of the scores are shown in a box plot below. (a) Write down the median score. (b) Write down the highest score. (c) Find the interquartile range.... (1)... (1) Martin scored 35 marks. (d) What percentage of the class scored a lower mark than Martin?......% (1) The interquartile range is a better measure of the spread of a distribution than the range. Explain why (1)

13 14. Simplify 4(3y² + w 7) 2(11 y² + 3w) Expand and simplify (5w 6)(2w + 7) Factorise completely (a) Factorise x² + 14x (b) Factorise 3y² + 10y 8...

14 18. Make x the subject of x =... (4) 19. The amount of medicine, s ml, to give to a child can be worked out using the formula. s is the amount of medicine, in ml. a is the adult dose, in ml. m is the age of the child, in months. A child is 20 months old. An adult s dose is 45ml. Work out the amount of medicine the child should be given....ml

15 20. Shown below is an isosceles triangle. Each side is measured in centimetres. Calculate the perimeter of the triangle....cm 21. x is an integer. Write down all the solutions of the inequality 3 < 2x + 1 < 13...

16 22. On the grid, clearly label the region which satisfies all three inequalities below x 2 y < 2x 2 x + y + 2 > 0 (4)

17 23. On the grid, draw the graph of 3x 2y = 6 (4)

18 24. A limited edition bag of flour contains 25% more than the standard bag. The limited edition bag contains 650g of flour. How much flour is in the standard bag?...g 25. Sally bought a piano for In each year the value of the piano increases by 11% of its value at the start of that year. (a) Find the value of the piano after one year.... (b) Calculate after how many complete years the value of the piano will be at least Solve y² + 9y + 2 = 8y years...

19 27. CE and FI are parallel lines. Angle EDH = 50 Angle DGF = 100 Show, giving reasons, that triangle DGH is isosceles. (4) 28. The bearing of A from B is 074 Work out the bearing of B from A Shown below are two identical regular polygons and an equilateral triangle. Calculate the number of sides each regular polygon has....

20 30. A yacht leaves the port, P, on a course that is an equal distance from PB and PL. Using ruler and compasses only, construct the course on the diagram. You must show your construction arcs. 31. The area of the trapezium is 34cm². Work out the value of x....cm

21 32. The circumference of a circle measures 19.5cm. Work out the area of the circle 33. There are 8 sweets in a bag. Three sweets are red, three sweets are blue and two sweets are green. Three sweets are selected at random without replacement. Calculate the probability that the sweets are not all the same colour (4) The perimeter of the sector is 1m. Find the length of y, the radius of the circle....cm (4)

22 35. The volume of the cuboid and the cylinder are equal. Find h in terms of x. Give your answer in its simplest form. 36. Two right-angled triangles are shown below. PQ is 10cm. QR is 3cm. Angle QRS is 65⁰... cm³ Calculate the size of angle PQS...⁰ (5)

23 37. Shown below is a triangular prism. Find the volume of the triangular prism. 38. Shown below is a cylinder....cm³ Calculate the curved surface area. Give your answer to 1 decimal place....cm²

24 39. Describe fully the single transformation that maps shape A onto shape B Here are the first 5 terms of a quadratic sequence Find an expression, in terms of n, for the nth term of this quadratic sequence....

25 41. Shown are two straight lines drawn on the grid. Line 1 has equation y = 3x 12 (a) Find the equation of Line 2... (4) (b) Are the two lines perpendicular? Explain your answer (1)

26 42. PDQ is a tangent at D. O is the centre of the circle. DEF is an isosceles triangle. (a) Work out the value of a.... (b) Work out the value of b....

27 43. A circle has equation x² + y² = 25 A straight line meets the circle at the points A and B. (a) Write down the equation of the straight line.... (1) (b) Find the coordinates of the points A and B. Give your answers in surd form. 44. Material A has a density of 5.8g/cm³. Material B has a density of 4.1g/cm³. A =.. and B =.. (4) 377g of Material A and 1.64kg of Material B form Material C. Work out the density of Material C...g/cm³ (4)

28 45. The pressure of a tyre is 32 pounds per square inch. Given 1 pound = kilograms 1 inch = 2.54 centimetres Work out the pressure in grams per square centimetre... (4) 46. The curved surface area of a cone is given by the formula where A is the curved surface area r is the radius of the base of the cone and l is the slant height Given A = 220 cm² correct to 3 significant figures, and r = 8 cm correct to 1 significant figure. Calculate the upper bound for l....cm

29 47. ABC is an isosceles triangle in which AC = BC. D and E are points on BC and AC such that CE = CD. Prove triangles ACD and BCE are congruent. 48. The test scores from the students in a school are summarised in the table. (4) Draw a histogram for this data

30 49. Nigel measures the time, t seconds, to complete a race as 14.8 seconds correct to the nearest tenth of a second. Write down the error interval for t. 50. Match each graph to the correct relationship Prove that the product of two odd numbers is always odd.

31 52. Solve the equations x² + y² = 25 x + y = 7... (5) 53. Shown is part of the curve y = cos x (a) Write down the coordinates of the point A. (...,...) (1) (b) Write down the coordinates of the point B. (...,...) (1)

32 54. Solve the inequality x² x Write x² + 4x + 13 in the form (x + a)² + b, where a and b are constants....

33 56. This is a sketch of the curve with equation y = f(x) The vertex of the curve is at the point (-6, 1) Write down the coordinates of the vertex of the curve with equation (a) y = f(x + 3) (b) y = f( x) (...,...) (1) (c) y = -f(x) (...,...) (1) (...,...) (1)

34 57. (a) Show the equation 3x³ + 7x = 5 has a solution between 0 and 1 (b) Show that 3x³ + 7x = 5 can be rearranged to give (c) Starting with use the iteration formula three times to find an estimate for the solution to 3x³ + 7x = 5

35 58. Prove that the angle at the centre is twice the angle at the circumference. (4) 59. The sketch shows a curve with equation y = ab x where a and b are constants and b > 0 The curve passes through the points (1, 14) and (4, 112) Calculate the value of a and b a =... b =...

36 60. A tree is located in the corner of a rectangular field. The field is 15 metres long and 12 metres wide. The tree is 5 metres tall. Calculate angle CAE.... (4)