Revision Questions Mathematics

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depth of milk Find the roots of the equation y = x² - 2x - 15 Answer x = 1.3 or x = -3.3 (1 d.p.) (2x - 3)(x + 5) Original Price = £350 Depth = = 3.497 m x = 5, x = -3 Theory Guide Quadratic Formula Factorising (Trinomials) Reverse % Pythagoras (Circles) Quadratic Equations (Factorising) Question 21. E has coordinates (5,3,1) Find the shortest distance between D and C 22. Find the equation of a straight line through (2,-5) and parallel to y = 3x - 5 23. Simplify 24. Solve 25. x ² (x ² + 3) x - 3(x-7)=9 Sketch the graph of y = 4cos2x for 0≤x≤ 360 Answer √35 y = 3x - 11 1 3 x4 + 3x2 x = 6 180⁰ N 360° Theory Guide 3D Vectors (Surds) Straight Line Indices Linear Equations Trig Graphs Question 26. Find the volume of a sphere with radius 9m, giving your answer to two significant figures 27. Remove the brackets and simplify (2x + 2)² - 2(x² − 2) 28. John paid £20,000 for a motorbike but it depreciated 5.5% each year for 7 years. What was its value after 7 years? 29. 1.2 km 35° 1-35 km Find length AB 30. Prove B sin³x + sinxcos²x = sinx Answer V = 3100m³ (2 s. f.) 2x² + 8x + 8 Value = £13,460.24 AB = 0.78 km sinx(sin²x + cos²x) = sinx sinx(1) = sinx sinx = sinx Theory Guide Volume (Sphere) Brackets Compound Interest (Depreciation 2 Cosine Rule Trig Identities Question 31. Evaluate without a calculator: 32. Does the point (-2,4) lie on the line y = 3x + 10? Explain your answer. 33. 2.1+3.2 x 5 23 Simplify √40 + 4√10+√90 34. Simplify 35. (x - 5)(3x - 2) Sketch the graph of y = 3sin(0.5x) for 0 ≤ x ≤ 360 Answer 2.2625 Point lies on the line since substituting x = -2 and y = 4 into y = 3x + 10 gives: 43x(-2) + 10 4 = 4 -3 9√10 3x² 17x + 10 360⁰ Theory Guide BODMAS Straight Line Surds (Simplifying) Brackets Trig Graphs Question 36. Solve 3x² + 3x - 7=0 giving your answer correct to 1 decimal place 37. Factorise 6x² 24x30 38. In a sale, a book now cost £36. What was it worth before a 20% discount? 39. Find the area of the triangle 40. 21cm Sketch 110 19 cm y = (x + 2)(x-3) Label the intercepts and turning point Answer x = 1.1 or 2.1 6(x - 5)(x + 1) £45 Area = 187.45cm² -2 -6 3 TP (0.5, -6.25) Theory Guide Quadratic Formula Factorising (Trinomials) Reverse % Area of a Triangle Quadratic Graphs Question 41. Express RP in terms of f, g and h 42. Chose the correct equation for the above graph a. y = 2x + 1 b. y = -2x + 1 43. Find the longest side of this right-angled triangle leaving your answer as a surd. 44. c. y = 2x1 d. y = 2x² - 1 45. 1m Solve 7m 112(1 + 3x) < 39 Solve 2tanx + 5 = -4 for 0° < x < 180° Answer RP = = = -f-g+h y = 2x - 1 5√2m x>-5 x = 102.5°, 282.5° Theory Guide Vectors (Journeys) Straight Line Pythagoras (Surds) Inequalities Trig Equations Question 46. The standard deviation of Find a 47. 1, 2, 2, 2, 8 is √a Multiply out the brackets and simplify (3x + 2)(x² - 4x + 3) 48. The population of the UK is 64.1 million. If it increased by 3% for the next 7 years, what would it be? 49. The square below has side length y. If the diagonal is 6m. Find the exact length y 50. Show that 1- cos² a cos² a = tan² a Answer a=8 3x³10x²+x+6 78.8 million (3 s.f.) y = 3√2m Use sin²a + cos²a = 1 and tanx = to prove LHS = RHS sinx cosx Theory Guide Standard Deviation Brackets Compound Interest (Appreciation Pythagoras (Surds) Trig Identities Question 51. Evaluate Give the answer in its simplest form 52. A straight line has gradient 4 and it passes through the points (2,4) and (1, a) Find the value of a 53. 2x2² Evaluate 54. 55. Change the subject of the formula to u 2⁰+ 3-1 केळवलतम स्वरुक्क v² = u² + 2as What is the equation of the graph below? A 30 60 90 120 Answer 25 27 a=0 1 3 u = √√√v² - 2as y = 5sin3x Theory Guide Fractions Straight Line Indices Change the Subject of the Formula Trig Graphs Question 56. Calculate the capacity of the cylindrical mug below 57. Factorise (100x² 500x - 2400) 59. 58. The restaurant bill included 8% tax. If the bill was £324, what was the bill before tax? -10 cm- 14 cm 8-4 cm/ Calculate angle PQR Q 60. 12.6cm 11-2cm R S Write down the turning point and the equation of the axis of symmetry y = (x − 3)² + 4 Answer V = 1099cm³ 100(x-8)(x + 3) £300 Angle PQR = 78.6° T.P. = (3,4) x = 3 Theory Guide Volume (Cylinder) Factorising (Trinomials) Reverse % Cosine Rule Quadratic Graphs Question 61. Express AB in terms of a & b Express OC in terms of a & b D 62. 63. E Find 64. Solve O Find the equation of this line B(4, 3) f A(-1,-7) 65. M, a h A 2 273 2x-1=*34 What is the equation of the graph below ہے 90° Answer AB= a + b OC=2(b-a) y = 2x - 5 2 273 = 9 8 || I 1|5 y = 2Cos4x Theory Guide Vectors (Journeys) Straight Line Indices Equations with Fractions Trig Graphs Question 66. Show that the s.d. of 1,1,1,2,5 is √3 and write down the s.d. of 101,101,101,102,105 67. Multiply out and simplify 2(x² - 4x + 3) x(x − 3) 68. Rob normally cycles a total distance of 56 miles per week. He increases his distance by 15% each week for the next three weeks. How many miles will he cycle in the third week? 69. Depth of water in the cylindrical tank is 5m. AB = 18m. Calculate the radius. 70. Show that tanx sinx 1 COSX Answer First part proof Second part s. d. = same = x2 – 5x+6 Miles in 3rd week = 85.169 r = 10.6m Use tanx = sinx COSX to prove LHS = RHS √3 Theory Guide Standard Deviation Brackets Compound Interest (Appreciation 2 Pythagoras (Circles) Trig Identities Question 71. Without using a calculator find 72. For the straight-line |equation y = mx + c When m> 0 and c < 0 sketch a possible graph 73. 17.5% of £90 Simplify 74. 75. Write as a single fraction NIX 6xy³ 8x4y2 2 + 4 x-2 Solve the equation 11cos x° 2 = 3 for (0≤x≤ 360°) Answer £15.75 么 3y 4x3 6x - 4 x(x - 2) x = 62.96°, 297.04° Theory Guide % Without a Calculator Straight Line Indices Algebraic Fractions Trig Equations Question 76. Find volume to 2 s.f. 77. 12 cm Factorise 17 cm 80. 16x² - 1 78. A 900g box has 20% extra washing powder. How much washing powder was in a standard size box? 79. EF = 18 m OF = radius= 15 m Find h h 10 Describe the nature of the roots y = x²-3x + 3 Answer = 870 cm³ V = (4x + 1)(4x − 1) 750g h = 27m There are no real roots Theory Guide Volume (Composite Shapes) Factorise (Difference of 2 Squares) Reverse % Pythagoras (Circles) Discriminant Question 81. Evaluate 82. 83. 2 Find the gradient and y- intercept for the straight line: 84. UIN 1 - 2 85. Express the below with a rational denominator in its simplest form 8 √8 3x - 17 = 15y Change the subject of the formula to R P = R³b-5 State the equation of the graph below MA 360 Answer m = 1 150 R = 1 15 !! 2√2 3P + 5 b 17 75 15 y = 4sin3x Theory Guide Fractions Straight Line Surds (Rationalise the Denominator) Change the Subject of the Formula Trig Graphs Question 86. Make two valid comparisons for the two maths scores: Class A: Mean = 65%, s.d. = 12% Class B: Mean = 59%, s.d. = 10% 87. Factorise 4a²60a - 136 88. A new car cost £25000. Its value was expected to decrease every year by 20%. Find its expected value after 7 years. 89. Find the length AB V₁---C B 90. Below is a graph of y=(x-a)² + b Find coordinates of c (-3,-4) 35 cm Answer • On average Class A have higher maths scores Class A have less consistent marks) 4(a 17)(a + 2) Value = £5248.88 AB= 42.66 cm Theory Guide Standard Deviation (Comparisons C (0,5) Factorising (Trinomials) Compound Interest (Depreciation 2 Pythagoras (Circles) Quadratic Graphs Question 91. Find Jul, the magnitude of 92. Find the equation of a straight line between (-7,4) and (-3,5) 93. 6 --[-13] = 18 Express in its simplest form y8x(y³)-2 94. Solve for y 95. 2(x-3)_y+5 4 3 Solve algebraically the equation √3sin x° -1 = 0 for 0≤x≤ 360 Answer |u| = = 23 4y - x = 23 y² y = 19 x = 35.5°, 144.7° Theory Guide Vectors (Magnitude) Straight Line Indices Equations with Fractions Trig Equations Question 96. Find the total volume of the shape below. 3.5 m 97. 3 m Multiply out and simplify (y-2)³ 99. 98. I bought a new racing bike for £1500. This included VAT at 2.5 m 20%. What was the cost before VAT was added? 100. Find the length SW 4.7 m 13-1 cm. Express in the form x²14x + 44 (x-a)² + b W Answer V = 30.75m³ y³ - 6y² +12y - 8 Cost = £1250 SW = 6.6cm (x-7)²-5 Theory Guide Volume (Composite Shapes) Brackets Reverse % Trig Triangles Completing the Square