Compound Interest Formula Depreciation Formula. P = principal r = the interest rate n = number of time periods A = final amount. opposite.

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1 Chapter Finance The simple interest rule I=Prt I = simple interest P = principal r = the interest rate t = the time Compound Interest Formula Depreciation Formula A= P( + 00 A= P( 00 P = principal r = the interest rate n = number of time periods A = final amount 4.5% pa would be 4.5 % per month. Chapter Trigonometry sin θ= opposite hypotenuse cosθ= adjacent hypotenuse tan θ= opposite adjacent c = a + b hypotenuse θ adjacent opposite Angle of elevation - the object is above the observer. Angle of depression - the object is below the observer. The square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. Chapter Statistics The Bo Plot is also known as the bo-and-whisker plot. The Median is the middle of a set of scores. The Lower Quartile is the middle of the bottom half of a set of scores. The Upper Quartile is the middle of the top half of a set of scores. The Mean describes the middle of the data. The Standard Deviation describes the spread of the data. Chapter 4 Graphs The graph of a quadratic function is a parabola. y Hyperbola: a y = Hyperbolas have two distinct curves called arms or branches. Circle: + y = r Centre (0,0 Radius = r (-r,0 (0,r (r,0 y = a is an eponential function (0,-r y=(+( is a polynomial 05

2 Review Eercise 5. Mental computation Spell Parabola What is the general equation of a parabola? What is the general equation of a hyperbola? 4 What is the general equation of a circle? Given the numbers:,,,, 4, 5, What is the median? 6 What is the lower quartile? 7 In the triangle, what is cos 45? 8 Two sides of a right-angled triangle are and, what is the hypotenuse? 9 What is the Simple Interest Formula? 0 Is a factor of +? Eercise 5. Find the simple interest charged on $ borrowed for years at 8.5% pa. If the charge for lending $5600 at 0.7% per month is $789.60, for how long was the $5600 lent? I = $7.60 P = $5600 r = 0.7% /month t =? months I = Prt 7.60 = t = t t = months If the charge for lending $6450 at 6.8% pa is $500, for how long was the $6450 lent? How much would need to be invested at 6.5% pa for 6 months in order to earn $500 interest (6 months = 0.5 years? 4 Cooper is charged $8000 for borrowing $ for 9 months. What simple interest rate per month is Cooper being charged? The simple interest rule I=Prt I = simple interest P = principal r = the interest rate t = the time $500 is invested at 5.8% pa compounded yearly. What will be the principal after years (round to the nearest dollar? A =? P = $500 A= P( + 00 r = 5.8% pa Compound Interest Formula 58. n = times A = 500( + 00 A= P( + A = $ $5 500 is invested at 5.% pa compounded yearly. What will be the principal after 4 years (round to the nearest dollar? 6 $ is invested at 6.7% pa compounded monthly. What will be the principal after years (round to the nearest dollar? 06

3 7 Which produces the better outcome over 5 years? a $ invested at 9% pa compounded yearly? b $ invested at 9% pa compounded monthly? Depreciation Formula r A= P( 00 8 A car is purchased for $ What is the value of the car after 5 years if it depreciates in value by 0% each year (round to nearest $000? 9 Use Pythagoras' theorem to find the length of the unknown side (round to two decimal places: a b.7 c n 6.8 b Use the sin, cos, or tan ratio to find the unknown (round to two decimal places: a b c β A plane flies due west for 47 km, then on a bearing of 60 T until the plane is due north of its starting point. How far is the plane from its starting point? T is 60 clockwise from North. From the top of a 0 m tower, the angle of depression to a fire is 6. How far away is the fire? 0m 90 6 = 84 6 From the top of a building 47 m high, the angle of depression to the bottom of a building across the street is 40. The angle of elevation to the top of the building across the street is. Find: a The height of the building across the street. 40 b The width of the street. 8 4 Find the unknown in the diagram. 5 5 Find the mode, median, and the mean of each of the following: a b Score Frequency Frequency 4 Score Chapter 5 Review 07

4 6 Find the mean, lower quartile, median, upper quartile, range, and standard deviation for the following set of data: 8., 8.0, 8., 8., 8.6, 8.9, 8., 8., 8.8, Draw a bo plot to represent the following data: 69, 4, 6, 60, 6, 5, 78, 57, 8, 65, 4, 58, 66, 4, 56, 76, 56 8 Depression affected patients were asked to self-rate their state of depression before and after treatment. Use bo plots to represent and then compare each data set. Before treatment 0,,, 9, 7, 5, 6, 5,, 6, 7, 4, 0,, 0,,, 6, 6, 7, 9, 0, 5, 0 After treatment 9, 7, 4,, 9, 9, 0, 0,,, 5, 4,, 5, 9,,,, 8, 6, 7,, 4, 0 9 To test the effectiveness of two different product displays, shoppers were asked how much they spent on impulse buying after passing each shopping display. Find the mean and standard deviation of each data set and use these descriptive statistics to compare the sets of data. Display A 5, 9, 0,,, 6, 9, 7, 0, 6, 0,, 7,, 6, 9, 9, 5, 8, 5, 7,, 0 Display B,, 0,,, 6,,,, 6, 0, 8,, 6, 0, 8,,, 0, 6,, 0, 9, 0, 5 0 Four-sevenths of the course is uphill and three-sevenths of the course is downhill. If Ella cycles uphill at an average speed of 5 km/h and cycles downhill at an average speed of 0 km/h. What is Ella average speed over the whole course? Graph the following quadratics by completing the table of values. Find the -intercept and the y-intercept from your graph. a y = b y = y = y = - Sketch each of the following quadratics by first sketching y = and then applying the appropriate transformations. a y = + 4 b y = -( 08

5 Find the centre and radius of the circle: ( + (y + = 4 4 Write the equation of the circle with centre (,- and radius units. 5 Graph the following hyperbola by completing the table of values, plotting the points, and drawing a smooth curve through the points. y = y = Sketch each of the following polynomials: a y = ( + ( ( + b y = ( + ( c y = -( ( + d + = 0 7 Sketch the following eponential functions by completing the table of values, plotting the points, and drawing a smooth curve through the points. y = y = A town's population of increases each year by %. a Use an eponential function to model the growth. b Estimate the town's population after 0 years. c When will the town's population double to 0 000? Review Eercise 5. Mental computation Spell Eponential What is the general equation of a parabola? What is the general equation of a hyperbola? 4 What is the general equation of a circle? Given the numbers:,,,, 4, 5, 6, What is the median? 6 What is the upper quartile? 7 In the triangle, what is cos 60? 8 Two sides of a right-angled triangle are and, what is the hypotenuse? 9 What is the Compound Interest Formula? 0 Is + a factor of +? Eercise 5.4 Find the simple interest charged on $ borrowed for years at.5% pa The simple interest rule I=Prt I = simple interest P = principal r = the interest rate t = the time Chapter 5 Review 09

6 If the charge for lending $5600 at 0.7% per month is $789.60, for how long was the $5600 lent? I = $7.60 P = $5600 r = 0.7% /month t =? months I = Prt 7.60 = t = t t = months If the charge for lending $5 000 at 6.8% pa is $6800, for how long was the $5 000 lent? How much would need to be invested at 6.% pa for 8 months in order to earn $000 interest (8 months =.5 years? 4 Joe is charged $000 for borrowing $ for 6 months. What simple interest rate per month is Joe being charged? $500 is invested at 5.8% pa compounded yearly. What will be the principal after years (round to the nearest dollar? A =? P = $500 A= P( + 00 r = 5.8% pa Compound Interest Formula 58. n = times A = 500( + 00 A= P( + A = $ $9500 is invested at 7.9% pa compounded yearly. What will be the principal after 4 years (round to the nearest dollar? 6 $5 000 is invested at 6.% pa compounded monthly. What will be the principal after 4 years (round to the nearest dollar? 7 Which produces the better outcome over 5 years? a $ invested at 9% pa compounded yearly? b $ invested at 9% pa compounded monthly? 8 A car is purchased for $ What is the value of the car after 5 years if it depreciates in value by % each year (round to nearest $000? 9 Use Pythagoras' theorem to find the length of the unknown side (round to two decimal places: a b c b 9.7 Depreciation Formula r A= P( 00 n

7 0 Use the sin, cos, or tan ratio to find the unknown (round to two decimal places: a b c β A plane flies due west for 96 km, then on a bearing of 57 T until the plane is due north of its starting point. How far is the plane from its starting point? From the top of a 0 m tower, the angle of depression to a fire is 5. How far away is the fire? From the top of a building 5 m high, the angle of depression to the bottom of a building across the street is 46. The angle of elevation to the top of the building across the street is 7. Find: a The height of the building across the street. b The width of the street Find the unknown in the diagram Find the mode, median, and the mean of each of the following: a b Score Frequency Frequency 4 Score 6 Find the mean, lower quartile, median, upper quartile, range, and standard deviation for the following set of data: 6., 6.9, 6.7, 6.5, 6.7, 6.7, 6.6, 6.8, 6.5, 6.5, Draw a stem and leaf plot and a bo and whisker plot to represent the following data: 54, 97, 8, 8, 7, 66, 94, 58, 94, 8, 75, 79, 6, 6, 5, 80 8 Year 0 students were tested on their bo plot knowledge before and after a week of inclass learning about bo plots. Use bo plots to represent and then compare each data set. Before learning 44, 70, 70, 4, 4, 56, 45, 56, 58, 40, 40, 64, 4, 57, 55, 56, 5, 47, 70, 58, m T is 57 clockwise from North = 85 4 After learning 80, 90, 88, 8, 86, 67, 75, 70, 85, 77, 76, 70, 8, 88, 90, 69, 79, 85, 90, 65, 8 5 Chapter 5 Review

8 9 Investigating the results of a three week ball deterity program, a PE teacher collected the following deterity indees before and after the program. Find the mean and standard deviation of each data set and use these descriptive statistics to compare the sets of data. Deterity (before 7,, 4, 0, 6, 8, 5, 8, 8, 9, 6, 7,, 8, 7, 5, 8,,, 7, 7, 7,,, 9,, 6 Deterity (after, 4,, 6, 5, 8, 9,, 8,, 8, 0, 8, 7, 4, 6, 9,, 8,,, 5,, 6, 8, 9, 8 0 Four-ninths of the course is uphill and five-ninths of the course is downhill. If William cycles uphill at an average speed of 5 km/h and cycles downhill at an average speed of 7 km/h, what is William's average speed over the whole course? Graph the following quadratics by completing the table of values. Find the -intercept and the y-intercept from your graph. y = y = - Sketch each of the following quadratics by first sketching y = and then applying the appropriate transformations. a y = b y = -( + Write the equation of the circle with centre (, and radius 5 units. 4 Graph the following hyperbola by completing the table of values, plotting the points, and drawing a smooth curve through the points. y = y = - 5 Sketch each of the following polynomials: a y = ( + ( ( b y = ( ( + c y = -( + ( d + = 0 6 Sketch the following eponential function by completing the table of values, plotting the points, and drawing a smooth curve through the points. y = y = The amount of a drug in the bloodstream is modelled by the eponential decay function A = t, where A is amount in milligrams and t is time in hours. a How much of the drug is in the bloodstream at time t = 0 hours? b How much of the drug is in the bloodstream after hours? c Plot the function and use it to estimate when there is 00 mg.