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The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm. 7 5 diagram not to scale Determine if this could be a right triangle. 8 No, it could not. The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm. H E G F 40 cm D C 30 cm A 22.5 cm B Calculate the length of [AC]. 37.5 cm x = 1.28 m 4.70 m The following diagram shows a carton in the shape of a cube 8 cm long on each side: (a) The longest rod that will fit on the bottom of the carton would go from E to G. Find the length l of this rod. = 11.3 cm (b) Find the length L of the longest rod that would fit inside the carton. = 13.9 cm B C D A F B G H A square garden with sides 100 m is divided into two triangular plots by a fence along one diagonal. a) What is the length of the fence in meters? 141 m b) If the fence costs $15.50 per meter, what is the total cost? $2186 In the diagram below, PQRS is the square base of a solid right pyramid with vertex V. The sides of the square are 8 cm, and the height VG is 12 cm. M is the midpoint of [QR]. Diagram not to scale (a) Write down the length of [GM]. = 4 cm (b) Calculate the length of [VM]. V P Q G S 8 cm 8 cm M R = 12.6 cm Two ships B and C leave a port A at the same time. Ship B travels in a direction 067 at a constant speed of 36 km/h. Ship C travels in a direction 157 at a constant speed of 28 km/h. Find the distance between them after 2 hours. 91.2 km Find the value of any unknown. x 29 5.39cm y 45 6.71cm A sailing ship sails 46 km North and then 74 km East. How far is the ship from its starting point? = 87.1 km Simplify a) (4x3y5)3 64x y 9 15 7 4 x y b) 2 6 x y 5 x 2 y Simplify 6 2c 64c a) 6 d d 6 2x b) 3 y 2 2 6 y 4 4x Solve for x: 5(x + 2) – 2(3 – 2x) = 3 1 x 9 Solve for x: x(2x + 1) – 2(x + 1) = 2x(x – 1) x=2 Solve for x: 4x 7 5 x 11 2 41 x 19 Solve for x: 5 11 4x 12 15 x 11 Solve for x: 2x 5 4 x 1 1 x 6 Solve for x. 4x = 8 3 x 2 Solve for x. 9 x 2 1 3 3 x 2 solve by elimination 2x + 7y = 2 3x + 5y = -8 (-6, 2) solve by substitution 5x – y = -11 4x + 12y = 4 (-2, 1) A caterer is planning a party for 232 people. •The customer has $808 to spend. •A $32 pan of pasta feeds 8 people and a $36 sandwich tray feeds 12 people. •How many pans of pasta and how many sandwich trays should the caterer make? p = no. of pans of pasta w = no. of trays of sandwiches 32p + 36w = 808 p = 14 8p + 12w = 232 w = 10 14 pans of pasta 10 sandwich trays The bill for 3 Big Macs and 2 Cokes is 59 Bsf. The bill for 7 Big Macs and 8 Cokes is 161 Bsf. What would be the bill for 2 Big Macs and 1 Coke? b = cost of 1 Big Mac c = cost of 1 Coke 3b + 2c = 59 b = 15 Bsf 7b + 8c = 161 c = 7 Bsf 2 Big Macs and 1 Coke would cost 37 Bsf. Your family is planning a 10 day trip to Florida. You estimate that it will cost $350 per day in Orlando and $310 per day in Miami. Your total budget for the 10 days is $3220. How many days should you spend in each location? m = no. of days in Miami d = no. of days in Orlando m + d = 10 m=7 350d + 310m = 3220 d=3 7 days in Miami 3 days in Orlando George is 10 years older than Jane. Three years ago Jane was ¾ as old as George. How old is George now? George is 43 years old. Write as powers of 2, 3, or 5 1 a) 4 =2-2 1 b) x 27 =3-3x 5 c) 125 5 =5-2 Solve for x. 1 x1 32 2 4 x 5 Find the equation of the line that goes through the points (-3, 6) and (-2, 4). y = -2x Write the equation, in standard form, of the line that passes through (-2, 5) and (3, 1) 4 x 5 y 17 Write the equation of the line, in standard form, with slope 3 and containing the point (4, -1). 4 3x + 4y = 8 Given that M is the midpoint of PT, find the coordinates of T if P is (6, -2) and M is 4, 11 T is (2, -9) 2 Find the midpoint of the line segment AB given A(-5, -3) and B(9, 3) (2, 0) Find the distance between (2, -4) and (-5, -1) Find the negative value of b given that the distance between (-2, 5) and (3, b) is 61 -1 = b A line passes through the point (-5, -7) and has a slope of 10. Write the equation for this line in slope-intercept form. y = 10x + 43 Graph x + 2y = 4 Write the equation of the graph below. Graph x = -2 Graph 3x – 5y = 15 by finding the x- and y-intercepts x-intercept: y-intercept: 3x – 5(0) = 15 3(0) – 5y = 15 x=5 y = -3 8 6 4 2 (5, 0) (0, -3) -8 -7 -6 -5 -4 -3 -2 -1 -2 -4 -6 -8 1 2 3 4 5 6 7 8 Graph the line with slope 0 and containing the point (3, -5) Use technology to find the point of intersection of 5x – y = -11 and 4x + 12y = 4. (-2, 1) Write the equation, in standard form, of the line containing the point (-1, 3) and parallel to the line 3x + 7y = 70. 3x + 7y = 70 3 y x 10 7 3 m 7 3 x 7 y 18 Write the standard form of the equation of the line perpendicular to x – 6y + 30 = 0 and passing through the point (5, 3) 6x + y = 33 Use the distance formula to determine if triangle ABC is scalene, isosceles or equilateral. A(2, 1) B(3, -2) C(5, 2). isosceles AB 10 BC 20 AC 10 Formulae you will need to know: • • • • • Distance Midpoint Slope Slope-intercept Pythagorean theorem 45