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The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.

The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm. diagram not to scale. Determine if this could be a right triangle. No, it could not. H G. E. F. 40 cm. D. C. 30 cm. A B. 22.5 cm.

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The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.

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  1. The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm. diagram not to scale Determine if this could be a right triangle. No, it could not.

  2. H G E F 40 cm D C 30 cm A B 22.5 cm The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm. Calculate the length of [AC]. 37.5 cm

  3. x = 1.28 m

  4. 4.70 m

  5. The following diagram shows a carton in the shape of a cube 8 cm long on each side: • 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. (b) Find the length L of the longest rod that would fit inside the carton. = 11.3 cm = 13.9 cm

  6. A square garden with sides 100 m is divided into two triangular plots by a fence along one diagonal. What is the length of the fence in meters? If the fence costs $15.50 per meter, what is the total cost? 141 m $2186

  7. V P Q 8 cm G M S R 8 cm 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 • Write down the length of [GM]. (b)Calculate the length of [VM]. = 4 cm = 12.6 cm

  8. 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

  9. Find the value of any unknown.

  10. A sailing ship sails 46 km North and then 74 km East. How far is the ship from its starting point? = 87.1 km

  11. Simplify • a) (4x3y5)3

  12. Simplify

  13. Solve for x: 5(x + 2) – 2(3 – 2x) = 3

  14. Solve for x: x(2x + 1) – 2(x + 1) = 2x(x – 1) x = 2

  15. Solve for x:

  16. Solve for x:

  17. Solve for x:

  18. Solve for x. 4x = 8

  19. Solve for x.

  20. solve by elimination 2x + 7y = 2 3x + 5y = -8 (-6, 2)

  21. solve by substitution 5x – y = -11 4x + 12y = 4 (-2, 1)

  22. 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 p = 14 w = 10 32p + 36w = 808 8p + 12w = 232 14 pans of pasta 10 sandwich trays

  23. 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 7b + 8c = 161 b = 15 Bsf c = 7 Bsf 2 Big Macs and 1 Coke would cost 37 Bsf.

  24. 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 = 7 d = 3 m + d = 10 350d + 310m = 3220 7 days in Miami 3 days in Orlando

  25. 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.

  26. Write as powers of 2, 3, or 5 =3-3x =5-2 =2-2

  27. Solve for x.

  28. Find the equation of the line that goes through the points (-3, 6) and (-2, 4). y = -2x

  29. Write the equation, in standard form, of the line that passes through (-2, 5) and (3, 1)

  30. Write the equation of the line, in standard form, with slope and containing the point (4, -1). 3x + 4y = 8

  31. Given that M is the midpoint of PT, find the coordinates of T if P is (6, -2) and M is T is (2, -9)

  32. Find the midpoint of the line segment AB given A(-5, -3) and B(9, 3) (2, 0)

  33. Find the distance between (2, -4) and (-5, -1)

  34. Find the negative value of b given that the distance between (-2, 5) and (3, b) is -1 = b

  35. 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

  36. Graph x + 2y = 4

  37. Write the equation of the graph below.

  38. Graph x = -2

  39. Graph 3x – 5y = 15 by finding the x- and y-intercepts x-intercept: 3x – 5(0) = 15 x = 5 y-intercept: 3(0) – 5y = 15 y = -3 (0, -3) (5, 0)

  40. Graph the line with slope 0 and containing the point (3, -5)

  41. Use technology to find the point of intersection of 5x – y = -11 and 4x + 12y = 4. (-2, 1)

  42. 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

  43. 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

  44. Use the distance formula to determine if triangle ABC is scalene, isosceles or equilateral. A(2, 1) B(3, -2) C(5, 2). isosceles

  45. Formulaeyou will need to know: • Distance • Midpoint • Slope • Slope-intercept • Pythagorean theorem

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