MFM 2P0
EXAM REVIEW: UNITS 1-3
Unit 1: Equations of Lines
Solve:
1. x – 4 = 10 2. 2y – 6 = 10 3. 6r – 6 = 3r – 9 4. (w-9)+6=4(w-2)-2(w-6)
5. 6. 2(x-3)-5=13-4x 7. 8. 2x-3x+4=5-15x+3
Solve and check:
9. 6-k=7k-5k 10. 12-3m=2(m+1) 11. 12. 5 + 4k – 7 = 4k – 2 – k
13. Solve each formula for the indicated variable: a) for m b) P = 2l + 2w for w
14. Use the formula for speed , to find the distance traveled by an aircraft cruising at a speed of 500 km/h for 1.5 h.
15. Graph these lines using a table of values: a) y = –x + 2 b) y = 3x – 5 c)
16. Graph these lines using the x- and y-intercepts: a) x – y = 2 b) c) x – 3y + 9 = 0
17. Find the slope by graphing: a) (1, 2) and (6, 5) b) (1, –-2) and (3, 2) c) (-4, 0) and (-1, -3)
18. Find the slope using the formula: a) (-2, 3) and (4, 6) b) (-6,-1) and (-2,5) c) (-5,7) and (-4,-2)
19. Graph these lines using the slope and y-intercept method: a) y = 2x + 1 b) c) y = –3x + 5
20. Find the equation of the line shown in each graph below:
21. Find the equation of the line passing through the given points:
a) (1,2) and (3,5) b) (2,3) and (-1,6) c) (-7,-2) and (-1,-8)
22. Write the following equations in y = mx + b form, and then graph the line.
a) 2x – y + 4 = 0 b) 3x + y + 6 = 0 c) x – 3y + 6 = 0
Unit 2: Solving Linear Systems
Solve each of the following linear systems by graphing. Check each of your solutions.
1. 2. 3. 4. 5.
Solve each of the following linear systems by substitution.
6. 7. 8. 9. 10.
Solve each of the following linear systems by elimination.
11. 12. 13. 14. 15.
For each of the following, introduce your variables, and write an equation to represent the information given.
16. A golf club charges an initiation fee of $2000, plus a monthly charge of $200.
17. Brian earns 15% commission on his sales as a car salesman, plus $400 a month.
18. It costs $1000 to rent a hall for a party, plus $5.00 per person who attends the dinner.
19. A flyer company charges $0.25 per flyer they print, plus $20 to cover start-up costs.
Unit 3: Quadratics (Part 1)
For each of the questions below, indicate which graphs are graphs of quadratic functions.
1. 2. 3. 4.
Graph each of the functions below. For each graph, state: the vertex, the y-intercept, the x-intercepts, the equation of the axis of symmetry, whether the graph is a maximum or a minimum and the value at that point.
5. y = 5x2 6. y = –x2 – 2 7. y = (x – 4)2 8. y = –(x – 2)2 – 4 9. y = 2(x + 1)2 – 8
For each of the table of values given below, calculate the finite differences and state whether each function is linear, quadratic, or neither. ***REMEMBER – once you find a constant value, stop calculating the differences.
EXAM REVIEW: UNITS 4-6
Unit 4: Quadratics (Part 2)
Expand and simplify.
1. (p – 2)(p + 3) 2. (n + 7)(n + 2) 3. (8 – x)(5 + x) 4. (w – 4)(w – 8) 5. (3x – 1)(5x +3)
Find each product.
6. (x – 3)(x + 3) 7. (g + 5)2 8. (y – 12)(y +12) 9. (9m – 4)2 10. (5p – 1)(5p + 1)
Factor fully by finding the GCF. Check by expanding.
11. 12 – 10q 12. 2w2 – 10w + 2 13. 15x + 25y 14. 27k3 – 36k5 15. 15a3 – 20a2 + 25a
Factor each binomial fully. Check by expanding.
16. n2 – 121 17. 16 – d2 18. 4m2 – 25 19. m2 – 1 20. t2 – 4
Factor each trinomial fully. Check by expanding.
21. x2 + 4x + 3 22. a2 – 11a + 30 23. m2 – 18m + 81 24. n2 – 3n – 10 25. x2 + 11x + 24
Solve each quadratic equation by factoring.
26. n2 – 9n + 18 = 0 27. m2 – 36 = 0 28. b2 + 8b = –16 29. y2 + 64 = 16y 30. x(x – 2) = 48
For each of the following: a) give the y-intercept b) find the x-intercept(s) c) sketch the graph
31. y = x2 – 1 32. y = x2 + 2x – 8 33. y = x2 + 4x + 3 34. y = –x2 + 4 35. y = –x2 – 2x + 3
Unit 5: Similar Triangles and Trigonometry
1. The triangles in each pair are similar. Find the unknowns. 2. Evaluate, round your answer to four decimal places:
a)/ b) / a) cos25o=______b) sin75o=______
c) tan210o=______d) cos90o=______
3. Determine the measure of each angle, to the
nearest degree:
a)
b)
4. With respect to angle X:
a) label the opposite side,
adjacent side, and the
hypotenuse
b) state the sin, cos and
tan of angle X.
5. Find the unknown measures to 1 decimal place. 6. Find the measure of the indicated angles, to the
nearest degree.
a) b) a) b)
Unit 6: Measurement
1. Write the complete measurement above each arrow on the following imperial ruler.
2. Complete the following conversions. If necessary, your round answers to one decimal place.
a) 350 mà km b) 2.1 L à mL c) 75 152 cm à km d) 42 kg à g
e) 2781 mm à m f) 21 dm à m g) 2 lbs. à oz. h) 16 qts à gal
i) 36" à ft j) 4 mi à ft k) 1600 oz à ton l) 1536 fl. oz. à gal
m) 10L à qts n) 5" à cm o) 12 km à mi p) 150 lbs à kg
q) 8 L à gal r) 10 fl. oz. à mL s) 3.5 ft à cm t) 5 km à ft
3. Calculate the surface area and volume of each of the following figures. Round your answers to two decimal places.
4. Calculate the volume of each of the following figures. Round your answers to two decimal places.