Math 9 Review (Chapters 1, 2, 10)
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1 Math 9 Review (Chapters 1, 2, 10) Problem 1. A concrete block has a rectangular prism-shaped hole extending through the block. Determine the total surface area of the block. 2. The slanted faces of the roof of a house must be covered with tiles. The area of each rectangular tile is 20 cm by 30 cm. How many tiles would be needed to cover the roof? 3. A can of waterproofing spray covers 8.1 m 2. How many cans of waterproofing spray do you need in order to treat the exterior of walls of the tent, excluding the bottom?
2 4. Whitney wants to repaint her bird feeder before she rehangs it in the yard. What is the surface area of the feeder? Express your answer to the nearest tenth of a square centimetre. 5. Jordan went to a pet shop and bought 8 tetra fish for $2.00 each, 3 goldfish for $2.75 each, and 2 angel fish for $3.75 each. What is the total cost of the fish, before taxes? 6. The mean of seven rational numbers is a) What is the sum of the rational numbers? b) If six of the numbers each equal 4.60, what is the seventh number? 7. Warren s father mowed of the lawn. Warren mowed of the lawn that was left by his father. Warren s two younger brothers finished mowing the rest of the lawn. a) What is the fraction of the entire lawn that Warren mowed? b) What fraction of the entire lawn did each of Warren s brothers mow?. 8. A rectangular swimming pool has a length that is four times its width. The pool covers an area of 144 m 2. What are the dimensions of the pool? 9. A circular garden has a diameter of 12 m. By how much should the diameter be increased to triple the area of the garden? Give your answer to two decimal places. 10. A resort had 425 people booked for 1 week. During the week, each person drank 2 cups of tea, 1.5 times that amount of juice, and 0.75 times that amount of milk per day. Tea costs $0.10 per cup, juice costs $0.22 per cup, and milk costs $0.16 per cup. What was the total cost of beverages for the week? 11. Circle O has chord CD drawn on it. Chord CD is 12.6 cm long. The centre of the chord, G, is 8.4 cm from the centre of the circle. What is the radius of the circle?
3 12. In the figure shown, what is the measure of AFB? Justify your response. 13. A round dining table has a centre, H, and a diameter of 1.2 m. The table is pushed into a corner of a dining room, as shown. Determine the distance between the corner of the wall, C, and the edge of the table. Express your answer to the nearest millimetre.
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5 Math 9 Review (Chapters 1, 2, 10) Answer Section PROBLEM 1. ANS: Surface area without hole: Surface area lost for holes in each end: Surface area inside hole: Total surface area: The total surface area of the concrete block is 158. PTS: 4 DIF: Difficult OBJ: Section 1.3 NAT: SS2 TOP: Surface Area KEY: surface area faces area of face 2. ANS: Size of tile 20 cm = 0.2 m 30 cm = 0.3 m Area of a tile: Area of slanted faces: Number of tiles needed to cover roof: 2660 tiles are needed to cover the slanted faces of the roof. PTS: 4 DIF: Average OBJ: Section 1.3 NAT: SS2 TOP: Surface Area KEY: surface area 3. ANS: Slant length of tent Surface area of slanted faces: Surface area of front and back triangular faces: Total surface area of walls of the tent Each can of waterproofing spray covers 7.4 m 2. The amount of spray needed to cover the walls. You need five cans of waterproofing spray must be purchased to treat all of the exterior walls of the tent. PTS: 5 DIF: Difficult OBJ: Section 1.3 NAT: SS2 TOP: Surface Area KEY: surface area faces area of face 4. ANS:
6 Surface area of top cylinder: Surface area of bottom cylinder: Surface area of join: Total surface area: The total surface area of Whitney s bird feeder is cm 2. PTS: 5 DIF: Difficult+ OBJ: Section 1.3 NAT: SS2 TOP: Surface Area KEY: surface area faces area of face cylinder 5. ANS: The fish cost $31.75 before taxes. PTS: 1 DIF: Average OBJ: Section 2.2 NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal Form KEY: rational numbers order of operations multiply add 6. ANS: a) Example: The sum of the rational numbers is b) Example: The seventh number is PTS: 1 DIF: Difficult OBJ: Section 2.2 NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal Form
7 KEY: order of operations decimal numbers problem solving 7. ANS: Example: a) Fraction of entire lawn that Warren mowed Warren mowed of the entire lawn. b) Fraction of entire lawn that each of Warren s brothers mowed Warren s brothers each mowed of the entire lawn. PTS: 1 DIF: Average OBJ: Section 2.3 NAT: N3 TOP: Problem Solving With Rational Numbers in Fraction Form KEY: fractions order of operations problem solving 8. ANS: Example: Let the width of the pool be represented by w. Let the length of the pool be represented by 4w. The width of the pool is 6 m and the length is 24 m. PTS: 1 DIF: Difficult OBJ: Section 2.4 NAT: N5 TOP: Determining Square Roots of Rational Numbers KEY: rational numbers square root area 9. ANS: Example:
8 Triple the area: Determine the radius and diameter of the larger garden. The diameter must be increased by approximately 8.78 m to triple the area of the garden. PTS: 1 DIF: Difficult+ OBJ: Section 2.4 NAT: N6 TOP: Determining Square Roots of Rational Numbers KEY: rational numbers square root problem solving area 10. ANS: For 1 person in 1 day: Cost for 1 person in 1 day: Cost for 425 people in 1 day: Cost for 425 people in 1 week: The total cost of beverages for the 1 week at the resort is $ PTS: 1 DIF: Difficult OBJ: Section 2.2 NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal Form KEY: rational numbers problem solving decimals 11. ANS: Use the Pythagorean Theorem to determine the length of the radius of circle O.
9 The radius of circle O is 10.5 cm. PTS: 1 DIF: Average OBJ: Section 10.2 NAT: SS1 TOP: Exploring Chord Properties KEY: Pythagorean relationship chord perpendicular bisector diameter 12. ANS: Since CE is a radius bisecting chord AB, ADC equals 90. The other angles, ACD and DAC, form an isosceles triangle with angles adding to 180. AFB is an inscribed angle subtended by the same chord as central angle ACB. AFB is half the size of ACB. AFB equals 45 AFB measures 45. PTS: 1 DIF: Average OBJ: Section 10.2 NAT: SS1 TOP: Exploring Chord Properties KEY: chord perpendicular bisector inscribed angle central angle 13. ANS:
10 The distance from the corner of the dining room to the edge of the table is approximately 249 mm. PTS: 1 DIF: Difficult+ OBJ: Section 10.3 NAT: SS1 TOP: Tangents to a Circle KEY: Pythagorean relationship radius problem solving
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