Math 9 Practice Test. Problem

Transcription

1 Math 9 Practice Test Problem 1. The surface area of a metal tube must be coated with lubricant. Determine the total surface area that must be covered, to the nearest tenth of a square centimetre. 2. Bonnie drives 100 km in 60 min. Laurie drives the same distance, but takes 5 min longer than Bonnie. a) Who is driving faster? b) How much faster is she driving? Give your answer in km/h, rounded to the nearest hundredth. 3. Pak owned 120 shares in a technology company. On Monday, the price of the stock was $34.16 per share. Pak sold all his shares of stock on Friday, for a total value of $ a) Determine how much money Pak lost or gained on the sale of his shares on Friday, compared to Monday s price. b) Determine the value of Pak s shares on Friday. 4. An engineer is building an ultralight airplane. The fuel tank has a mass of 4.5 kg. Each litre of fuel has a mass of 737 g. The total mass of the fuel plus the tank cannot exceed 22 kg. How many litres of fuel can the fuel tank hold, without exceeding the maximum weight? Round your answer to the nearest tenth of a litre. 5. A culture of bacteria triples every hour. How many bacteria were there 3 h ago? 6. The product of the ages of a set of triplets is 12 times the sum of their ages. Determine how old the triplets are. 7. Jamie needs to create a scale diagram of his property for a project. He makes measurements as shown below. If Jamie s diagram uses a scale of 1 cm: 1.3 m, what would the distance x be on the diagram? Give your answer to the nearest tenth of a centimetre.

2 8. Karen estimates that there are x gophers in each corn field on her farm. Each wheat field has two less than twice as many gophers as a corn field. Write a simplified expression to describe the number of gophers on her farm if she has 5 corn fields and 7 wheat fields. 9. In a classroom, the number of tables is represented by the variable t. The number of chairs in the classroom is equal to the square of the number of tables. The number of reference textbooks in the classroom is equal to 5 more than 3 times the number of chairs. a) Write an expression to show the number of each of these three items. Simplify the expression. b) Determine the total number of these three items if there are 6 tables. Check your answer another way. 10. a) Write a simplified expression representing the perimeter of the figure. b) If s = 5 cm, what is the perimeter of the figure? 11. A brick patio has 10 rectangular bricks in the first row. Each row of bricks in the patio has 2 more bricks than the previous row. a) Create a table of values showing the relationship between the first 4 rows and the number of bricks in each row. b) What equation represents the relationship between the row number, r, and the number of bricks, n? c) How many bricks are in the 9th row? d) There are 68 bricks in the final row. How many rows of bricks are in the patio? 12. The number of baskets of apples, N, that can be produced by x trees in an orchard is given by the formula. a) What is an expanded form of this formula? b) How many baskets of apples can be produced by 110 trees?

3 13. The volume of a speaker is m 3. The width of the speaker is x m and the depth is x + 1 m. What is the height of the speaker? 14. Tarek completes his weekly grocery shopping at Shop Safe. The total bill for his order is $ Tarek buys the same products the next week at Grocery Rite. The subtotal bill for his order at Grocery Rite is 1.4 times greater than his bill from the previous week. He hands the cashier $6.75 in discount coupons. How much cash does Tarek need to pay? Show your answer to the closest cent. 15. Two positive integers have a sum that is less than 61. One of the integers is 7 more than the other. Determine the possible values for the smaller integer. 16. Ryan bought gallons of paint. After he had used some of the paint to paint his garage, he still had more than gallons left. How much paint did he use? 17. Determine the measures of NPQ, POR, < QOR, and PQR. Explain your work.

4 Math 9 Practice Test Answer Section PROBLEM 1. ANS: Surface area of cylinder without cutout: Surface area of the end cutout circles: Surface area of inside of tube: Total surface area of tube: The surface area of the tube that needs to be covered is cm 2. PTS: 5 DIF: Difficult+ OBJ: Section 1.3 NAT: SS2 TOP: Surface Area KEY: surface area faces area of face cylinder 2. ANS: a) Bonnie is driving faster. b) Answers may vary slightly depending on the method used and when the rounding is done. Example: Laurie s speed: Bonnie s speed: = 7.66 km/h Bonnie is driving 7.66 km/h faster than Laurie. PTS: 5 DIF: Difficult OBJ: Section 2.2 NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal Form KEY: rational numbers problem solving 3. ANS: a) Monday s stock value = 120 $34.16 = $ Friday s stock value = $ Change = +$ Pak gained $ by selling on Friday.

5 b) Value of stock on Friday = Total sale value on Friday number of stocks = = The value of each share on Friday was $ PTS: 1 DIF: Difficult OBJ: Section 2.2 NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal Form KEY: rational numbers problem solving money 4. ANS: Example: 1000 g = 1 kg 737 g = kg 1 kg = 1 L Let f represent the amount of fuel, in litres f = f = 17.5 f = The tank can hold 23.7 L of fuel without exceeding the maximum weight. PTS: 1 DIF: Average OBJ: Section 2.2 NAT: N3 TOP: Problem Solving With Rational Numbers in Decimal Form KEY: decimal numbers order of operations rational numbers problem solving 5. ANS: Let P represent the population of bacteria. There were approximately 3704 bacteria 3 h ago. PTS: 1 DIF: Difficult+ OBJ: Section 3.4 NAT: N1 TOP: Using Exponents to Solve Problems KEY: population growth problem solving negative exponents 6. ANS: Let x represent the age of the triplets. The product of the ages of the triplets is x x x,or x 3. Twelve times the sum of the ages of the quadruplets is 12(x + x + x), or 12(3x). Divide both sides by x.

6 The triplets are 6 years old. PTS: 1 DIF: Difficult OBJ: Section 3.2 NAT: N2 TOP: Exponent Laws KEY: quotient of powers evaluate powers problem solving 7. ANS: On Jamie s diagram, the distance x would be 16.2 cm. PTS: 1 DIF: Average OBJ: Section 4.3 NAT: SS4 TOP: Similar Triangles KEY: similar triangles problem solving 8. ANS: Number of gophers in corn field = x Number of gophers in wheat field = Karen s farm has gophers. PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR5 TOP: Equivalent Expressions KEY: expression term 9. ANS: a) Number of tables is represented by. Number of chairs = Number of reference books = There are tables, chairs, and books in the classroom.

7 b) Number of tables = 6 Number of chairs = 36 Number of reference books = 155 If there are 6 tables, then there are a total of 155 items in the classroom. PTS: 1 DIF: Difficult OBJ: Section 5.3 NAT: PR5 TOP: Adding and Subtracting Polynomials KEY: expression simplify 10. ANS: a) b) If s = 5 cm, the perimeter of the figure is 101 cm. PTS: 1 DIF: Average OBJ: Section 5.2 Section 5.3 NAT: PR6 TOP: Equivalent Expressions Adding and Subtracting Polynomials KEY: perimeter expression simplify 11. ANS: a) Row Number, r Number of Bricks, n b) The equation that represents the relationship between the row number and the number of bricks is. c) There are 26 bricks in the 9th row. d)

8 There are 30 rows of bricks in the patio. PTS: 1 DIF: Average OBJ: Section 6.1 NAT: PR1 TOP: Representing Patterns KEY: table of values equation from table of values extend patterns substituting values 12. ANS: a) An expanded form of the formula is. b) In this orchard, 110 trees can produce 1540 baskets of apples. PTS: 1 DIF: Average OBJ: Section 7.2 NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a polynomial by a monomial expand 13. ANS: The height of the speaker is 2 m. PTS: 1 DIF: Average OBJ: Section 7.3 NAT: PR7 TOP: Dividing Polynomials by Monomials KEY: dividing a polynomial by a binomial volume 14. ANS: Example: Let g represent Tarek s total bill at Grocery Rite. Tarek pays $ in cash. PTS: 1 DIF: Average OBJ: Section 8.4 NAT: PR3 TOP: Solving Equations: ax = b + cx, ax + b = cx + d, a(bx + c) = d(ex + f) KEY: multi-step equation multiplication subtraction money problem solving 15. ANS: Let n represent the smaller integer. Then n + 7 is the larger integer.

9 The smaller integer is less than 27, but greater than 0, because it is positive. PTS: 1 DIF: Difficult+ OBJ: Section 9.3 NAT: PR4 TOP: Solving Multi-Step Inequalities KEY: multi-step inequality subtraction division problem solving 16. ANS: Let p be the number of gallons of paint used. Ryan used less than gallons of paint. PTS: 1 DIF: Difficult OBJ: Section 9.2 NAT: PR4 TOP: Solving Single-Step Inequalities KEY: single-step inequality reverse the inequality symbol subtraction problem solving 17. ANS: NPQ = 90. Example: When a diameter meets a tangent at the point of tangency, the angle formed between them is 90 POR = 60. Example: This angle is one of three in an equilateral triangle. All angles in an equilateral triangle are 60. QOR = 120. Example: This angle forms a straight line with another angle, which is 60. Angles in a straight line add to 180. PQR = 30. Example: PQR is an inscribed angle subtended by the same chord as central angle, POR. Inscribed angles are half the central angle subtended by the same chord or arc. PTS: 1 DIF: Average OBJ: Section 10.3 NAT: SS1 TOP: Tangents to a Circle KEY: tangent chord inscribed angle central angle