Mathematics 10 Sample Questions

Transcription

1 Mathematics 10 Sample Questions

2 Math The following questions have been constructed to illustrate the various types of questions (, and Analysis) for each of the units of study in Mathematics 10. This document is in draft form and is not intended to illustrate questions for every outcome in Mathematics 10 but rather to clarify the types of questions and to provide some sample questions for each of the units of study. Cognitive Levels Cognitive levels indicate the type of intellectual process required to respond to each question. Facility in using mathematics, or reasoning about mathematical situations, depends on mathematical knowledge and familiarity with mathematical concepts. of a wide range of mathematical terminology, number properties, geometric properties, basic facts, and mathematical procedures open the door to the development of a deeper mathematical understanding and purposeful mathematical thinking. questions will require students to recall and recognize previously learned concepts/skills and solve routine mathematical procedures. questions include recognition or recall of terminology, formulae, algorithms, graphs, geometric figures, properties, and theorems. Questions at this level include key words such as: identify, measure, find, solve, use, list, define, classify, and name. questions require students to answer questions that are typical of, but not identical to, the problems studied in class. Students are expected to understand the problem, as well as, identify and use the appropriate strategy to solve the problem. Questions at this level include key words such as: organize, estimate, interpret, predict, translate, summarize, solve, explain, describe, and apply. Analysis An analysis question requires students to use reasoning to solve multi step and non routine problems. Students must draw on knowledge and understanding from previous learning and from different areas of mathematics to solve more complex problems. The student must make connections and generalize their learning to new situations. Questions at this level will include key words such as: analyze, investigate, prove, explain, generalize, justify, and infer. DRAFT May 2014 Page 1

3 Measurement SI and Imperial Convert 350 m to yards, feet, and the nearest inch. Find the perimeter, in feet, of a deck that is 5 yards long and 8 3 wide. A logger cuts down a tree that has a trunk 25 metres long. The logger is told to cut it into lengths that are 47 long. How many lengths could she cut? A truck is carrying a 9 5 wide load that is 8 11 high. Is it possible for this truck to pass through a tunnel that is 360 cm wide and 3 metres high? Justify your answer. Analysis A landscaper is supplying bark to cover the gardens shown below. If one bag of bark will cover 40 square feet of garden, how many bags does the landscaper need to complete this job? DRAFT May 2014 Page 2

4 Measurement Surface Area/Volume A cylinder has a volume of cm 2 and a height of 8.5 cm. What is the radius of the cylinder? Or: Determine the surface area of a sphere with a diameter of 10 cm. The Louvre Museum in Paris has a glass pyramid at the entrance with a height of 70 ft. and a square base with sides of 115 ft. The Muttart Conservatory in Edmonton has its own glass pyramid with a side length of 19.5 m and a height of 18.0 m. Which pyramid has the greatest surface area and by how much? Round your answer to the tenth and include units. A pharmacist is filling medicine capsules. The capsules are cylinders with half spheres on each end. If the length of the cylinder is 12 mm and the radius is 2 mm, how many cubic mm of medication can one capsule hold? Analysis 11 A standard cylindrical tin soup can measures 2 16 inches in diameter and 4 inches in height. If the same amount of soup is in a cubical container, will more or less tin be used? How much more or less? Ignore the thickness of the can in your analysis. When buying a room air conditioner, it is important to purchase a unit that is neither too big nor too small for the room. If the unit is too large, it will cool too quickly and will not remove humidity from the air, thus wasting money and energy. If the unit is too small, it will run continually without ever cooling to the desired temperature, again wasting energy and money. How high is the ceiling in this room if a model that cools 1100 to 1300 cubic feet is the right size to cool this bedroom? DRAFT May 2014 Page 3

5 Measurement Trigonometry Some Sample Questions Mathematics 10 On a sunny day, the CN Tower, 1814 ft. high, casts a shadow on the ground. A tourist stands at the end of the shadow and measures the angle of elevation of the sun to be Determine, to the nearest foot, the length of the shadow. Determine the height of the ledge shown below. Determine the height of the building, h. Find the length of x. For the triangle shown below determine the length of the side x. DRAFT May 2014 Page 4

6 Analysiss In an isosceles triangle, two legs are 50 cm in length. The third side is much longer. The largest angle in this triangle is 120. Determine the area of this triangle. 120 Determine the height of the mountain in the diagram shown below: The length of the body diagonal in this rectangular prism is 61 cm. The width of the prism is 29 cm. The measure of AFH is 23. Determine the height and the length of the rectangular prism. A B 29 cm 61 cm D H C G E F 23 DRAFT May 2014 Page 5

7 Algebra and Number Exponents and Radicals : Evaluate : A. B. C. D. : can be simplified to obtain 3 4. Show, clearly, how this can be done without the use of a calculator. Analysis: If the area of the square ABCD is 567 cm 2 and the triangles DEF and DAC are similar with a ratio of 3 to 1. a. Find the side length of? b. What is the area of the triangle DEF? DRAFT May 2014 Page 6

8 Algebra and Number Polynomials: Multiplying and simplifying : Expand and simplify a) 2x(2x y) b) (2x 3y) (x+2y+4) Simplify : Determine the values of m and k if: Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region 3 x + 8 x 3 x x + 6 Analysis: The area of the triangle is equal to the area of the rectangle. Find the length of the hypotenuse of the triangle. 2x + 4 x + 4 x + 15 x + 11 DRAFT May 2014 Page 7

9 Algebra and Number Polynomials: Factoring : Factor each of the following: a) Factor: x 2 25 b) Factor: x 2 + 4x + 4 c) Factor: 4x + 12 d) Factor: e) Factor: : Find an integer to replace so that 42 9 is a perfect square. The area of a square is 4x x + 36, what is it s perimeter? Analysis: Given the triangle below, find the measure of x. Your answer must be fully simplified (3a+1) x Find the value of k so that 2x 2 + kx + 18 factors as a perfect square. DRAFT May 2014 Page 8

10 Algebra and Number Distance and Midpoint Formulas : The midpoint of line is (4,5). If point A is located at ( 4, 2), find the coordinates of point B. Determine the length of AB if A( 3,4) and B(5,2). : Find the perimeter and area of the following triangle: Analysis: A rectangle is given by points A(, 1), B(, 1), C(, 1) and D(, 1). Point O is the midpoint of the line joining points A and C. Prove that the triangle OAC is equilateral. Find a point on the x axis that is equidistant from the points A (1, 5) and B (4, 2). DRAFT May 2014 Page 9

11 Relations and Functions Linear Equations Basics Find the x intercept of the line with the equation ⅔x ½y = 1. If f(x) defines a linear function, and f(0) = 3 and f(2) = 0 find the equation of f(x) in slope intercept form. Analysis Find the perpendicular distance from the point (5, 4) to the line with the equation y = 2x + 4. Relations and Functions: Linear Equations Modeling What is the slope of the line in this graph? a. 4 b. 0 c. Undefined d. ¼ Identify the following system of lines as parallel, perpendicular or neither. 4x + 3y = 18 ½x ⅔y = 4 Find the equation of the line that passes through the points C (5, 7) and F (2, 4). DRAFT May 2014 Page 10

12 Find the area of the triangle bounded by the x axis, the y axis and the line 5x + 5y = 20. A line passes through the points A (0, 2) and B (4, 0). Show algebraically that the point D (8, 2) also lies on this line. In order to hunt caribou in Cape Breton, a caribou hunting license is required. Since the hunter can sell the caribou he catches he can use the proceeds to pay for part or all of the cost of the license. If he only catches 3 caribou he is still in debt by $ but if he catches 7 caribou he makes a profit of $ The Cape Breton Gaming Society allows a limit of 10 caribou per hunter. Let c be the number of caribou caught and let d by the number of dollars profit made and assume that c and d are related by a linear function. a. Which variable should be dependent and which should be independent? (knowledge) b. Write a linear equation that represents this relationship. (application) c. What would be a suitable domain for the independent variable? (application) d. Calculate both the d and c intercepts and explain what they represent. (application) e. What does the slope represent? (application) Analysis Find the area of the triangle bounded by the line x = 3, the line y = 2 and the line 5x + 5y = 20. The point P ( 5, K + 2) is on the line that passes through the A (0, 2) and B (4, 0). Find the value of K. DRAFT May 2014 Page 11

13 Relations and Functions Systems of Equations 3 6 Consider the following system of linear equations y = x and 3x 5y = 6. How many solutions 5 5 would there be to this system? a) 0 b) 1 c) 2 d) Infinite Manson has $2.50 worth of nickels and dimes. He has 36 coins in all. How many nickels and dimes does he have? Analysis Consider the following system of equations: x + y = 2 and qx + y = 3. Find a value for q so that this system has infinite solutions. DRAFT May 2014 Page 12

14 Financial Mathematics Best Buy and Currency Exchange One store sells 375 g of organic granola for $5.99. Another store sells 900 g of organic granola for $ Which is the better buy? If Sam paid US$120 for a skateboard, how much is this in Canadian dollars? 1C$=US$ You and your sister both need indoor and outdoor soccer cleats. Three competing stores are offering these deals: Deal 1: $84.99, now 35% off! Deal 2: $84.99, buy one, get 2 nd half off! Deal 3: $84.99, buy three, get one free! Since you need four pairs of cleats, which store has the better deal? Ellen is shopping online on ebay for Pokemon fabric. She finds 2 metres listed for 30 plus 10% shipping. How much will this cost Ellen in Canadian dollars if C$1= ? Analysis Ellen is shopping online on ebay for Pokemon fabric. She finds 2 metres listed for 30 plus 10% shipping. The 3 metres of the same fabric sells for 50 plus 12% shipping. Which fabric would be the best buy? She looks at the current exchange rate and C$1= and C$1= DRAFT May 2014 Page 13

15 Financial Mathematics Types of Salary Karen earns $11.50 per hour and works 35 hours per week. The deductions from her weekly pay are: E.I. = $9.06 C.P.P. = $14.41 Income Tax = $49.10 Company pension plan = $10.77 Health plan = $4.85 Determine Karen's weekly: a. gross pay b. total deductions c. net pay Barinder s job is selling shoes. He makes $11.00 an hour plus a commission of 3.50% on all he sells. Last week he worked 40 hours and sold $1295 worth of shoes. Analysis Hugh, a shoe salesperson, receives a salary of $830 a month plus a commission of 8% on all sales in excess of his monthly quota of $3000. His total sales last month were $ What were his total earnings for the month? DRAFT May 2014 Page 14

16 Examination Specifications The NSE Mathematics 10 is constructed in accordance with tables of specifications and the Nova Scotia Assessment Development Model. They include questions (items) that have met the following criteria: rigorous content review by the provincial mathematics examination advisory group for alignment with outcomes as listed in the appendices and for possible bias and construction flaws; field testing under monitored conditions in Mathematics 10 classrooms; statistical analysis of the students responses following the field testing to determine levels of difficulty, validity, and reliability of each question. Specification Tables Table 1 Specifications for Mathematics 10 Unit of study Approximate Weighting Measurement 25% 30% Algebra and Number 20% 25% Relations and Functions 35% 40% Financial Mathematics 10% 15% Table 2 Examination specifications according to question format Question Format # of Questions Approximate Weighting Selected response (multiple choice) Constructed response (short answer and extended response) 40 45% 55% 10 45% 55% Table 3 Examination specifications according to cognitive level Cognitive Level Approximate Weighting 20% 25% 55% 65% Analysis 15% 20% DRAFT May 2014 Page 15

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