# application of Mathematics grade 12 level 3

Subject: ; Class: ; with 45 questions; test in 60 minutes; update 19/07/2018
 Time 60 minutes Time to take the test Start exam Click button start to test. Guide to the test Subjects Math test Update 19/07/2018 Class Grade 12 Number of questions 45 View 527 Tested 0

Question 1.

At each point in the maze below, there is an equally likely chance that either path will be chosen. What is the probability that a person entering at point A will exit at point D?

 (A) $$1\over 2$$ (B) $$5\over 8$$ (C) $$3\over 4$$ (D) $$7\over 8$$

Question 2.

Determine the mean on an examination where grades of 70 and 88 have standard scores of −0 6. and 1.4 respectively.

 (A) 73.1 (B) 75.4 (C) 76.9 (D) 79

Question 3.

Annie’s friend Bruno lives 3 blocks north and 5 blocks east of Annie’s house. How many different routes are there from A to B if all routes progress either north or east?

 (A) 21 (B) 35 (C) 56 (D) 70

Question 4.

A hut is located 4 km from the centre of a circular island. There is water 8 km due north and 12 km due south of the hut. What is the radius of the island?

 (A) 8.24 km (B) 10.10 km (C) 10.58 km (D) 10.95 km

Question 5.

In the diagram below, a spider, S, is located on a wall 1 m from the ceiling and 1 m from the corner. The spider wants to crawl across the ceiling to a bug, B, located 1 m from the ceiling and 2 m from the corner. If the dimensions of the room are as shown in the diagram, what is the shortest distance the spider must crawl?

 (A) 5.10 m (B) 6.08 m (C) 6.32 m (D) 7.07 m

Question 6.

Four golf balls are tightly packed in a box that is the shape of a square-based prism. Which of the following is the best approximation of the ratio of the total volume of golf balls to the volume of air in the box?

 (A) 0.62 : 1 (B) 1.10 : 1 (C) 1.16 : 1 (D) 2.22 : 1

Question 7.

Given the matrices Q2×3 and R3×2 , what are the dimensions of the product matrix QR?

 (A) 2 x 2 (B) 2 x 3 (C) 3 x 2 (D) 3 x 3

Question 8.

Determine the value of p for the matrix equation below.

 (A) 0 (B) 1 (C) 5 (D) 12

Question 9.

An airline has connecting flights between four cities as shown below.

Which flight matrix below represents these connecting flights?

 (A) (B) (C) (D)

Question 10.

Solve the following system for x:

3x - y + 2z = 9

x - 3z = -1

2y - z = -3

 (A) -2 (B) -1 (C) 1 (D) 2

Question 11.

The formula “ = SUM(A..D1) / 6” is entered into cell A5 of the spreadsheet below.

What will be the contents of cell A5?

 (A) 9 (B) 24 (C) 37 (D) 89

Question 12.

An investor has $100 000 to invest in either Plan A or Plan B. If the money is invested for a 10-year period, which of the plans would yield a better return, and by how much? (Accurate to the nearest dollar.) Plan A: 6% per annum, compounded monthly Plan B: 6$$1\over 8$$ % per annum, compounded annually  (A) Plan A by$732 (B) Plan A by $2 123 (C) Plan B by$732 (D) Plan B by $2 123 Question 13. . A set of three cube-shaped plastic tubs, decreasing in size, fit inside each other. The volume of the largest tub is 125 000 cm3. The edge length of each tub decreases to $$3\over 4$$ of the previous edge length. What is the volume of the smallest tub to the nearest cm3?  (A) 17 813 (B) 22 247 (C) 39 550 (D) 70 313 Question 14. Which graph best represents the solution of the inequality 4x - 3y > 12 ?  (A) (B) (C) (D) Question 15. The graph below shows the feasible region for a linear programming problem, with corner points A(5, 0), B(3, 4), C(0, 5), D(0, 0). The objective function is P = ax + by where a> 0 and b > 0. For what condition on a and b will the maximum value of P occur at both A and B?  (A) a > 2b (B) b > 3a (C) a = 2b (D) b = 3a Question 16. What type of function is f(x) = $$3\over x + 4$$?  (A) power (B) reciprocal (C) polynomial (D) exponential Question 17. Determine the y-intercept of the graph of y = log(x + 12) - 3.  (A) -3 (B) -2 (C) -1.92 (D) 0.95 Question 18. What is the minimum value of y if y = -4cos(3x) + 7?  (A) -4 (B) -3 (C) 3 (D) 7 Question 19. The graph below shows the height, h, in metres, of the tip of one paddle of a windmill at time, t, in seconds. How many rotations does the paddle make in 3 hours?  (A) 1 800 (B) 2 700 (C) 3 600 (D) 7 200 Question 20. The population of trout in a certain lake varies sinusoidally with time. The population was at a maximum of 28 000 trout on June 1, 1995 and reached its next minimum of 16 000 trout on June 1, 1999. Determine the expected population on June 1, 2006 to the nearest thousand trout.  (A) 18 000 (B) 19 000 (C) 23 000 (D) 24 000 Question 21. If line $$\ell$$ is tangent to the circle at A, which angle must be equal to $$\measuredangle$$1?  (A) 2 (B) 3 (C) 4 (D) 5 Question 22. A country wants to position three satellites in order to communicate with all parts of the earth. What is the minimum distance in km from the centre of the earth that these satellites should be located? (Assume the radius of the earth is 6 400 km.)  (A) 6 400$$\sqrt2$$ (B) 6 400$$\sqrt 3$$ (C) 12 800 (D) 19 200 Question 23. Which correlation coefficient, r, shows the strongest relationship between two variables?  (A) -0.9 (B) -0.3 (C) 0.2 (D) 0.8 Question 24. Which one of the points, P(-3, -2), Q(-2, 0.5), R(0, 5.5) or S(3, 3), lies exactly on the least squares line of best fit for the data?  (A) P (B) Q (C) R (D) S Question 25. In a normal distribution, what percentage of the population have z-scores greater than zero?  (A) 50% (B) 68% (C) 75% (D) 100% Question 26. The volume of the contents of a soft drink can is normally distributed with a mean of 356 mL and a standard deviation of 1.4 mL. Calculate the z-score for a can containing 354 mL.  (A) -1.6 (B) -1.43 (C) 1.43 (D) 1.6 Question 27. Quiz results for thirty students are recorded in the frequency table shown below. Determine the mean score for this quiz.  (A) 2 (B) 2.3 (C) 2.5 (D) 3 Question 28. An insurance company analyzed its claims per policy as summarized in the table below. What is the expected amount of money that will be paid out per policy in a year?  (A)$45 (B) $60 (C)$105 (D) $120 Question 29. On a standardized achievement test, the mean score is 74.6 with a standard deviation of 11.3. If a random sample of 81 tests is selected, determine a 90% confidence interval for the mean score of these tests.  (A) 67.1 < µ < 82.1 (B) 71.7 < µ <77.5 (C) 72.1 < µ < 77.1 (D) 72.5 < µ < 76.7 Question 30. What is the probability that a three-digit telephone extension number has one or more repeated digits (assuming no digit is more likely than another to be used)?  (A) 0.2 (B) 0.28 (C) 0.3 (D) 0.33 Question 31. How many different paths are there from P to Q on a 4 x 4 square if only moves to the right and downward are allowed?  (A) 16 (B) 32 (C) 64 (D) 70 Question 32. A cylindrical tank with no top has radius 50 cm and height 200 cm. It is filled with water to a height of 100 cm. If a solid cube of metal 30 cm on each edge is lowered to the bottom of the cylinder, how much will the height of the water rise?  (A) 0.34 cm (B) 1.72 cm (C) 3.44 cm (D) 13.75 cm Question 33. AB is a chord of a circle with centre O. Point P is located on chord AB such that AP = 21, BP = 9 and OP = 10. Determine the radius of the circle.  (A) 11 (B) 15 (C) 17 (D) 19 Question 34. Given , which of the following matrix operations is possible?  (A) PQ (B) QP (C) P + Q (D) Q + P Question 35. A sports store had the following sales of hockey equipment for the months shown. If the profit on shoulder pads is$48 and on shin pads is $36, which of the following column matrices represents the profits for these months?  (A) (B) (C) (D) Question 36. Three stores, A, B and C, were surveyed to determine costs of the same weight and brand of bread, flour and sugar. The amounts to be purchased and the prices charged are shown in the matrices below. If all three items are purchased at the same store, what is the lowest total price?  (A)$11.40 (B) $11.58 (C)$17.74 (D) $18.00 Question 37. Solve for y:  (A) -4 (B) -1 (C) $$1\over 3$$ (D) 4 Question 38. An airline offers flights between Vancouver, Calgary, Edmonton and Regina. The flight matrix below shows the connections between the cities. How many ways can a person travel from Vancouver to Regina with either one or two stopovers?  (A) 2 (B) 4 (C) 5 (D) 6 Question 39. Solve for x :  (A) -6 (B) 6 (C) $$\pm$$6 (D) $$\pm$$18 Question 40. Which formula could be used to calculate the amount in cell F11?  (A) 0.07 * F9 (B) 1.07 * F9 (C) 0.07 * (F9 + F10) (D) 1.07 * (F9 + F10) Question 41. What is the rate of depreciation for a sports car in the first year?  (A) 40% (B) 45% (C) 50% (D) 55% Question 42. To apply for a mortgage, a couple must calculate their combined annual income. Details of their earnings are summarized below. What is their combined annual income?  (A)$47 025 (B) $50 775 (C)$67 275 (D) $83 775 Question 43. Finance companies offer discount loans where part of the loan is used to pay the total interest before the funds are advanced. James obtains a discount loan for three years at a rate of 10.25% compounded quarterly. At the end of the three-year period, he must pay back$25 000, which includes both the principal and interest. How much does James actually receive at the start of the three-year period?

 (A) $1 692.10 (B)$18 453.42 (C) $22 437.50 (D)$23 172.57

Question 44.

A couple arranges a $100 000 mortgage at 8% per annum compounded semi-annually. What is the total amount paid if the mortgage is amortized, with monthly payments, over 20 years? (Answer to the nearest one hundred dollars.)  (A)$107 000 (B) $196 600 (C)$198 800 (D) \$200 000

Question 45.

What is the amplitude for the function y = -2sin3x ?

 (A) -2 (B) 2 (C) $$2\pi \over 3$$ (D) 2$$\pi$$