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application of Mathematics grade 12 level 4

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; Subject: ; Class: ; with 45 questions; test in 60 minutes; update 23/07/2018
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Question 1.

A hive contains 300 bees. If the population of bees in the hive doubles every week, and no bees die, how many bees are in the hive after five weeks?

(A)

1 500

(B)

3 000

(C)

4 800

(D)

9 600

Question 2.

The volume, in litres, of air in the lungs at time t seconds can be approximated by the function V(t) = -0.37sin(\(\pi t\over 2\)) + 0.45. Determine the number of litres of air in the lungs at time 2.5 seconds.

(A)

0.20

(B)

0.45

(C)

0.64

(D)

0.71

Question 3.

A set of four nested cube-shaped boxes is to be constructed. The boxes are open at one end so that a smaller box fits inside a larger box. The largest box has a side of length 10 cm. Each successive box has a side of length 85% of the previous one. What is the volume of the smallest box? (Accurate to the nearest cm3.)

(A)

232 

(B)

377

(C)

550 

(D)

614

Question 4.

The Wheel of Theodorus is constructed as follows:

• T1 is an isosceles right triangle with legs of length one unit

• T2 is a right triangle constructed with one leg the hypotenuse of T2, and the other leg of length one unit

• The process is continued as shown in the diagram

What is the length of the hypotenuse of T5?

(A)

2

(B)

3.24

(C)

\(\sqrt5\)

(D)

\(\sqrt6\)

Question 5.

The diagram below shows the first two iterations in the generation of a fractal. Two circles are added to the original circle and then two circles are added to these new circles and so on. The radius of the first circle is 8 cm. Each successive circle has a radius that is one-half the radius of the previous circle.

What is the area, in cm2 , enclosed by all circles in Iteration 3?

(A)

112\(\pi\)

(B)

120\(\pi\)

(C)

124\(\pi\)

(D)

126\(\pi\)

Question 6.

Using the graph of y = asin(bx + c) + d from the graphing calculator, determine b.

(A)

1

(B)

1.5

(C)

2

(D)

\(\pi\)

Question 7.

A rubber ball is dropped on a hard surface from a height of 6 m. It makes a sequence of bounces, each one 75% as high as the preceding one. After how many bounces does the ball rebound to a height of less than 0.5 m?

(A)

6

(B)

7

(C)

8

(D)

9

Question 8.

Each face of this three-dimensional piece is to be painted a different colour. How many colours are required?

(A)

6

(B)

8

(C)

10

(D)

12

Question 9.

A 90∞ sector is removed from a circular sheet of metal with radius 8 cm. A cone is formed from the remaining sector by joining edges OP and OQ, as shown in the diagram.

Determine the height, in cm, of this cone.

(A)

\(\sqrt{28}\)

(B)

\(\sqrt{48}\)

(C)

8

(D)

10

Question 10.

Which of the following is a vector quantity?

(A)

time

(B)

mass

(C)

force

(D)

volume

Question 11.

If a vector, \(\overrightarrow v\),is multiplied by a scalar, k, what must be true about k if \(\overrightarrow{kv}\) is shorter than \(\overrightarrow v\), but in the same direction?

(A)

k is positive and less than 1

(B)

k is positive and greater than 1

(C)

k is negative and less than -1

(D)

k is negative and greater than -1

Question 12.

A river flows from west to east at a rate of 4.75 km/h. A kayaker who can paddle at a rate of 8.25 km/h in still water heads due north across the current. Determine her rate and bearing.

(A)

7.48 km/h, 29.9º

(B)

7.48 km/h, 60.1º

(C)

9.52 km/h, 29.9º

(D)

9.52 km/h, 60.1º

Question 13.

A helicopter company offers transportation for skiers to three mountain glaciers.

• From Glacier A, the flight is 43 km to reach Glacier B.

• From Glacier B, the flight is 28 km to reach Glacier C.

\(\measuredangle\)ABC is 80º.

How far is it directly from Glacier C to Glacier A? (Give your answer to the nearest km.)

(A)

33

(B)

47

(C)

51

(D)

55

Question 14.

If the probability that an event will occur is p, what is the probability that p will not occur?

(A)

-p

(B)

1 - p

(C)

p - 1

(D)

-(p +  1)

Question 15.

Licence plates are formed using 6 characters. Letters are used for the first 3 characters except for I, L, O, Q and Z, while the other 3 characters are numbers. How many different licence plates are possible?

(A)

6 751 269 

(B)

8 000 000

(C)

9 261 000 

(D)

14 196 000

Question 16.

A survey of 200 male students between the ages of 10 and 15 determined that

• 65 played soccer

• 42 played basebal

l • 26 played both soccer and baseball

How many played neither soccer nor baseball?

(A)

67 

(B)

93

(C)

119 

(D)

135

Question 17.

The lengths of the nails in a manufacturing process are normally distributed with a mean of 45 mm and a standard deviation of 1.5 mm. What is the probability that a nail, selected at random, will be longer than 47 mm?

(A)

0.09

(B)

0.16

(C)

0.84 

(D)

0.91

Question 18.

For the triangular letter arrangement given below, start at the top and work diagonally left or right towards the bottom. How many different paths will spell EUCLID?

(A)

31

(B)

32

(C)

63

(D)

64

Question 19.

A young boy and his mom are playing a game, each taking turns tossing a tetrahedral (4-sided) die with sides numbered 1, 2, 3 and 4. The boy wins if he tosses a 1, 2 or 3. The mom wins if she tosses a 4. The boy tosses first, and they keep tossing until one of them wins. What is the probability that the mom will win on her second turn?

(A)

\(1\over 4\)

(B)

\(1\over 16\)

(C)

\(3\over 16\)

(D)

\(3\over 256\)

Question 20.

A delivery truck driver has six stops to make on his route before returning to his starting point. The order of his deliveries is randomly selected. What is the probability that the route selected will be the shortest possible route?

(A)

\(1\over 360\)

(B)

\(1\over 180\)

(C)

\(1\over 36\)

(D)

\(1\over 18\)

Question 21.

A theatre company knows that on average 5% of the people who buy tickets do not show up. Consequently, it regularly oversells tickets to its 200-seat theatre by six seats. What is the probability that more ticket holders show up than there are seats available?

(A)

less than 5%

(B)

5% to 7%

(C)

7% to 9%

(D)

greater than 9%

Question 22.

Which of the following matrices can be subtracted from matrix A2×2?

(A)

M2×2

(B)

M2×3

(C)

M3×2

(D)

M3×3

Question 23.

For what value of k will the following equation be true?

(A)

-3

(B)

-2

(C)

2

(D)

3

Question 24.

P, Q, and R represent three car rental locations. The diagram below shows the probabilities associated with rentals and returns to and from each location.

Which of the following is a transition matrix for this diagram?

(A)

(B)

(C)

(D)

Question 25.

Determine an expression for y for the following matrix multiplication.

(A)

-a

(B)

3a

(C)

-b - 2

(D)

3b + 1

Question 26.

A computer room has 219 terminals. Initially, all terminals are working. Each day there is a 3% chance that a working terminal will break down and a 70% chance that a broken terminal will be repaired. In the long term, how many computers in the room should be working?

(A)

199

(B)

210

(C)

212

(D)

219

Question 27.

Jennifer bought shares of Broax at $50.85 for each share. A year later each share was worth $5.18. What was the percent loss on the original investment over this one-year period?

(A)

10.2%

(B)

11.3%

(C)

88.7% 

(D)

89.8%

Question 28.

The spreadsheet below shows the beginning of the amortization schedule for a loan of $9 500 at an interest rate of 6% per annum compounded monthly. The loan is to be paid off in 3 years with 36 equal monthly payments of $289.01.

Determine the value that should appear in cell F11.

(A)

9 210.99

(B)

9 258.49

(C)

9 363.54

(D)

9 452.50

Question 29.

Danielle wants to purchase a boat valued at $26 000 by making monthly payments over a three-year period with no down payment. If the interest rate is 4% per year, compounded monthly, determine her monthly payment.

(A)

 $751.11

(B)

$767.62

(C)

$775.38 

(D)

$814.14

Question 30.

Determine the vertical shift of the graph of y = 2sin3(x + 4)  + 5with respect to the graph y = sinx.

(A)

2

(B)

3

(C)

4

(D)

5

Question 31.

Determine the phase shift (horizontal shift) of the graph of y = sin(3x + \(\pi \over 2\)) + 4.

(A)

\(\pi \over 2\) to the left

(B)

\(\pi \over 2\) to the right

(C)

\(\pi \over 6\) to the left

(D)

\(\pi \over 6\) to the right

Question 32.

According to statistical data, the rodent population, r, in a certain region varies sinusoidally and can be modelled by the function r(t) = 300sin(\(\pi t\over 2\)) + 1 200, where t is the number of years since 1990. Use this function to predict the maximum rodent population in this region.

(A)

1 200

(B)

1 350

(C)

1 500 

(D)

1 800

Question 33.

The following equation provides an estimate of the average monthly temperature in a northern village.

T = 22.5sin(0.53M - 1.9) - 12

If T is the temperature (∞C) and M is the number of the month of the year (January is 1, February is 2, …), what is the average monthly temperature for June in degrees Celsius?

(A)

3.1

(B)

3.3

(C)

9.6

(D)

9.9

Question 34.

The height of a bicycle pedal above the ground can be modelled by the sinusoidal function graphed below.

Determine the amplitude of this function.

(A)

11 cm

(B)

19 cm

(C)

22 cm

(D)

30 cm

Question 35.

A fractal is created as shown below. Each new set of sides, at right angles to the previous side, is one-half the length of the previous side. Determine the length of the smallest side created in the 8th iteration.

(A)

\(3\over 16\) cm

(B)

\(3\over 32\) cm

(C)

\(3\over 64\) cm

(D)

\(3\over 128\) cm

Question 36.

The diagram below illustrates the fractal pattern known as the Sierpinski carpet.

How many shaded squares are in iteration 4?

(A)

29 = 512

(B)

36 = 729

(C)

4= 1024

(D)

84 = 4096

Question 37.

The diagram below shows the first three patterns of a fractal consisting of spheres.

If this pattern is continued forever, what is the total surface area of all the spheres in the fractal (in cm2 )?

(A)

\(1024\pi \over 3\) \(\approx\) 1072

(B)

384\(\pi \approx\) 1206

(C)

512 \(\pi \approx\) 1068

(D)

\({16384\pi \over 21} \approx\) 2451

Question 38.

A contractor is ordering concrete for the foundation footing of a house. The foundation footing is 40 cm wide and 25 cm high.

If 70 metres of footing are required and concrete costs $85.00/m3, determine the approximate cost of the concrete for the foundation footing

(A)

$250

(B)

$550

(C)

$600 

(D)

$825

Question 39.

Circular disks with a diameter of 6 cm are punched from a sheet of metal measuring 78 cm x 120 cm, as shown in the diagram. Determine the maximum number of disks that can be punched from this sheet.

(A)

260 

(B)

331

(C)

496

(D)

1 040

Question 40.

Determine the cost of plastering the walls and ceiling of a banquet room 12 m long, 10 m wide and 6 m high if the cost is $9.75 per square metre. Subtract 75 m2 for doors and windows.

(A)

$1 842.75

(B)

$3 012.75

(C)

$3 744.00

(D)

$4 182.75

Question 41.

A skateboard ramp is set up as shown in the diagram below.

Determine the area of the shaded part of the ramp.

(A)

1.5 m2

(B)

2.0 m2

(C)

2.5 m2

(D)

3.1 m2

Question 42.

If 250 mL of water is poured into a cone with radius 10 cm and height 30 cm, what is the height, h, of the water in the cone?

(A)

4.30 cm

(B)

8.48 cm

(C)

9.15 cm

(D)

12.90 cm

Question 43.

Which of the following is a vector quantity?

(A)

a mass of 300 kg

(B)

a distance of 15 km

(C)

 a speed of 75 km/h

(D)

a force of 12 N downward

Question 44.

Which of the following numbers cannot describe the probability of an event?

(A)

-\(1\over 2\)

(B)

0

(C)

\(1\over 2\)

(D)

1

Question 45.

In an experiment two fair dice are rolled. Which of the following events are mutually exclusive?

(A)

rolling doubles with a sum of 3

(B)

rolling doubles with a sum of 4

(C)

rolling doubles with a sum of 6

(D)

rolling doubles with a sum of 8

Question 1    Question 2    Question 3    Question 4    Question 5    Question 6    Question 7    Question 8    Question 9    Question 10    Question 11    Question 12    Question 13    Question 14    Question 15    Question 16    Question 17    Question 18    Question 19    Question 20    Question 21    Question 22    Question 23    Question 24    Question 25    Question 26    Question 27    Question 28    Question 29    Question 30    Question 31    Question 32    Question 33    Question 34    Question 35    Question 36    Question 37    Question 38    Question 39    Question 40    Question 41    Question 42    Question 43    Question 44    Question 45   
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