Mathematics Test Act 1874fpre Answers

Choice C

$$\frac{x}{5}=\frac{6}{3} \\$$ $$ \Rightarrow x= 10$$

Choice K

$$p=\frac{1}{35-3}=\frac{1}{32}$$

Choice B

$$2x+7=15 \\$$ $$ \Rightarrow x= 4$$

Choice J

$$f(3)=5(3)^2-7(4\times 3+3)=-60$$

Choice D

$$p = \frac{8}{5+7+8}=\frac{8}{20}=\frac{2}{5}$$

Choice H

$$40+2n=35+3n \\ $$ $$\Rightarrow n=5$$

Choice D

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Choice G

$$\frac{8x-3}{x}=\frac{8\times \frac{1}{2}-3}{\frac{1}{2}}=2$$

Choice D

$$x=\frac{3+1}{2}=2 \\$$ $$ y=\frac{8+(-4)}{2}=2$$

Choice G

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Choice D

$$slope=\frac{-5-1}{2-(-2)}=-\frac{3}{2}$$

Choice H

$$(x-30)\times 17 = 221 \\$$ $$ \Rightarrow x = 43$$

Choice B

$$x=\frac{12}{8}=\frac{3}{2} \\$$ $$ y=\frac{22-10}{2}=6 \\ $$ $$\Rightarrow x +y=7\frac{1}{2}$$

Choice H

Median = Average = 420 ÷ 5 = 84

→ sum of the 4 scores that are NOT the median = sum - median = 420 - 84 = 336

Choice D

$$||-8+4|-|3-9||=|4-6|=2$$

Choice K

$$x^{\frac{2}{3}}=\sqrt[3]{x^2}$$

Choice B

By rearranging the equation into slope intercept form, we have:

y =(4/7)x-(5/7)

Therefore the slope is 4/7.

Choice K

The sum of an odd integer and an even integer will always be an odd integer. For example, 1 + 2 = 3

Choice B

$$AB=\sqrt{32^2+24^2}=40 \\$$ $$\Rightarrow \frac{AB}{2}=20$$

Choice K

It is not given that the triangle is a right triangle, so you can't use the Pythagorean theorem. The length of DF ranges from, not inclusively, (√30-3) to (√30+3).

Choice B

$$Area = (8\times 10 + 8\times15)\times2-60=340$$

Choice F

$$[w+(w+5)]\times 2=40 \\$$ $$ \Rightarrow w=7.5$$

Choice C

$$8\% \cdot60=\frac{1}{5}x \\$$ $$ \Rightarrow x= 24$$

Choice J

$$14x\geq 175 \\$$ $$ \Rightarrow x \geq 12.5 \\ $$ $$\Rightarrow x_{min}=13$$

Choice A

$$\frac{4.8\times10^{-7}}{1.6\times10^{-11}}=3.0\times 10^{-7+11}=3.0\times 10^{4}$$

Choice H

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Vector CA which points from C to A has components given as <3, 4>. Thus, the vector that points from C to B = -CA = <-3, -4>. Hence, the coordinates of point B is (-4,-2).

Choice A

$$x^3-64=(x-4)(x^2+4x+16)$$

Choice H

$$\frac{4\times90-80+96}{4}= 94$$

Choice E

$$a^2=(-2.5)^2=6.25$$

Choice J

There is 7/9 of the original pizza remaining. Thus, each brother will get (1/3)(7/9) = 7/27 of the original pizza.

Choice E

$$30030=30\times1001=(2\times3\times5)\times(7\times11\times13)$$

Choice G

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Area of the scale drawing = (28 + 40) · 16 / 2 = 544 square inches

Choice E

$$Length \ of green \ side=\sqrt{16^2+12^2}=20 \\$$ $$ \Rightarrow Perimeter = 20+28+16+40=104 \ inches = 104\times 1.5 \ feet = 156 \ feet$$

Choice H

$$\frac{40}{28}=142\frac{6}{7}\%$$

Choice C

The area of the walkway can be arrived at by deducting the area of bigger rectangular (30' x 36') from that of the smaller rectangular (30' x 24'):

Area of walkway = 30' x 36' - 30' x 24' = 360 square feet

Choice J

There are 3 rooms so 3 fans will cost 3($52) = $156. There are 3 small and 1 large windows so the total cost of the curtains will be 3($39.50)+1($79) = $197.50. Therefore, the total cost is $156+$197.50 = $353.50.

Choice A

Because the chance of raining on a particular day is independent of the chance of rain on another day, the probability that it rains two consecutive days is (0.2)(0.2) =0.04

Choice K

An irrational number cannot be written as a ratio of two integers. (F) evaluates to √(1/4) = 1/2. (G) evaluates to √(4) = 2 = 2/1. (H) evaluates to 2 = 2/1. (J) evaluates to √(16) = 4 = 4/1. (K) cannot be simplified further and cannot be written as a ratio of two integers.

Choice D

$$\tan \theta = \frac{4}{10}=\frac{2}{5}$$

Choice K

$$|2x-8|=2 \\$$ $$ \Rightarrow 2x-8=2 \ or \ 2x-8=-2 \\$$ $$ \Rightarrow x=5 \ or\ x=3$$

Choice A

There are 12 students who have scores between 65-70 but 13 who have scores in that range plus the range of 71-80 (totalling a range of 65-80). Thus, there are 13-12 = 1 student with scores between 71-80.

Choice G

For this sound, I = 1000K, so d = 10log(1000K/K) = 10(3) = 30

Choice C

$$score = 1\times 80 \times 75 \% + 2 \times60 \times90 \%+3\times60 \times 25\%=213$$

Choice F

The graph is moved to the right for n units whenever x is substitute for x - n.

Choice A

The volume of the toy soldier can be found by deducting the volume of the rectangular container after the submerging of the toy soldier from that before:

Volume of toy soldier = 8 x 6 x 6.6 – 8 x 6 x 4 = 125

Choice J

Volume of the box = 18³

Volume of the cube = π(6)(12)²

--> Volume of packing material = 18³ - π(6)(12)²

Choice B

1 yard = 3 feet

1 feet = 12 inches

Area of the floor = 15 feet x 21 feet = 5 yard x 7 yard = 35 square yards

Choice G

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Choice B

The area is simply the area of the trapezoid spanned from x = 0 to 2 plus the area of the rectangle from x = 2 to 3 plus the area of the triangle from x = 3 to 5. Thus, the area = .5(4+3)(2)+(1)(3)+.5(3)(2) = 13

Choice J

x + y = 151

x=19+√y

--> x²-37x+210=0

--> (x-7)(x-30)=0

--> x = 7 or 30

If x = 7, √y<0, therefore x cannot be 7

--> x = 30, y = 121

-->y-x = 91

Choice C

The list of number is ordered from the highest to the lowest.

The median of the list is 25, therefore (30+X) / 2 = 25 –> X = 20

The mode of the list is 15, therefore Y = 15

The mean of the list = (41+35+30+20+15+15) / 6 = 26

Choice F

Substituting y for x², we have

s·x² + r·x – t = 0

For the equation to have two different solutions,

Δ = r² + 4st › 0

Choice A

$$a_{3}=13 \\ a_{4}=18 \\$$ $$ \Rightarrow d=a_{4}-a_{3}=5 \\$$ $$ \Rightarrow a_{50}= a_{4} +(50-4)\times d =248$$

Choice H

The Pythagorean trigonometric identity is expressed as:

sin² x + cos² x = 1

Therefore, y = sin² x + cos² x = 1

Choice E

The regular period of csc(x) is 2π. Thus, csc(4x) represents a compression of csc(x) towards the y axis by a factor of 4. Thus, the period will be 2π/4 = π/2

Choice H

For the toss of a penny, the probability of it landing with its head faceup is 50%. If it lands with its head up, the awarded value is 3 points. Otherwise the point is 0. Therefore the expected value of the point awarded for the toss of a penny is 3 x 50% + 0 x 50% = 3/2.

The same can also be said of the toss of a nickel and a dime. Therefore the expected value of the total points awarded is 3/2 +3/2 +3/2 = 9/2.

Choice B

We wish to find k for which k2-12 = k. Rearranging yields k2-k-12 = (k-4)(k+3) = 0. Thus, k = 4

Choice F

If i² = -1, then i^4 = (-1)² = 1. And notice that (i^4)k = i^4k = 1k = 1, k ∈ ℤ. In other words, i^4 = i^8 = i^12 = … = 1. Thus, we may conclude that 4|n (4 divides n; you do not need to know this notation).

Choice A

Recall that |sinθ| ≤ 1 for all θ ∈ R. Thus, we need only to find θ where sinθ = ±1. Going back to your unit circle, those values are θ = ±π/2

Choice K

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