# Full-Length TASC Math Practice Test-Answers and Explanations

Did you take the TASC Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## TASC Mathematics Practice Test Answers and Explanations

1- **Choice B is correct**

\(5^5=5×5×5×5×5=3,125\)

2- **Choice B is correct**

The area of the floor is: \(9 \)cm\( × 16\) cm \(= 144\) cm\(^2 \)

The number of tiles needed \(= 144 ÷ 12 = 12\)

3- **Choice A is correct**

average \(= \frac{sum of terms }{number of terms}=\frac{14+ 11+5+19+24+17}{6} = \frac{90}{6} = 15\)

4- **Choice C is correct**

Use Pythagorean Theorem: \(a^2+b^2=c^2 \)

\(6^2 + 8^2 = c^2 ⇒ 36+64=c^2 ⇒ 100=c^2⇒c=10\)

5- **Choice C is correct**

Let \(x\) be the number. Write the equation and solve for \(x. (36 – x) ÷ x = 5\)

Multiply both sides by \(x. (36 – x) = 5x\), then add x both sides. \(36 = 6x\), now divide both sides by 6.

\(x = 6\)

6- **Choice D is correct**

Use percent formula: part \(=\frac{ percent}{100}×\)whole

\(75=\frac{percent}{100}×50 ⇒ 75=\frac{percent ×50}{100} ⇒ 75=\frac{percent ×5}{10}\), multiply both sides by \(10. 750=\)percent \(×5\), divide both sides by \(5. 150=\)percent

7- **Choice B is correct**

Use this formula: Percent of Change \(\frac{New Value-Old Value}{Old Value}×100\%\)

\(\frac{20000-25000}{25000} ×100\%=20\%\) and \(\frac{16000-20000}{20000}×100\%=20\%\)

8- **Choice A is correct**

Let \(x\) be the number of years. Therefore, $1,800 per year equals \(1800x\).

starting from $21,000 annual salary means you should add that amount to \(1800x\). Income more than that is: \(I > 1800x + 21000\)

9- **Choice C is correct**

Let \(x\) be the original price.

If the price of the sofa is decreased by \(12\%\) to $528, then: \(88\%\) of \(x=528 ⇒ 0.88x=528 ⇒ x=528÷0.88=600\)

10- **Choice C is correct**

The sum of supplement angles is 180. Let \(x\) be that angle. Therefore, \(x + 5x = 180 \)

\(6x = 180\), divide both sides by \(6: x = 30\)

11- **Choice C is correct**

Write the equation and solve for \(B\):

\(0.80 A = 0.40 B\), divide both sides by 0.40, then:

\(\frac{0.80}{0.40} A=B\), therefore: \(B=2A\), and \(B\) is 2 times of \(A\) or it’s \(200\%\) of \(A\).

12- **Choice B is correct**

The weight of 9.8 meters of this rope is: \(9.8×450 \)g\(=4,410\) g

\(1\) kg \(= 1,000\) g, therefore, \(4,410\) g\(÷1000=4.41\) kg

13- **Choice D is correct**

The average speed of john is: \(120÷5=24\) km

The average speed of Alice is: \(168÷6=28\) km

Write the ratio and simplify. \(24 : 28 ⇒ 6 : 7\)

14- **Choice C is correct**

\($14×10=$140\), Petrol use: \(10×3=30\) liters

Petrol cost: \(30×$2=$60\)

Money earned: \($140-$60=$80\)

15- **Choice D is correct**

Let \(x\) be the original price.

If the price of a laptop is decreased by \(15\%\) to $476, then:

\(85\%\) of \(x=476 ⇒ 0.85x=476 ⇒ x=476÷0.85=560\)

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16- **Choice B is correct**

The percent of girls playing tennis is: \(60 \% × 20 \% = 0.60 × 0.20 = 0.12 = 12 \%\)

17- **Choice A is correct**

The area of the circle is less than \(16 π\). Use the formula of areas of circles.

Area \(= πr^2 ⇒ 81 π> πr^2⇒ 81 > r^2⇒ r < 9\)

The radius of the circle is less than 9. Let’s put 9 for the radius. Now, use the circumference formula:

Circumference \(=2πr=2π (9)=18π\)

Since the radius of the circle is less than 9. Then, the circumference of the circle must be less than \(18 π\). Only choice A is less than \(18 π\).

18- **Choice D is correct**

\(3.5\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution. Then: \(3.5\%\) of \(x=49\) ml \(⇒ 0.035 x=49 ⇒ x=49÷0.035=1400\)

19- **Choice A is correct**

\(\begin{cases}x-3y=9\\3x+y=7\end{cases}→\)Multiply the button equation by 3 then,

\(\begin{cases}x-3y=9\\9x+3y=21\end{cases} → \)Add two equations

\(10x=30→x=3\) , plug in the value of \(y\) into the first equation

\(x-3y=9→3-3y=9→-3y=9-3 → -3y=6 →y=-2\)

20- **Choice C is correct**

If the length of the box is 24, then the width of the box is one-fourth of it, 6, and the height of the box is 2 (one-third of the width). The volume of the box is: \(V = lwh\) = \((24) (6) (2) = 288\)

21- **Choice B is correct**

Use the formula for Percent of Change \(\frac{New Value-Old Value}{Old Value}×100\%\)

\(\frac{24-30}{30}×100\%= –20\%\) (Negative sign here means that the new price is less than the old price).

22- **Choice C is correct**

To find the number of possible outfit combinations, multiply the number of options for each factor: \(5×2×6=60\)

23- **Choice D is correct**

Use simple interest formula: I=prt (I = interest,p = principal,r = rate,t = time)

\(I=(14,000)(0.032)(5)=2,240\)

24- **Choice B is correct**

The area of the trapezoid is:

Area\(=\frac{1}{2}h(b_1+b_2 )=\frac{1}{2}(x)(9+7)=96→8x=96→x=12\) \(y=\sqrt{9^2+12^2}=\sqrt{81+144}=\sqrt{225}=15\)

25- **Choice B is correct**

Use distance formula: Distance \(=\) Rate \(×\) time ⇒ \(486 = 60 × \)T, divide both sides by \(60. \frac{486 }{ 60} =\) T \(⇒\) T \(= 8.1\) hours.

Change hours to minutes for the decimal part. 0.1 hours \(= 0.1 × 60 = 6 \)minutes.

26- **Choice B is correct**

If the score of Mia was 50, therefore the score of Ava is 25. Since the score of Emma was half as that of Ava, therefore, the score of Emma is 12.5.

27- **Choice B is correct**

The equation of a line is in the form of \(y=mx+b\), where m is the slope of the line and b is the y-intercept of the line.

Two points \((5,2)\) and \((3,6)\) are on line A. Therefore, the slope of the line A is:

slope of line A\(=\frac{y_2- y_1}{x_2 – x_1 } = \frac{6-2}{3-5}=\frac{4}{-2}=-2\)

The slope of line A is \(-2\). Thus, the formula of the line A is:

\(y=mx+b=-2x+b\), choose a point and plug in the values of \(x\) and \(y\) in the equation to solve for b. Let’s choose point \((5, 2)\). Then:

\(y=-2x+b→2=-2(5)+b→b=2+10=12 \)

The equation of line A is: \(y=-2x+12 \)

Now, let’s review the choices provided:

A. \((-1,2) y=-2x+12→2=2+12=14\) This is not true.

B. \((2,8) y=-2x+12→8=-4+12=8\) This is true.

C. \((3,5) y=-2x+12→5=-6+12=6\) This is not true.

D. \((-2,-4) y=-2x+12→-4=4+12=16\) This is not true!

28- **Choice A is correct**

Formula for the Surface area of a cylinder is: \(SA=2πr^2+2πrh→144π=2πr^2+2πr(21)→r^2+21r-72=0 \)

\((r+24)(r-3)=0→r=3\) or \(r= -24\) (unacceptable)

29- **Choice A is correct**

Let \(x\) be the number. Write the equation and solve for \(x\).

\(\frac{1}{4} ×20= \frac{2}{3} × x ⇒ \frac{1×20}{4}= \frac{2x}{3}\) , use cross multiplication to solve for \(x\).

\(20×3=2x×4 ⇒60=8x ⇒ x=7.5\)

30- **Choice C is correct**

To find the discount, multiply the number by (\(100\% –\) rate of discount).

Therefore, for the first discount we get: \((D) (100\% – 25\%) = (D) (0.75) = 0.75 D\), For increase of \(15 \%: (0.75 D) (100\% + 15\%) = (0.75 D) (1.15) = 0.8625 D = 86.25\%\) of \(D\)

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31- **Choices C is correct**

Some of prime numbers are: \(2, 3, 5, 7, 11, 13\)

Find the product of two consecutive prime numbers:

\(2 × 3 = 6\) (not in the options) \(3 × 5 = 15\) (not in the options)

\(5 × 7 = 35\) (bingo!) \(7 × 11 = 77\) (not in the options)

32- **Choice A is correct**

Let \(x\) be the smallest number. Then, these are the numbers:

\(x, x+1, x+2, x+3, x+4,x+5 \)

average=\(\frac{sum of terms }{number of terms} ⇒ \)

\(16.5=\frac{x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)}{6}⇒16.5=\frac{6x+15}{6} ⇒ 99=6x+15 ⇒ 84=6x ⇒ x=14\)

33- **Choice B is correct**

Let’s compare each fraction:

\(\frac{1}{4}<\frac{2}{5}< \frac{3}{7}<\frac{5}{8}\) Only choice C provides the right order.

34- **Choice D is correct**

Use the information provided in the question to draw the shape.

Use Pythagorean Theorem: \(a^2+ b^2=c^2 \)

\(50^2+ 120^2=c^2 ⇒ 2500+14400= c^2 ⇒ 16900=c^2 ⇒ c=130\)

35- **Choice D is correct**

The ratio of boys to girls is \(2:5\). Therefore, there are 2 boys out of 7 students.

To find the answer, first, divide the total number of students by 9, then multiply the result by 2. \(49÷7=7 ⇒ 7×2=14 \)

There are 14 boys and \(35 (49 – 14)\) girls. So, 21 more boys should be enrolled to make the ratio \(1:1\)

36- **Choice A is correct**

Add the first 5 numbers. \(30 + 35 + 40 + 35 + 50 = 190\)

To find the distance traveled in the next 5 hours, multiply the average by the number of hours. Distance \(=\) Average \(×\) Rate \(= 45 × 5 = 225\)

Add both numbers. \(190 + 225 = 415\)

37- **Choice C is correct**

The question is this: 600 is what percent of 750?

Use percent formula:

part\(=\frac{percent}{100}×\)whole

\(600=\frac{percent}{100}×750 ⇒ 600= \frac{percent ×750}{100} ⇒ 60000 =\)percent \(×75 ⇒\) percent\(=\frac{60000}{75}=80\)

600 is \(80 \%\) of 750. Therefore, the discount is: \(100\% –80\%=20\%\)

38- **Choice D is correct**

If 24 balls are removed from the bag at random, there will be one ball in the bag.

The probability of choosing a red ball is 1 out of 25. Therefore, the probability of not choosing a red ball is 24 out of 25 and the probability of having not a red ball after removing 24 balls is the same.

39- **Choice B is correct**

average \(=\frac{sum of terms }{number of terms}\)

The sum of the weight of all girls is: \(25×48=1200\) kg

The sum of the weight of all boys is: \(30×60=1800\) kg

The sum of the weight of all students is: \(1200+1800=3000\) kg

average\(=\frac{3000 }{55}=54.54\)

40- **Choice C is correct**

Write the numbers in order:

\(5, 7, 11, 13, 15, 17, 21\)

Since we have 7 numbers (7 is odd), then the median is the number in the middle, which is 13.

41- **The answer is 8**

average\(=\frac{sum of terms }{number of terms} ⇒ 15=\frac{12+17+23+x}{4}⇒60=52+x⇒x=8\)

42- **The answer is 6**

Use PEMDAS (order of operation):

\(-12-3×(–4)+[4-9×(-2)]÷2-5=-12+12+[4+18]÷2-5=[22]÷2-5=11-5=6\)

43- **The answer is 5**

\(-4x+7=19→-4x=19-7=12→x=\frac{12}{4}=3\)

Then; \(3x-4=3 (3)-4=9-4=5\)

44- **The answer is 72**

First, draw an isosceles triangle. Remember that the two sides of the triangle are equal.

Let put a for the legs. Then:

a\(=12⇒\) area of the triangle is \(=\frac{1}{2} (12×12)=\frac{144}{2}=72\)

45- **The answer is 13.5**

The rate of construction company\(=\frac{15 cm}{1 min}=15 \frac{cm}{min}\)

Height of the wall after 60 minutes \(= \frac{15 cm}{1 min}×60\) min\(=900\) cm

Let \(x\) be the height of wall, then \(\frac{2}{3} x=900 \)cm\(→x=\frac{3×900}{2}→x=1350\) cm\(=13.5\) m

46- **The answer is 138**

The question is this: 1.83 is what percent of 1.32?

Use percent formula: part \(=\frac{ percent}{100} ×\) whole

\(1.83 = \frac{percent}{100} × 1.32 ⇒ 1.83 = \frac{percent ×1.32}{100} ⇒183 =\) percent \(×1.32 ⇒\) percent \(= \frac{183}{1.32} = 138\)

47- **The answer is 60**

The relationship among all sides of a special right triangle

\(30^\circ-60^\circ- 90^\circ\) is provided in this triangle:

In this triangle, the opposite side of the 30\(^\circ\) angle is half of the hypotenuse.

Draw the shape of this question.

The ladder is the hypotenuse. Therefore, the ladder is 60 feet.

48- **The answer is 3**

Let x be the length of an edge of a cube, then the volume of a cube is: \(V=x^3\)

The surface area of a cube is: \(SA=6x^2\)

The volume of cube A is \(\frac{1}{2}\) of its surface area. Then:\( x^3=\frac{6x^2}{2}→x^3=3x^2\), divide both side of the equation by \(x^2\). Then: \(\frac{x^3}{x^2} =\frac{3x^2}{x^2} →x=3\)

49- **The answer is 147**

The perimeter of the trapezoid is 51.

Therefore, the missing side (height) is \(= 51 – 16 – 12 – 9 = 14 \)

Area of a trapezoid: A \(= \frac{1}{2} h (b_1 + b_2) = \frac{1}{2} (14) (9 + 12) = 147\)

50- **The answer is 6**

The input value is 3. Then: \(x=3, f(x)=-x^2+5x→ f(3)=-3^2+5(3)=-9+15=6\)

51- **The answer is -12**

Since N\(=3\), substitute 3 for N in the equation \(\frac{x+2}{4}=-\)N, which gives \(\frac{x+2}{4}=-3\). Multiplying both sides of \(\frac{x+2}{4}=-3\) by 4 gives \(x+2=-12\) and then subtract 2 from both sides of

\(x+2-2=-12-2\) then, \(x=-12\).

52- **The answer is \(\frac{1}{3}\) or 0.33**

Write the ratio of 6a to \(5b. \frac{6a}{5b}=\frac{2}{5}\)

Use cross multiplication and then simplify.

\(6a×5=5b×2→30a=10b→a=\frac{10b}{30}=\frac{b}{3}\)

Now, find the ratio of a to b. \(\frac{a}{b}=\frac{\frac{b}{3}}{b}→\frac{b}{3}÷b=\frac{b}{3}×\frac{1}{b}=\frac{b}{3b}=\frac{1}{3}=0.33\)

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