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## Question Explanations For

##
*Practice Test 5 (Math No-Calculator)*

## 1.

The Correct Answer is (A) —
Since Ivan sells

*r*regular cones for $2 each, the revenue he makes from regular cones is 2*r*dollars. Similarly, the revenue he makes from waffle cones is 3*w*. You can add these together to get the total revenue, 2*r*+ 3*w*.## 2.

The Correct Answer is (C) —
If

If you chose (B) you may have missed that it lacks units (millions of people).

*P*(*x*) is the population of Japan in millions, then the minus 0.15*x*in the equation would mean the decrease in population over*x*years. Put simply, each year the population decreases by 0.15 million.If you chose (B) you may have missed that it lacks units (millions of people).

## 3.

The Correct Answer is (D) —
One cubic meter measures 1 m × 1 m × 1 m = 100 cm × 100 cm × 100 cm = 1,000,000 cubic centimeters.

If you chose (A), you may have calculated the number of centimeters in a meter. If you chose (C), you may have found the number of square centimeters in a square meter.

If you chose (A), you may have calculated the number of centimeters in a meter. If you chose (C), you may have found the number of square centimeters in a square meter.

## 4.

The Correct Answer is (A) —
Subtract the latter expression from the former, making sure to collect like-terms and simplify as you go:

(4

= -7

(4

*x*^{2}+3*x*-9)-(7*x*^{3}-12*x*^{2}-8*x*)= -7*x*^{3}+4*x*^{2}+12*x*^{2}+3*x*+8*x*-9= -7

*x*^{3}+16*x*^{2}+11*x*-9## 5.

The Correct Answer is (D) —
Raquel has 50 balloons now, plus 10 additional balloons for each pack she buys. If she buys

*p*packs, this means she will have 10*p*+ 50 balloons in total.## 6.

The Correct Answer is (D) —
Since the triangle in the diagram is right-angled, you can use the Pythagorean Theorem to find an expression for the length of the hypotenuse in terms of

If you chose (A), you may only have found the sum of AB and AC. If you chose (B), you may have found the value of BC

*x*:If you chose (A), you may only have found the sum of AB and AC. If you chose (B), you may have found the value of BC

^{2}, not BC. If you chose (C), you may have forgotten that the terms under the square root should be squared.## 7.

The Correct Answer is (A) —
The slope of the line in the question can be found by rearranging the equation to get

If you chose (D), you may have been tried to find a parallel line.

*y*= (*/*^{ – x}_{2}) –^{3}/_{2}, which is in the form*y*=*m**x*+*b*, where*m*is the slope. Therefore, this line has a slope of^{ –1}/_{2}. The slopes of perpendicular lines are negative reciprocals of each other, meaning that any line perpendicular to this one must have a slope of 2. Of the answer choices, only (A) has a slope of 2.If you chose (D), you may have been tried to find a parallel line.

## 9.

The Correct Answer is (D) —
You can find the solutions for

*x*in a rational expression by setting the numerator to 0 and solving for*x*. Here, you can factor the numerator to get (*x*+ 3)(*x*– 2) = 0, meaning that*x*= –3 or*x*= 2. However, you need to make sure your solutions are not extraneous by checking that they do not make the denominator zero. In this case,*x*= –3 makes the denominator equal to zero, so it isn’t a valid solution. Therefore,*x*is equal to 2.## 10.

The Correct Answer is (B) —
The book is printed at

If you chose (C) you may have found the dollar value of the book when it is printed.

*y*= 0, so at that time, its dollar value is^{1}/_{4}(0 – 4)^{2}+ 2 =^{1}/_{4}(16) + 2 = 6. The book will be worth the least when the squared term is equal to zero (since that term can never be negative), at which point the dollar value of the book will be 0 + 2 = 2. To find the difference, you can subtract the two values to get 6 – 2 = 4.If you chose (C) you may have found the dollar value of the book when it is printed.

## 11.

The Correct Answer is (B) —
Jake has 5 pieces of art already made, and makes 3 new pieces each week. If he works for

Since he will be finished in more than 14 weeks, he needs at least 15 weeks to complete his submission.

If you chose (C), you most likely calculated the number of weeks until he is one piece of art away from completion.

*w*weeks, he will have 5 + 3*w*pieces of art. Since he needs 48 pieces in total, you can set 5 + 3*w*equal to 48 and solve for*w*:Since he will be finished in more than 14 weeks, he needs at least 15 weeks to complete his submission.

If you chose (C), you most likely calculated the number of weeks until he is one piece of art away from completion.

## 12.

The Correct Answer is (C) —
You can find the

If you got (A), you calculated

*x*-intercepts of a quadratic function by setting*y*equal to zero. In this case, 0 =*x*^{2}+ 2*x*– 24 = (*x*– 4)(*x*+ 6), meaning that the*x*-intercepts occur when*x*= 4 and when*x*= –6. Since the point (–*a*, 0) is to the left of the*y*-axis in the diagram, you know that*a*= 6 and*b*= 4, so*a*–*b*= 6 – 4 = 2.If you got (A), you calculated

*b*–*a*. If you got (D), you may have calculated*b*–*a*and thought that*a*= –6.## 14.

The Correct Answer is (D) —
The quadratic formula tells you that an equation of the form 0 =

The only answer choice bigger than ~1 is (D).

*a**x*^{2}+*b**x*+*c*has no real solutions when*b*^{2}-4*ac*(the discriminant) is negative. You know that*b*= 3 and*a*= 2, so you can solve the inequality 0 >*b*^{2}– 4*a**c*for*c*:The only answer choice bigger than ~1 is (D).

## 16.

The Correct Answer is (2) —
The correct answer is 2. You can add 5 to both sides of the equation to get 15 = 15

*x*, then divide both sides by 15 to get*x*= 1. Therefore, 2*x*= 2.## 18.

The Correct Answer is (2) —
You can rearrange the second equation to get 2

Since the question states that

*y*= 12 –*x*^{2}. Plug this into the first equation and solve for*x*:Since the question states that

*x*is an integer, you know that*x*= 2. You can then find the value of*y*by substituting*x*= 2 into either equation: 6*y*– 4(2) = 16, meaning that*y*= 4. Therefore,*y*–*x*= 4 – 2 = 2.## 20.

The Correct Answer is (100) —
To find the specific heat capacity of iron, plug the relevant values into the equation

You know that the

*E*=*Sm*Δ*T*:You know that the

*S*value for iron is five times the specific heat capacity of mercury, so*S*_{mercury}= 1/5. To find the energy required to heat 10 grams of mercury, you can again use the equation provided in the question: E=(1/5)(10)(100 – 50)=100 Joules.