## 1.

The result is –18

*x*. If you chose (C), you probably multiplied the exponents rather than adding them.

## 2.

If you chose (F), you probably divided the exponent by 2 as well.

## 3.

*x*= 15, therefore 20% of

*x*is 15. So:

75% of 120 is (120)(0.75) = 90.

## 4.

Add this to the 5 hours to get a total of 5.25 hours driving, then multiply by speed to find distance:

## 5.

If you chose (B), you probably added the discounts rather than applying them sequentially.

## 6.

## 7.

*x*= –2 into the expression and evaluate:

\begin{align*} &= ((-2)^3+6)((-2)^2-3) \\ &= (-8+6)(4-3) \\ &= (-2)(1) \\ &= -2 \end{align*}

## 8.

The only value of

*k*that gives the same distance from (

*k*, 2) and (2, 6) is

*k*=5, where:

Note that the points (-1,2) and (2,6) must form the base in this question. If one of the other sides were to form the base, then

*k*would have to equal 4, which is not an answer choice.

## 9.

*x*is a common factor in the expression. After factoring

*x*out, you are left with

*x*(

*x*— 16) = 0. The only possible values of

*x*that would make the equation true are

*x*= 0 and

*x*= 16.

## 10.

## 11.

*blueprint*:

*structure*is 15:45, which reduces to 1:3. Now, you know that the length of the structure is 3 times as large as indicated on the blueprint. (8)(3) = 24 and (10)(3) = 30. Adding all the sides together, you find that 24 + 30 + 45 = 99 meters of metal are needed.

## 12.

*a*:

## 13.

*s*shirts is 5

*s*. Similarly, she pays 6

*j*per jacket. To find the total cost of

*s*shirts and

*j*jackets, just add those two terms together. Finally, add the initial fee of $9 to get the final expression 5

*s*+ 6

*j*+ 9.

## 14.

*x*coordinates of where the parabola intersects the

*x*-axis. The roots are the values of

*x*that make the function equal to zero. Graphically, this is represented by the

*x*-intercepts of the parabola. From the graph, you can see that the roots are —38 and 10. (—38) + 10 = —28.

## 15.

*b*is the

*y*-intercept. Substitute either given point to find the value of

*b*.

*b*= 4.

## 16.

^{a}and 2

^{a+1}. The exponent increases by 1, which means

*b*will increase by a factor of the base, which is 2. So,

*b*doubles in size.

## 17.

If you chose (C), you probably found the number of original options and stopped there. If you chose (B), you probably found the number of new outfit options and stopped there.

## 18.

*x*:

$$23 \geq -(17+5x)$$

$$-23 \leq 17+5x$$

$$-40 \leq 5x$$

$$-8 \leq x$$

If you chose (G), you probably forgot to flip the direction of the inequality after multiplying through by a negative.

## 19.

## 21.

## 22.

## 23.

*x*, rearrange the equations such that

*y*is expressed in terms of

*x*and equate the two equations to each other and solve:

\begin{align*} 2y&=1-x \\ y&=1-x \\ x^2-1&=1-x \\ x^2+x-2&=0 \\ (x+2)(x-1)&=0 \end{align*}

The possible values of *x* are -2 and 1. The only possible value that is listed in the answer choices is 1.

## 24.

## 25.

^{7}to have a base of 3. Using exponent laws, reduce 81

^{7}to have a base of 3:

## 26.

*x*is the sector angle in radians. From the equation, you can determine that is equivalent to 90°.

## 27.

If you chose (E), you probably gave the number of days that would give a fine of $4.00.

## 28.

## 29.

If you are familiar with trigonometric identities, you may recognize that .

## 30.

*n*is doubled, giving . The number is then tripled, giving . The number is then divided by 4, giving .

## 31.

If you are familiar with logarithm rules, you may recognize that this equation can be simplified to .

## 32.

## 33.

## 34.

## 35.

where

*x*is the smallest number. In the interest of time, it may be easier to substitute answer choices and select the correct answer through process of elimination.

## 36.

If you are familiar with the Gaussian method of adding arithmetic sequences, recognize that the pattern of this sequence is , where

*n*is the

*n*th day. On the 10th day, Fred will have deposited . Sum of deposits .

## 37.

## 38.

\begin{align*} c^2&=a^2+b^2 \\ (13)^2&=5^2+b^2 \\ (13)^3-5^2&=b^2 \\ 144&=b^2 \\ 12&=b \end{align*}

Since a height of -12 ft. is impossible, the height of the tent is 12 ft.

You may have recognized that 13-12-5 is a Pythagorean Triple. If you did, solving this question would have been much easier and quicker.

## 39.

*x*represent Corwin’s favorite number:

## 40.

Recall the equation of a circle,
, where *h* and *k* are the center.

You know from the equation that the center is at (15, 4) and that the radius is 9. The circle will not cross the *y*-axis, since the center is further from the *y*-axis than the length of the radius. The circle will, however, cross the *x*-axis because the distance from the center of the circle to the *x*-axis is smaller than the length of the radius. Since the *x*-axis is not tangent to the circle, it will intersect the circle twice.

If you chose (G), you may have missed that a circle will intersect the *x*-axis more than once. If you chose (F), you may have miscalculated the radius or center of the circle and misplaced it on the coordinate plane.

## 41.

**i**unit vector (parallel to the

*x*-axis) and 3 units in the direction of the

**j**unit vector (parallel to the

*y*-axis). Hence, the component form is .

## 42.

If you chose (G) or (J), you may have found just the value of x or y without multiplying them together.

## 43.

*r*in for

*r*.

The volume will increase by a factor of 27.

## 44.

## 45.

Answer choice (A) is from (2, -1) and (2, -1) is from (-2, 3). Answer choice (C) is 4 units away from both provided points. Answer choice (D) is 4 units away from both provided points. Answer choice E is from (2, -1) and (2, -1) is from (-2, 3). Answer choice (B) is from (-2, 3) but (-2, 3) is from (2, -1).

## 46.

## 47.

\begin{align*} &=3x+5a-(x-2a) \\ &=3x+5a-x+2a \\ &=2x+7a \end{align*}

## 48.

\begin{align*} (\frac{10}{\sqrt{2}})^2+(\frac{10}{\sqrt{2}})^2&=c^2 \\ \frac{100}{2}+\frac{100}{2}&=c^2 \\ 100&=c^2 \\ c&=10 \end{align*}

## 49.

## 50.

Using the Pythagorean Theorem, you can find the diagonal of the garden:

\begin{align*} (10)^2+(10)^2&=d^2 \\ 200&=d^2 \\ d&=\sqrt{200} \\ \end{align*} Now, you can find the length of the clothesline.

\begin{align*} (\sqrt{200})^2+5^2&=c^2 \\ 200+25&=c^2 \\ 225&=c^2 \\ c&=15 \end{align*}

## 51.

Now, find the area that one wooden plank will cover. The question gives you the length, width, and height of the planks – realize that you only need the length and the width to answer this question. . Divide the total area that needs to be covered by the area of one planks.

## 52.

You can see that there are 6 triangles formed, hence the sum of all the interior angles is (180ᣞ)(6)=1080ᣞ. Since the polygon is a regular hexagon, you know that all the interior angles are of equal size. Therefore, divide 1080ᣞ by 6 to get 120ᣞ.

## 53.

\begin{align*} ab&=(x-\frac{1}{2})(x+\frac{1}{3}) \\ ab&=x^2-\frac{1}{2}x+\frac{1}{3}x-\frac{1}{6} \\ &=x^2-\frac{1}{6}x+-\frac{1}{6} \end{align*}

## 54.

Section A, with radius 5:

Section B, with radius 6:

Section C, with radius 7:

Section D, with radius 8:

Keep your answers in terms of π to avoid messy calculations. Section B has the smallest area.

## 55.

On the diagram, label all the information that you know. By doing this, it is easy to see that the distance from D to B is 100 m. If his total trip was 900 m, subtract the distances that you know he travelled to find the distance between points A and D:

## 56.

You know that tanθ=√3, therefore you know that the triangle will be a 30-60-90 triangle. From this, you can find that .

## 57.

If the side lengths of the square is 8 and the circular pool is perfectly inscribed in the square to create the maximum area, then the radius must be half the length of the square, or 4. Therefore, the area of a circle with radius 4 is .

## 58.

## 59.

*x*equals a negative number, then and the inequality is no longer true; you can eliminate answer choice (D). Realize that when

*x*is equal to any number that is equal to or greater than 2, and the inequality is no longer true; you can eliminate answer choice (B). Therefore, (A) is the correct answer.

## 60.

*f(x)*to

*g(x)*, therefore answer choices (H) and (K) can be eliminated. The period of has not changed from

*f(x)*to

*g(x)*, therefore answer choice J can be eliminated. The amplitude of the function has changed from

*f(x)*to

*g(x)*, and it has increased, therefore

*a*increased.