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## Question Explanations For

##
*NEW SAT PRACTICE TEST 3 (No Calculator Math Test)*

## 1.

The Correct Answer is (B) —
We can multiply 3

*x*= 15 by 2 to get 6*x*= 30. Similarly, multiplying 2*y*= 10 by 2 gives us 4*y*= 20. 6*x*+ 4*y*= 30 + 20 = 50.## 2.

The Correct Answer is (D) —

*f*(*x*) = 2*x*^{2}– 8*x*+ 6 describes an upwards-opening parabola with roots at*x*= 1 and*x*= 3, which we can find by setting the equation equal to 0 and factoring. Therefore, any*x*-value between but not including 1 and 3 will be less than zero; 2 is the only option that satisfies this condition. Plugging this value into the equation confirms that at this point*f*(*x*) is less than zero.## 3.

The Correct Answer is (D) —
We can find the slope of line

*p*by using the formula slope = rise/run. Rise equals the difference between the*y*values (9 – 3 = 6), and run is the difference between the*x*values (5 – 2 = 3). Therefore, slope = 6/3 = 2. Answer D) is the only solution with the correct slope.## 4.

The Correct Answer is (B) —
If the printer can produce 40 tank tops in 5 hours, they can produce 8 tank tops in one hour. Therefore they can make 8 × 7 = 56 tank tops in 7 hours. You can also set up the proportion 40/5 =

*x*/7 and solve for*x*.## 5.

The Correct Answer is (A) —
The graph shows the basic absolute value graph shifted in the negative

*y*direction. To shift the function down (that is, in the negative*y*direction), you must subtract a quantity outside of the absolute value signs. Answer A) is the only equation that does this.## 6.

The Correct Answer is (C) —
Since there are 180 degrees in a triangle, we can find the third angle in the top triangle by calculating 180 – (75 + 75) = 30 degrees. Because opposite angles are always congruent, we know that the top angle in the larger triangle is also 30 degrees. That means that the larger triangle is a 30-60-90 triangle, so its hypotenuse (

*x*) is twice the length of its shorter side — in this case, 5. Twice 5 is 10.## 7.

The Correct Answer is (B) —
Answer A) describes linear growth; answer B) describes exponential growth. Exponential growth is always faster than linear growth, so A) is incorrect. Answer C) describes a power function (because the exponent is constant); exponential growth, where the exponent is a variable, also increases faster than a power function. Finally, answer D) is another linear equation. Answer B) grows the fastest.

## 8.

The Correct Answer is (C) —

4 + 16 = 20

*f*(-1) = 3(-1) + 7 = 4*f*(3) = 3(3) + 7 = 164 + 16 = 20

## 9.

The Correct Answer is (C) —
Using the FOIL method, we get 2

*i*^{2}+ 11*i*+ 12. Since*i*= √ -1 ,*i*^{2}= -1, so the expression is equal to -2 + 11*i*+ 12 = 10 + 11*i*.## 10.

The Correct Answer is (B) —
Although this problem can quickly be solved using guess-and-check, we can also multiply both sides by 3 to get 6

*x*+*x*= 15*x*or 7*x*= 15*x*. It’s clear at this point that the only possible value of*x*that will satisfy this equation is 0.## 11.

The Correct Answer is (C) —
The fastest way to find the answer is to plug numbers into the given equations. Answer A) can be eliminated by plugging in 1 for

*x*. Answer B) can be eliminated by plugging in 2 for*x*. Answer D) can be eliminated by plugging in 0 for*x*. This leaves answer C), which satisfies all values in the table.## 12.

The Correct Answer is (C) —
Squaring both sides gives 5

*x*– 5 =*y*^{2}+ 1 and rearranging gives*y*^{2}= 5*x*– 6. Plugging in each pair of values shows that only answer C) is correct (for example, plugging in (1, 2) for*x*and*y*gives 22 = 5(1) – 6, or 4 = 1, which is false, but plugging in (3, 3) gives 32 = 5(3) – 6, or 9 = 9).## 13.

The Correct Answer is (A) —

258 – 38 = 220

*g*(5) =*f*(15) = 152 + 2(15) + 3 = 225 + 30 + 3 = 258*f*(5) = 52 + 2(5) + 3 = 25 + 10 + 3 = 38258 – 38 = 220

## 14.

The Correct Answer is (A) —
We can rearrange the second equation to get

*x*= 35 – 2*y*. Plugging this into the first equation gives us 2(35 – 2*y*) +*y*= 10, or 70 – 4*y*+*y*= 10. Simplifying gives 3*y*= 60, or*y*= 20. Alternatively, you can multiply either equation by -2 and add them. It’s fastest to eliminate*x*by doing this to the bottom equation: -2*x*– 4*y*= -70. Adding this to the top equation gives -3*y*= -60, so*y*= 20.## 15.

The Correct Answer is (B) —
The pattern involves adding the next integer in the sequence 1, 2, 3, 4… to the previous term in the given sequence. We start with 1 + 1 = 2. We take this answer and add 2: 2 + 2 = 4. We take this answer in turn and add 3: 4 + 3 = 7, then take that answer and add 4: 7 + 4 = 11. Continuing this pattern gives us 11 + 5 = 16.

## 16.

The Correct Answer is (10) —
The ratio of chickens to land is 5:1.5, so multiplying by 2 gives us 10:3 – Jeff and Liz will purchase 10 chickens for 3 acres of land.

## 17.

The Correct Answer is (5) —
Rewriting the bottom equation gives us

*x*= 4 +*y*. Plugging this into the top equation gives (4 +*y*)^{2}–*y*^{2}= 20, or 16 + 8*y*+*y*^{2}–*y*^{2}= 20. Simplifying and rearranging gives 8*y*= 4, so*y*= ½. Plugging this into either equation gives us*x*= 4½, so*x*+*y*= ½ + 4½ = 5. Alternatively, we can rewrite the first equation as (*x*–*y*)(*x*+*y*) = 20. Since*x*–*y*= 4,*x*+*y*must equal 5.## 18.

The Correct Answer is (0) —
Plugging the first equation into the second gives us

*y*= -2(2*y*+ 6) – 3 = -4*y*– 12 – 3. Simplifying and rearranging gives 5*y*= -15, so*y*= -3. Plugging this into the first equation gives*x*= 2(-3) + 6 = 0, so*xy*= (0)(-3) = 0.## 19.

The Correct Answer is (16) —
If we double a variable that is then squared, the effect is to multiply that squared variable by 4: (2

*x*)^{2}= 4*x*^{2}. The result of this operation is to reduce the force to one-fourth of its previous value, since the change is to the denominator. 64/4 = 16. We can also plug the given values into the equations to give us 64 =*x*/42, where*x*is*G*×*m*_{1}×*m*_{2}, which do not change. Solving for*x*gives us*x*= 1024. To find the force of gravity, we can write*F*= 1024/8^{2}= 1024/64 = 16.## 20.

The Correct Answer is (48) —
The perimeter of a triangle is the sum of the lengths of its sides. The base is the x-value when y = 0. y = 0 = -4x/3 + 16, so x = 12. The left side is the y-value when x = 0. y = -4(0)/3 + 16 = 16. We can draw this as below:

The triangle is a 3-4-5 triangle, with each side multiplied by 4, so the hypotenuse is 5 × 4 = 20 (the hypotenuse can also be found from the Pythagorean Theorem:

The triangle is a 3-4-5 triangle, with each side multiplied by 4, so the hypotenuse is 5 × 4 = 20 (the hypotenuse can also be found from the Pythagorean Theorem:

*c*^{2}=*a*^{2}+*b*^{2}= 122 + 162 = 144 + 256 = 400, so*c*= 20). 12 + 16 + 20 = 48.