Ask your homework questions to teachers and professors, meet other students, and be entered to win $600 or an Xbox Series X 🎉Join our Discord! # Cracking The SAT ## The Princeton Revew ## Chapter 3 ## Practice Test 3 ## Educators ### Math Test Calculator - Problem 1 The population,$P,$of Town$Y$since 1995 can be estimated by the equation$P=1.0635 x+3,250,$where$x$is the number of years since 1995 and$0 \leq x \leq$20 . It the context of this equation, what does the number 1.0635 most likely represent? A) The estimated population of town$Y$in 1995 B) The estimated population of town$Y$in 2015 C) The factor by which the population of town$Y$increased yearly D) The factor by which the population of town Y decreased yearly Check back soon! ### Math Test No Calculator - Problem 1 Which of the following equations has a vertex of$(3,-3) ?$A)$y=5(x-3)^{2}-3$B)$y=5(x+3)^{2}-3$C)$y=5(x-3)^{2}+3$D)$y=5(x+3)^{2}+3$Check back soon! ### Math Test No Calculator - Problem 2 A beverage store charges a base price of$x$dollars for one keg of root beer. A sales tax of a certain percentage is applied to the base price, and an untaxed deposit for the keg is added. If the total amount, in dollars, paid at the time of purchase for one keg is given by the expression$1.07 x+17$, then what is the sales tax, expressed as a percentage of the base price? A) 0.07$\%$B) 1.07$\%$C) 7$\%$D) 17$\%$Check back soon! ### Math Test No Calculator - Problem 3 Syed took out a cash advance of$d$dollars from a financing company. The company deducts a fee of$\frac{1}{3}$of the original advanced amount along with a wire transfer fee of$\$30.00 .$ Which of the following represents the final advanced amount that Syed receives after all applied fees, in dollars?
A) $\frac{1}{3} d-30$
B) $\frac{1}{3}(d-30)$
C) $\frac{2}{3}(d-30)$
D) $\frac{2}{3} d-30$

Check back soon!

### Math Test No Calculator - Problem 4

What is the equation of a line that contains the point $(1,6)$ and has a $y-$ intercept of 4$?$
A) $y=\frac{1}{2} x+4$
B) $y=x+4$
C) $y=2 x+4$
D) $y=4 x+2$

Check back soon!

### Math Test No Calculator - Problem 5

The number of bonus points, $B(p),$ that a credit card holder receives is given by the function $B(p)=4 p+7,$ where $p$ represents the number of purchases made. If the number of purchases is increased by $3,$ by how much does the number of bonus points increase?
A) 3
B) 4
C) 12
D) 19

Check back soon!

### Math Test No Calculator - Problem 6

Jeff tests how the total volume occupied by a fluid contained in a graduated cylinder changes when round marbles of various sizes are added. He found that the total volume occupied by the fluid, V, in cubic centimeters, can be found using the equation below, where x equals the number of identical marbles Jeff added, one at a time, to the cylinder, and r is the radius of one of the marbles.
$$v=24 \pi+x\left(\frac{4}{3} \pi r^{3}\right)$$
If the volume of the graduated cylinder is 96$\pi$ cubic centimeters, then, what is the maximum number of marbles with a radius of 3 centimeters that Jeff can add without the volume of the fluid exceeding that of the graduated cylinder?
A) 1
B) 2
C) 3
D) 4

Check back soon!

### Math Test No Calculator - Problem 7

If $b$ is two more than one-third of $c,$ which of the following expresses the value of $c$ in terms of $b$ ?
A) $c=\frac{b-2}{3}$
B) $c=\frac{b+2}{3}$
C) $c=3(b-2)$
D) $c=3(b-6)$

Check back soon!

### Math Test No Calculator - Problem 8

The rotation rate of a mixing blade, in rotations per second, slows as a liquid is being added to the mixer. The blade rotates at $1,000$ rotations per second when the mixer is empty. The rate at which the blade slows is four rotations per second less three times the square of the height of the liquid. If $h$ is the height of liquid in the mixer, which of the following represents $R(h)$ , the rate of rotation?
A) $4-9 h^{2}$
B) $1,000-(4-3 h)$
C) $1,000-(9 h-4)$
D) $1,000-\left(3 h^{2}-4\right)$

Check back soon!

### Math Test No Calculator - Problem 9

A dental hygiene company is creating a new 24-ounce tube of toothpaste by combining its most popular toothpastes, Cavity Crusher and Bad Breath Obliterator. Cavity Crusher contains 0.25% of sodium fluoride as its active ingredient, and Bad Breath Obliterator contains 0.30% of triclosan as its active ingredient for a total of 0.069 ounces of active ingredients in both toothpastes. Solving which of the following systems of equations yields the number of ounces of Cavity Crusher, c, and the number of ounces of Bad Breath Obliterator, b, that are in the new toothpaste?
A) $\quad c+b=0.069$
$0.25 c+0.3 b=24$
B) $\quad \qquad c+b=24$
$0.0025 c+0.003 b=0.069$
C) $\quad c+b=24$
$0.025 c+0.03 b=0.069$
D) $c+b=24$
$0.25 c+0.3 b =0.069$

Check back soon!

### Math Test No Calculator - Problem 10

$$\frac{2 d^{2}-d-10}{d^{2}+7 d+10}=\frac{d^{2}-4 d+3}{d^{2}+2 d-15}$$
In the equation above, what is the value of $d$ ?
A) $-4$
B) 2
C) 4
D) 6

Check back soon!

### Math Test No Calculator - Problem 11

Which of the following is a possible equation for a circle that is tangent to both the $x$ -axis and the line $x=4 ?$
A) $(x+2)^{2}+(y+2)^{2}=4$
B) $(x+2)^{2}+(y-2)^{2}=4$
C) $(x-2)^{2}+(y+4)^{2}=4$
D) $(x-6)^{2}+(y-2)^{2}=4$

Check back soon!

### Math Test No Calculator - Problem 12

Reactant A is placed in a beaker, to which Reactant $\mathrm{B}$ will be added.
Reactants $\mathrm{A}$ and $\mathrm{B}$ will not react unless $\mathrm{B}$ gets to a certain concentration. Once the reaction starts, both concentrations decrease until $\mathrm{B}$ has been consumed. Which of the following graphs, showing concentration in moles as a function of time in seconds, represents the reaction?

Check back soon!

### Math Test No Calculator - Problem 13

$$-2 y \leq 8$$
$$\begin{array}{c}{y-3 \leq x} \\ {\frac{1}{3} y+1 \geq x}\end{array}$$
Which of the following graphs shows the solution to the system of inequalities above?

Check back soon!

### Math Test No Calculator - Problem 14

If rectangle $A B C D$ has an area of 48 and the tangent of $\angle B C A(\text { not shown) }$ is $\frac{3}{4},$ then which of the following is the length of $\overline{B D}$ (not shown)?
A) 5
B) 10
C) 13
D) It cannot be determined from the given information.

Check back soon!

### Math Test No Calculator - Problem 15

Which of the following is equivalent to $\frac{2 m+6}{4} \times \frac{6 m-36}{3 m+9} ?$
A) $\frac{12 m^{2}-216}{12 m+36}$
B) $\frac{8 m-30}{3 m+13}$
C) $\frac{m-6}{4}$
D) $m-6$

Check back soon!

### Math Test No Calculator - Problem 16

A rectangular box has sides $3,4,$ and $x$ and a volume of $18 .$ What is the value of $x ?$

Check back soon!

Jeanne babysits Chuy one day each week. Jeanne charges a $\$ 20$fee for the day, plus$\$5.50$ for every 30 minutes of babysiting. How much has Jeanne earied after three hours of babysiting? (Disregard the \$$sign when gridding your answer.) Check back soon! ### Math Test No Calculator - Problem 18 The parabola y=-x^{2}+5 x+6 is intersected by the line y=-\frac{1}{2} x+12 . What is the y -coordinate of the intersection closest to the x -axis? Check back soon! ### Math Test No Calculator - Problem 19$$ \begin{aligned} 13 r+8 v &=47 \\ 22 v &=63-17 r \end{aligned}$Based on the system of equations above, what is the sum of$r$and$v ?$Check back soon! ### Math Test No Calculator - Problem 20 A gardener has a cultivated plot that measures 4 feet by 6 feet. Next year, she wants to double the area of her plot by increasing the length and width by$x$feet. What is the value of$x ?$Check back soon! ### Math test calculator - Problem 2 If$x^{2}+12 x=64$and$x>0,$what is the value of$x ?$A) 2 B) 4 C) 8 D) 16 Check back soon! ### Math test calculator - Problem 3 Sai is ordering new shelving units for his store. Each unit is 7 feet in length and extends from floor to ceiling. The total length of the walls in Sai's store is 119 feet, which includes a length of 21 feet of windows along the walls. If the shelving units cannot be placed in front of the windows, which of the following inequalities includes all possible values of$r,$the number of shelving units that Sai could use? A)$r \leq \frac{119-21}{7}$B)$r \geq \frac{119+21}{7}$C)$r \leq 119-21+7 r$D)$r \geq 119+21-7 r$Check back soon! ### Math test calculator - Problem 4 The scatterplot above shows the weight, in ounces, of the fruits on a certain truffula tree from days 55 to 85 after flowering. According to the line of best fit in the scatterplot above, which of the following is the closest approximation of the number of days after flowering of a truffula fruit that weighs 5.75 ounces? A) 63 B) 65 C) 77 D) 81 Check back soon! ### Math test calculator - Problem 5 Hannah placed an online order for shirts that cost$\$24.50$ per shirt. A tax of 7$\%$ is added to the cost of the shirts, before a flat, untaxed shipping rate of S6 is charged. Which of the following represents Hannah's total cost for $s$ shirts, in dollars?
A) 0.07$(24.50 s+6)$
B) 1.07$(24.50+6) s$
C) $1.07(24.50 s)+6$
D) $1.07(24.50+s)+6$

Check back soon!
1 2 3 4 5 ... 7