Practice Test 2 - HSPT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

The mean score of a group of 8 students on a test was 75.5. Two new students take the same test, and the mean score of all 10 students becomes exactly 78. If one of the new students scored 15 points higher than the other, what was the lower score of the two new students?
The numbers in the set $S_1 = \{10, 15, x, 25, 30\}$ are listed in increasing order, and its median is 18. The numbers in the set $S_2 = \{5, y, 30, 40\}$ are also listed in increasing order. If the mean of $S_1$ is equal to the median of $S_2$ , what is the value of $y$ ?
A paint mixture requires red, blue, and yellow paint in the ratio $7:4:3$ . If the total volume of paint needed is $2.8$ liters, but the painter only has $0.6$ liters of blue paint available, what is the maximum volume of paint mixture that can be made using the correct ratio?
If $4x - 7 = 2x + 13$ , what is the value of $3x + 5$ ?
Solve for $p$ : $\dfrac{4}{3}p-2=\dfrac{1}{6}(12p+6).$
A 25-foot ladder is placed against a vertical wall such that the base of the ladder is 7 feet from the base of the wall. If the top of the ladder slides down the wall by 4 feet, how much farther does the base of the ladder slide away from the wall?
A chord in a circle has a length of 24 inches. The shortest distance from the center of the circle to the chord is 5 inches. What is the area of the circle?
Water flows into a cylindrical tank at 5 liters per minute. The tank has an interior radius of 0.5 m and a height of 2 m. Approximately how many minutes will it take to fill the tank? (Use $\pi\approx3.14$ and $1\text{ m}^3=1000\text{ L}$ .)
Evaluate: $0.3 + \frac{4}{5} \times (1 \frac{1}{2} - \frac{2}{3})$
The median of the set $\{x,\ 8,\ 11,\ 15,\ 21\}$ is $12$ . What is a possible value of $x$ ?
How many zeros are at the end of $20 \times 15 \times 12$ ?
The vertices of a square are located at (a, b), (a, b+s), (a+s, b), and (a+s, b+s). If the function f(x, y) = (x+y, x-y) is applied to each vertex of the square, the new vertices form a new quadrilateral. What is the area of this new quadrilateral?
Two gears are connected such that their rotation speeds are inversely proportional to their radii. If gear A has radius $6$ cm and rotates at $150$ rpm, while gear B has radius $9$ cm, and gear C is added such that all three gears maintain the inverse relationship, what must be the radius of gear C if it rotates at $75$ rpm?
Solve the literal equation $A = \frac{1}{2}h(b_1 + b_2)$ for $b_1$ .
A farmer wants to build a rectangular fence. He has 120 feet of fencing material. One side of the fenced area will be along a river, so it does not need fencing. What is the maximum possible area he can enclose?
A $30\text{ ft}$ rope is tied from the ground to the top of a tree. If the stake is $18\text{ ft}$ from the base of the tree, how tall is the tree?
Solve for $x$ : $5-2(x-4)=3(x+1)+2.$
If the least common multiple of $6$ and $n$ is $42$ , which of the following is a possible value of $n$ ?
A rhombus has diagonals of length 14 cm and 48 cm. What is the sum of the measures of any two consecutive interior angles?
Which of the following numbers has exactly three different prime factors?

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