Basic Algebra Diagnostic Test Review

Comprehensive practice flashcards based on the Basic Algebra Diagnostic Test transcript, covering topics in interest, algebra simplification, scientific notation, geometry, and logic.

In the motorboat speed problem, what are the boat's speed in still water ($x$) and the current's speed ($y$) given a $16\,\text{mile}$ trip takes $20\,\text{minutes}$ downstream and $30\,\text{minutes}$ upstream?

$x = 40\,\text{mph}$ and $y = 8\,\text{mph}$

How many milliliters of a $10\%\,\text{NaCl}$ solution and a $5\%\,\text{NaCl}$ solution are required to create $150\,\text{ml}$ of an $8\%\,\text{NaCl}$ solution?

$90\,\text{ml}$ of the $10\%\,\text{NaCl}$ solution and $60\,\text{ml}$ of the $5\%\,\text{NaCl}$ solution

What is the solution set for the inequality $7 - 3|x + 2| \ge -14$?

$[-5, 5]$ (Note: Derived from solving $|x + 2| \le 7$)

How much principal must be deposited to earn $P10,000$ in interest over $10\,\text{years}$ at a $10\%$ simple interest rate?

$$P10,000$$

If Harry's initial deposit of $P12,500$ grows to $P15,500$ after $4\,\text{years}$, what is the simple interest rate?

$$6\%$$

What is the final amount withdrawn from $COL\,\text{Finance}$ after investing $P100,000$ for one year at $8\%$ interest compounded semi-annually?

$$P108,160$$

In a simple interest scenario with a rate of $10\%$, how many years does it take for the invested amount to double?

$$10\,\text{years}$$

What is the contrapositive of the proposition 'If it's late, then It's free'?

If it's not free, then it's not late.

Given $P$ is 'RM is the best review center' and $Q$ is 'I will pass the UPCAT', which compound statement is false if both $P$ and $Q$ are true?

RM is the best review center and I will not pass the UPCAT.

Evaluate the expression $\frac{3x^2 + 2y}{4(x + y) - 3}$ when $x = 3$ and $y = -3$.

$$-7$$

What is the simplified result of the exponent expression $\frac{(3x^3y^2)^2}{2(x^2y)^4}$?

$$\frac{9}{2x^2}$$

What is the result of the calculation $132,000,000,000 \div 0.000000004$ in scientific notation?

$$3.3 \times 10^{19}$$

What is the apparent diameter of a virus ($2.3 \times 10^{-8}\,\text{meter}$) under a microscope magnification of $5 \times 10^2$?

$$1.15 \times 10^{-5}\,\text{meters}$$

What is the expression for the volume of a cube where each side is represented as $3x - 4$?

$$27x^3 - 108x^2 + 144x - 64$$

Find the greatest value among the following radicals: $2\sqrt{5}$, $3\sqrt{4}$, $4\sqrt{3}$, and $5\sqrt{2}$.

$$5\sqrt{2}$$

Calculate the time in seconds it takes for a stone to hit the ground if dropped from a $100\,\text{foot}$ tall building, modeled by $h = -16t^2 + 100$.

$$2.5\,\text{sec.}$$

Find the general equation of the line that passes through the points $(2, -5)$ and $(-3, 1)$.

$$6x + 5y + 13 = 0$$

What is the slope of the line described by the equation $x + y = 4$?

$$-1$$

Determine the equation of a line that passes through $(-3, -4)$ and is parallel to the line $y = -2x + 7$.

$$2x + y = -10$$

What is the simplified form of the radical expression $\sqrt{45} - \sqrt{20} + 4\sqrt{80}$?

$$17\sqrt{5}$$