BACE: Applied Mathematics Practice Questions & Answers

Leading zeros (0.0...) are never significant. Captive zeros (between non-zero digits, like the 0 in 504) are significant. Trailing zeros after a decimal point (the final 0) are significant to indicate precision. Therefore, the digits '5', '0', '4', '0' are significant.

Move the decimal point 5 places to the right to get a number between 1 and 10 ($4.58$4.58). Since the original number was less than 1, the exponent is negative: $4.58 \times 10^{-5}$4.58×10−5.

There are 1,000 microliters ($\mu$μL) in 1 milliliter (mL). To convert $\mu$μL to mL, divide by 1,000: $\frac{450}{1000} = 0.45 \text{ mL}$1000450​=0.45 mL

Molarity (M) is defined as the number of moles of solute dissolved in one liter of total solution ($mol/L$mol/L).

Use $C_1V_1 = C_2V_2$C1​V1​=C2​V2​: $(50X)(V_1) = (1X)(1000 \text{ mL})$(50X)(V1​)=(1X)(1000 mL). Solve for $V_1$V1​: $V_1 = \frac{1000}{50} = 20 \text{ mL}$V1​=501000​=20 mL. To find the volume of water, subtract the stock volume from the total volume: $1000 \text{ mL} - 20 \text{ mL} = 980 \text{ mL}$1000 mL−20 mL=980 mL.

Percent (w/v) means grams per 100 mL. A 2.5% solution means 2.5 g in 100 mL. For 50 mL (which is half of 100 mL), you need half the mass: $2.5 \text{ g} \times \frac{50 \text{ mL}}{100 \text{ mL}} = 1.25 \text{ g}$2.5 g×100 mL50 mL​=1.25 g.

Substitute $y = 0.52$y=0.52 into the equation and solve for $x​$x​: $0.52 = 0.5x + 0.02$0.52=0.5x+0.02 ​$0.50 = 0.5x$0.50=0.5x ​$x = \frac{0.50}{0.5} = 1.0 \text{ mg/mL}$x=0.50.50​=1.0 mg/mL

The P200 pipettor has a range of 20–200 $\mu$μL. 150 $\mu$μL falls squarely within this range. A P1000 could measure it, but P200 offers higher precision for this specific volume. P20 and P10 are too small.

First calculate moles needed for 0.5 L (500 mL) at 0.5 M: $\text{Moles} = M \times L = 0.5 \text{ mol/L} \times 0.5 \text{ L} = 0.25 \text{ moles}$Moles=M×L=0.5 mol/L×0.5 L=0.25 moles Then convert moles to grams: $\text{Mass} = \text{Moles} \times \text{MW} = 0.25 \text{ mol} \times 58.44 \text{ g/mol} = 14.61 \text{ g}$Mass=Moles×MW=0.25 mol×58.44 g/mol=14.61 g

In multiplication, the result must be rounded to the same number of significant figures as the factor with the fewest significant figures. $4.5$4.5 has 2 sig figs. $1.002$1.002 has 4 sig figs. The answer must be rounded to 2 sig figs. $4.5 \times 1.002 = 4.509$4.5×1.002=4.509, which rounds to 4.5.