In the parallelogram below, what is the measure of ∠WXY?

F. 25°
G. 55°
H. 65°
J. 100°
K. 120°

Solution

With the information given, you can find that the measure of angle WZY = 180° − (25° + 55°) = 100°.

Since WXY is opposite WZY in the same parallelogram, it also equals 100°.

If 9 − x³ + 2 = 19, what is the value of x?

A. −2
B. −1
C. 2
D. 3
E. 8

Solution

This simple algebra problem asks you to solve for x.

Combine like terms and isolate x on one side of the equation.

9 − x³ + 2 = 19

−x³ + 11 = 19

−x³ = 8

x³ = −8

x = −2

For all x ≠ 1,$\frac{x^{2}− 2x + 1}{x − 1}$ is equal to ?

F. 1
G. x + 2
H. x²
J. $\frac{x + 2}{x − 1}$
K. x − 1

Solution

To answer this question, you need to first expand the equation and then simplify it:

$\frac{x^{2} − 2x + 1}{x-1}$

$\frac{(x − 1)(x − 1)}{x-1}$

The (x − 1) from the numerator cancels out the (x −1) in the denominator, so the equation is equal to x − 1.

3.234 × 0.01 =?

A. 323.4
B. 32.34
C. 3.234
D. 0.3234
E. 0.03234

Solution

Multiplying by 0.01 is the same as dividing by 100, since 0.01 = $\frac{1}{100}$.

Move the decimal place two spaces to the left to get 0.03234.

Which of the following is equivalent to 4.2 × 10⁻⁵?

F. 0.000042
G. 0.00042
H. 42,000
J. 420,000
K. 4,200,000

Solution

The expression 4.2×10⁻⁵ is in scientific notation.

The −5 exponent means that the decimal point has been moved five spaces to the right of its original position.

So, move the decimal five places to the LEFT back to its original position: 0.000042.

In the figure below, l₁ is parallel to l₂, and l₃ is parallel to l₄. Which of the following angles is NOT equal to angle x?

A. a
B. b
C. c
D. d
E. e

Solution

The best approach to this problem is to identify the relationships between the angles.

Since a and b are vertical angles formed from the intersection of parallel lines and transversals, they are equal in measure.

Since the same transversal (l₁) creates angle x, angle x is equal to angles a and b.

Eliminate answer choices A and B.

Angle c is a supplementary to angle x, which means that angle c + angle x = 180◦.

There are no right angles in the figure, so angle c is NOT equal to angle x; answer choice C is correct.

Molality, m, tells us the number of moles of solute dis-solved in exactly 1 kilogram (kg) of solvent. Molality is represented by the equation, m = ^s⁄_k, were s represents the moles of solute and k represents the mass of the solvent in kilograms. A solution is known to have a molality of 0.2 and contain 13 kg of solvent. What is the number of moles of solute contained in the solution?

F. 0.01
G. 2.6
H. 3.2
J. 26
K. 32

Solution

Since you are given the equation for molality, m = ^s⁄_k, and you are given m = 0.2 and k = 13, plug in the values and solve:

0.2 = $\frac{s}{13}$

s = 2.6

Fred works at a car wash where he makes $40.00 per day plus $1.75 per car that he washes. Yesterday, Fred made a total of $61.00. How many cars did he wash yesterday?

A. 10
B. 12
C. 17
D. 20
E. 34

Solution

To solve this problem, set up an equation showing that Fred’s total daily income equals his fixed daily income.

($40.00) + the amount he earns for washing cars.

Set the number of cars equal to C: $61.00 = $40.00 + $1.75C.

Solve for C: $1.75C = $21.00

C = 12

The 65-member high school band raised money to go on a trip by having a bake sale. If the original cost per band member for the trip is $18.50 and the band members earned a total of $585.00 at the bake sale, how much more money does each band member need in order to pay for the trip?

F. $9.00
G. $9.50
H. $18.50
J. $46.50
K. $65.00

Solution

The first step is to calculate the total cost of the trip by multiplying the number of people in the band (65) by the cost per member:

65 × 18.50 = $1202.50

A total of $585.00 was raised from the bake sale, $1202.50 − $585.00 = $617.50, which is the total amount left to earn. That means that each of the 65 members must pay an additional $\frac{617.50}{65}$ , or $9.50.

In triangle ABC below, the measure of angle A is 20 and the measure of angle B is 3 times larger than the measure of angle C. What is the measure of angle B?

A. 40°
B. 60°
C. 80°
D. 120°
E. 160°

Solution

Given that angle A is 20° and that angle B is three times larger than angle C, you can set up the following equation. 20°+ B + C = 180°.

Since B = 3C, you have 20°+3C+C = 180°.

Combine like terms: 20°+4C = 180°. Solve for C: 4C = 160°;

C = 40°. If C = 40°, then B = (40°)(3) = 120°.

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