Math Skills Test

If 𝒙is 25% of 250, what is the value of 𝒙?a.62.5b.100c.1000d.6250

A: Another way of expressing the fact that 𝑥is 25% of 250 is:𝑥=(0.25)250

Which of the following are complementary angles?a.71° and 19°b.90° and 90°c.90° and 45°d.15° and 30°

A: Complementary angles are two angles that add to90°.

Solve for 𝒙in the following inequality:𝟒𝒙+𝟐𝟑>−𝟑𝒙−𝟔a.𝑥>−4.14b.𝑥<−4.14c.𝑥>4.14d.𝑥<4.14

A: First, bring the −3𝑥to the left side of the equation and the 23 to the right side of the equation tomake it easier to solve

Given the functions, 𝒇(𝒙)=𝟑𝒙+𝟔and 𝒈(𝒙)=𝟐𝒙−𝟖, what is the solution of the equation, 𝒇(𝒙)=𝒈(𝒙)?a.𝑥=−12b.𝑥=−8c.𝑥=−14d.𝑥=−10

A: First, subtract5𝑥from both sides to get the variable to one side of the equation:

If 𝟐𝒙=𝟓𝒙−𝟑𝟎, what is the value of 𝒙?a.10b.-10c.4.3d.-4.3

A: First, subtract5𝑥from both sides to get the variable to one side of the equation:

What is 10% of 40%?a.4%b.30%c.50%d.400%

A: Recall that 𝑥%is the same thing as 𝑥100, and finding 𝑥%of a number is the same as multiplying that number by 𝑥%. This is true even when the number is itself a percentage. So, 10% of 40% is 40%×10%=40%×10100=40%×110=4%

Given the functions, 𝒇(𝒙)=𝟑𝒙+𝟔and 𝒈(𝒙)=𝟐𝒙−𝟖, what is the solution of the equation, 𝒇(𝒙)=𝒈(𝒙)?a.𝑥=−12b.𝑥=−8c.𝑥=−14d.𝑥=−10

A: The area of a square is equal to the square of the length of one side. If the area is 64in2, the side length must therefore be √64in2=8in. The circle is inscribed in the square, so the side length of the square is the same as the circle's diameter. If the circle's diameter is 8 in, then the circle's radius must be half of that, or 4 in. The area of a circle is equal to 𝐴=𝜋𝑟2=𝜋(4in)2=16𝜋in2.

If the measures of the three angles in a triangle are 2 : 6 : 10, what is the measure of the smallest angle?a.20 degreesb.40 degreesc.60 degreesd.80 degrees

A: The sum of the measures of the three angles of any triangle is 180. The equation of the angles of this triangle can be written as 2𝑥+6𝑥+10𝑥=180, or 18𝑥=180. Therefore, 𝑥=10. Therefore, the measure of the smallest angle is 20

Simplify the following expression:(𝟐𝒙𝟐+𝟑)(𝟐𝒙−𝟏)a.4𝑥3−2𝑥2+6𝑥−3b.2𝑥2+6𝑥-3c.4𝑥3−2𝑥2+6𝑥+3d.4𝑥3−2𝑥2−6𝑥−3

A: Use the FOIL method to expand the expression:

If 𝟏𝟔𝒙+𝟒=𝟏𝟎𝟎, what is the value of 𝒙?a.6b.7c.8d.9

A:First, subtract 4 from both sides to isolate the variable, Then, divide both sides by 16 to solve for 𝑥:

Expand the following expression: (𝟐𝒙−𝟐𝟎)(𝟓𝒙+𝟏𝟎)a.10𝑥2−80𝑥−200b.70𝑥−200c.10𝑥2−80𝑥+200d.10𝑥2−120𝑥−200

A:Start withthe FOIL methodto evaluate the multiplication and then combine like terms:

In the following equation, solve for 𝒙by factoring:𝟐𝒙𝟐−𝟕𝒙=𝒙𝟐-𝟏𝟐a.𝑥=−3,−4b.𝑥=3,4c.𝑥=3,−4d.𝑥=−3,4

B: First, bring all terms to the left side of the equationand combine like termsto make it easier to factor:

What is the value of 𝟑𝒙𝟐𝒚+𝒚/𝟐−𝟔𝒙, if 𝒙=𝟒and 𝒚=𝟏𝟎?a.221b.461c.872d.1916

B: First, substitute the given values into the expressionand then follow the order of operations to simplify

On a six-sided die, each side has a number between 1 and 6. What is the probability of throwing a 3 or a 4?a.1 in 6b.1 in 3c.1 in 2d.1 in 4

B: On a six-sided die, the probability of throwing any number is 1 in 6. The probability of throwing a 3 or a 4 is double that, or 2 in 6. This can be simplified by dividing both 2 and 6 by 2.Therefore, the probability of throwing either a 3 or 4 is 1 in 3.

Which of the following inequalities is correct?a.13<27<512b.27<13<512c.512<27<13d.512<13<27

B: One way to compare fractions is to convert them to equivalent fractions which have common denominators. In this case the lowest common denominator of the three fractions is 7×12=84. Converting each of the fractions to this denominator, 13=1×283×28=2884, 27=2×127×12=2484, and 512=5×712×7=3584. Since 24<28<35, it must be the case that 27<13<512.

The perimeter of a square is 24 m. What is its area?a.30m2b.36m2c.42m2d.24m2

B: The 4 sides of a square are all of equal length, so the side length is 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟4=244m=6m. Nowwe can calculate the area of the square described in the question:

At a school carnival, three students spend an average of $10. Six other students spend an average of $4. What is the average amount of money spent by all nine students?a.$5b.$6c.$7d.$8

B: The average is the total amount spent divided by the number of students. The first three students spend an average of $10, so the total amount they spend is 3×$10=$30. The other six students spend an average of $4, so the total amount they spend is 6×$4=$24. The total amount spent by all nine students is $30+$24=$54, and the average amount they spend is $54÷9=$6.

If a circle has a diameter of 12cm, what is its approximate area?a.38cm2b.113cm2c.276cm2d.452cm2

B: The formula for the area of a circle is 𝜋𝑟2. The diameter of a circle is equal to twice its radius. Therefore, to find theradius, it is necessary to divide the diameter by 2: 12cm2=6cm. Then, use the formula to find the area of the circle:

If a rectangle has a length of 5cm and a width of 7cm, what is its area?a.24cm2b.35cm2c.42cm2d.56cm2

B: The formula for the area of a rectangle is 𝑙𝑒𝑛𝑔𝑡ℎ×𝑤𝑖𝑑𝑡ℎ. Using the measurements given in the question, the area of the rectangle can be calculated:

If the volume of a cube is 𝟖𝐜𝐦𝟑, what is the length of the side of the cube?a.1cmb.2cmc.3cmd.4cm

B: The volume of a cube is calculated by cubing the side lengthof the cube.In this case,where 𝑥can represent the length of the cube: 8cm3=𝑥×𝑥×𝑥. To find the length, we must figure out whatnumber cubed equals 8.The answer is 2: 8cm3=2cm×2cm×2cm

If 𝟐𝒙𝟐=−𝟒𝒙𝟐+𝟐𝟏𝟔, which of the followingis a possiblevalue of 𝒙?a.4b.5c.6d.7

C: First, add 4𝑥2to both sides to isolate 𝑥:

A classroom contains 13 boys and 18 girls. If a student's name is chosen randomly, what is the probability it will be a girl's name?a.36%b.42%c.58%d.72%

C: First, find the total number of students in the classroom: 13+18=31. There is an 18 in31 chance that a name chosen randomly will be a girl's name.To express this as a percentage, divide 18 by 31, then multiply that number by 100:1831⁄×100%=58%

If 𝒘=𝟕, calculate the value of the following expression:𝟖𝒘𝟐−𝟏𝟐𝒘+(𝟒𝒘−𝟓)+𝟔a.279b.285c.337d.505

C: First, substitute the given value of winto the expression each time it appears.Then, follow the order of operations to find the result:

If 𝒙/𝟑+𝟕=𝟑𝟓, what is the value of 𝒙?a.9.33b.14c.84d.126

C: First, subtract 7 from both sides to isolate 𝑥:

Solve for yin the following inequality:−𝟐𝒚≥𝟐𝟒+𝟔a.𝑦≤15b.𝑦≥15c.𝑦≤−15d.𝑦≥−15

C: The key thing to remember to simplify this inequality is that when both sides are divided by a negative number, the direction of the sign must be reversed:

A rectangular solid measures 12cm by 3cm by 9cm. What is its volume?a.36cm3b.108cm3c.324cm3d.407cm3

C: To find the volume of a rectangular solid, the formula is 𝑙𝑒𝑛𝑔𝑡ℎ×𝑤𝑖𝑑𝑡ℎ×ℎ𝑒𝑖𝑔ℎ𝑡.Therefore:

If 𝟐𝒙+𝟓𝒙=𝟑𝒙+𝒙+𝟑𝟎, what is the value of 𝒙?a.2.72b.4.29c.6d.10

D: First, bring all of the terms containing 𝑥to the left side of the equation to make it easier to solve:

The length of a square is 15cm. What is its area?a.30cm2b.60cm2c.150cm2d.225cm2

D: The general equation to find the area of a rectangleis 𝑙𝑒𝑛𝑔𝑡ℎ×𝑤𝑖𝑑𝑡ℎ.Since the length and width of a square are equal, we can calculate the area of the square described in the question:

Simplify the following expression: (𝟐𝒙𝟒𝒚𝟕𝒎𝟐𝒛)×(𝟓𝒙𝟐𝒚𝟑𝒎𝟖)a.10𝑥6𝑦9𝑚10𝑧b.7𝑥6𝑦10𝑚10𝑧c.10𝑥5𝑦10𝑚10𝑧d.10𝑥6𝑦10𝑚10𝑧

D: To simplify this expression, the law of exponents that states that 𝑥𝑚×𝑥𝑛=𝑥𝑚+𝑛must be observed.

Simplify the following expression:(𝟐𝒙𝟒)𝟑+𝟐(𝒚𝟓)𝟓a.8𝑥64+2𝑦3125b.6𝑥7+2𝑦10c.6𝑥12+2𝑦25d.8𝑥12+2𝑦25

D:To simplify this expression, the law of exponents that states that (𝑥𝑚)𝑛=𝑥𝑚×𝑛must be observed: