Answers

Answers to the Example Problems

Here are the answers and explanations to our free sample test.

The answers and explanations are taken from our Math Power Download.

Before reviewing these answers and explanations, you should first have a look at our math formulas for the exam.

Answers – Question 1:  The correct answer is 20 combinations.

Look at the equation and the problem and substitute the values for S and N:

(N!) ÷ [(N − S)! × S!] =

(6 × 5 × 4 × 3 × 2 × 1) ÷ [(6 − 3) ! × (3 !)] =

(6 × 5 × 4 × 3 × 2) ÷ [(3 !) × (3 × 2 × 1)] =

(6 × 5 × 4 × 3 × 2) ÷ [(3 × 2 × 1) × 6] =

720 ÷ (6 × 6) =

720 ÷ 36 = 20

In other words, 20 different three-letter combinations can be made from a set of six different letters.




Answers – Question 2: The correct answer is (−2, −3).

Calculate for midpoint x:

(−6 + 2) ÷ 2 =

(−4) ÷ 2 =

−2 = midpoint x

Calculate for midpoint y:

(8 + −2) ÷ 2 =

(−6) ÷ 2 =

−3 = midpoint y

The midpoints are represented as (x, y) coordinates for your final answer:

(−2, −3)

Answers – Question 3:  The correct answer is  54 = 625.

a = logbc is always the same as: ba = c




Answers – Question 4:  The correct answer is 25x2 − 20xy + 4y2.

(5x − 2y)2 = (5x − 2y)(5x − 2y)

Using the FOIL method, we see that the first terms are 5x and 5x: (5x − 2y)(5x − 2y)

FIRST: 5x × 5x = 25x2

The outside terms are 5x and −2y: (5x − 2y)(5x2y)

OUTSIDE: 5x × −2y = −10xy

The inside terms are −2y and 5x: (5x2y)(5x − 2y)

INSIDE: −2y × 5x = −10xy

The last terms are −2y and −2y: (5x2y)(5x2y)

LAST: −2y × −2y = 4y2

Add these up for your final result:

25x2 − 10xy − 10xy + 4y2 =

25x2 − 20xy + 4y2

Answers – Question 5:  The correct answer is 0.33π.

Remember that the formula for area of a circle is: π × radius2

Area of circle B: 0.72π = 0.49π

Area of circle C: 0.42π = 0.16π

To determine how much larger the area of circle B is than circle C, we then subtract:

0.49π − 0.16π = 0.33π

Answers – Question 6:  The correct answer is 1.8π.

The formula to calculate the circumference of a circle is: π × diameter

Remember that the diameter is equal to the radius × 2.

π × 0.9 × 2 = 1.8π

Answers – Question 7:  The correct answer is x intercept = (3, 0) and y intercept = (0, 27).

Substitute 0 for x and y.

Solution for x intercept:

6x2 + 2y = 54

6x2 + (2 × 0) = 54

6x2 + 0 = 54

6x2 ÷ 6 = 54 ÷ 6

x2 = 9

x = 3

x intercept = (3, 0)

Solution for y intercept:

6x2 + 2y = 54

(6 × 0) + 2y = 54

0 + 2y = 54

2y ÷ 2 = 54 ÷ 2

y = 27

y intercept = (0, 27)

Answers – Question 8:  The correct answer is 6 permutations.

Remember the formula for permutations: N! ÷ (N − S)!

When you see the exclamation point in equations such as (N!) you have to multiply that number by each number that is lower than it.

For instance, 4! = 4 × 3 × 2 × 1

In this question, N = 3 and S = 2

N! ÷ (N − S)! =

(3 × 2 × 1) ÷ (3 − 2)! =

(3 × 2 × 1) ÷ 1 =

6 ÷ 1 = 6

In other words, 6 two-character permutations can be made from this 3 letter set.

Answers – Question 9:  The correct answer is 4.5.

Slope formula: y = mx + b

Substitute the values and solve.

15 = m2 + 6

15 − 6 = m2 + 6 − 6

9 = m2 + 6 − 6

9 = m2

9 ÷ 2 = m2 ÷ 2

4.5 = m

Answers – Question 10:  The correct answer is 192π.

Volume of a cone: (π × radius2 × height) ÷ 3

You will know by now that the diameter is twice the radius. In this problem, the radius is therefore 8.

So we substitute the values to get the volume:

(π82 × 9) ÷ 3 =

(64π × 9) ÷ 3 =

576π ÷ 3 =

192π

Answers – Question 11:  The correct answer is 35 units.

The formula for the area of a rectangle is: length × width

Substitute the values for the length and the width, which are stated in the question, in order to determine the area:

5 × 7 = 35 units

Answers – Question 12:  The correct answer is 9.

Formula to calculate the area of a triangle: (base × height) ÷ 2

triangle area = (3 × 6) ÷ 2 = 18 ÷ 2 = 9

Answers – Question 13:  The correct answer is 18 units.

Here is the formula for calculating the perimeter of squares and rectangles:

(length × 2) + (width × 2)

So the perimeter is calculated as follows:

(length × 2) + (width × 2) =

(4 × 2) + (5 × 2) =

8 + 10 = 18 units

Answers – Question 14:  The correct answer is x + 2.

(x2 − 4) ÷ (x − 2) = ?

Look at the term and integer in the first set of parentheses.

The 4 in the first set of parentheses becomes −4 because the integer is preceded by the minus sign.

We have to divide −4 by −2, because −2 is the integer in the second set of parentheses.

−4 ÷ −2 = 2

Therefore the result is expressed as (x + 2).

Answers – Question 15:  The correct answer is x = 4.

To solve this type of problem, do multiplication of the items in parentheses first.

If 6x − 3(x + 4) = 0, then x = ?

6x − 3(x + 4) = 0

6x − 3x − 12 = 0

3x − 12 = 0

Then move the integer to the other side of the equation.

3x − 12 = 0

3x − 12 + 12 = 0 + 12

3x = 12

x = 4