# PERT Practice Test (Math)

#### This pie chart shows the market share of 5 brands of shirts, based on a survey of 300 shoppers in Canada.

The number of degrees in a circle is 360.

The total number of people purchasing cleaner was 300.

The angle for those who bought B was 198.

The number who bought B was 198/360 x 300 = 165.

#### A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday.

What is the equation of the axis of symmetry of this graph?

It is clear from the diagram that the T -axis is the mirror line or axis of symmetry of this diagram.

The equation of the T- axis is t = 0.

The equation of the axis of symmetry of this graph is t = 0

#### What is the x value such that y =30 - 5x and y = 0?

y =30-5x and y = 0

Hence 30 - 5x = 0

Hence 30 = 5x, divide both sides to 5. x = 6

#### There is a 12% sales tax. The pre-tax cost of a mobile phone is $280.

What is the tax payable on this mobile phone?

The sale price of the phone is 1.12×280 = $313.60.

The tax is $313.60 - $280 = $33.60.

#### (2x^2 + x - 6)/(x + 2) = ?

Begin by factoring the numerator. Assume that (the denominator) is one of the factors for a quick start to the process.

At this point, you should have the following: 2x² + x - 6 = (x + 2) (2x - ?).

The first term of the second set of parentheses must be 2x because 2x² ÷ x = 2x.

The sign of the second set must be negative because a positive times a negative equals a negative, and the original problem has -6 as the final term in the numerator.

To determine what replaces the “?” above, determine what number multiplied by 2 equals 6. The answer is 3.

Now you have fully factored the numerator:2x² + x - 6 = (x + 2) (2x - 3).

Rewrite the original problem, substituting the factored numerator for the original numerator and solve:

(2x² + x - 6) / (x + 2) = ((x + 2) (2x - 3)) / (x + 2) = 2x - 3

#### Charles thinks of a number, adds 10 then multiplies the number so obtained by 3 and gets 42.

If the number is n then write an equation for this.

Adding 10 to n gives n + 10.

Multiplying the number obtained by 3 gives 3(n + 10).

Making this equal to 42 gives 3(n + 10) = 42.

#### In a coordinate plane, triangle ABC has coordinates: (−2,7), (−3,6), and (4,5). If triangle ABC is reflected over the y-axis, what are the coordinates of the new image?

The correct answer is (2,7), (3,6), (−4,5).

One way to solve this problem is to draw the figure and then count how many units each point is from the y-axis, and to then count the same number of units in the opposite direction to find each point’s reflection. A more efficient method is to recognize that reflecting over the y-axis causes the x-value to switch sign and does not influence the y-value of the point.

Reflecting (−2,7), (−3,6), (4,5) across the y-axis produces the points (2,7), (3,6), (−4,5).

#### Which of the following expressions is a factor of the polynomial x² - 4x - 21

The polynomial can be factored as (x - 7) (x + 3). Thus, (x - 7) is a factor of the given polynomial.

#### In the diagram below, which line has a positive slope?

The coordinates of A are (1,2), the coordinates of B are (3,2). The slope of AB is (2-2)/( 3-1) = 0

The coordinates of A are (1,2), the coordinates of D are (-2,4). The slope of AD is (4-2)/( -2-1) = -4/3

The coordinates of A are (1,2), the coordinates of C are (2,4). The slope of AB is (4-2)/( 2-1) = 2

The coordinates of D are (-2,4), the coordinates of B are (3,2). The slope of DB is (2-4)/( 3− -2) = -4/5

#### Put these four fractions in order from smallest to largest: 1/4, 2/3, 4/7, 1/2

If 1/4, 2/3, 4/7, 1/2 are converted to decimals we get 0.25, 0.6666...., 0.571....., 0.5 then the correct order is obvious

or

If 1/4, 2/3, 4/7, 1/2 are converted to fractions with a common denominator 21/84, 56/84, 48/84, 42/84 then the correct order is obvious.

#### What is 181.5% of 18?

The correct answer is 32.67. Recall that the % symbol means ‘per hundred.’ So, 181.5% is equivalent to 181.5/100 or 1.815.

Converting a percentage to a decimal always entails moving the decimal point two places to the left. Multiply this decimal value with 18 to answer the question:

1.815 × 18 = 32.67

#### The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. How high was the initial height of the shrub?

h =15 + 3.2t gives the height of a shrub in inches after t weeks.

When planting occurs the height is 15 + 3.2× 0 = 15 inches.

After one week the height is 15 + 3.2× 1 = 18.2 inches

The rate at which the height increases is 18.2 - 15 = 3.2 inches

#### Factor the equation :

Begin by looking for anything that is common to all three terms.

You should notice that each of the coefficients is divisible by three and that each of the x-terms has a power of 2 or more.

Factor out a 3 from each term and you have 3(4x⁴ - 9x³ + 2x²).

Next, factor out x2 from each term and you are left with 3x²(4x² - 9x + 2).

The portion inside the parentheses can be further factored as follows:

3x²(4x² - 9x + 2) = 3x²(4x - 1) (x - 2)

This step may take a bit of trial and error, but you should be able to find it without too much trouble.

Look at the answer choices to get a hint. If a combination you are considering is not a choice, then it is not the correct answer.

If you are having trouble factoring the problem, you can always work backwards. Look at the answer choices and multiply them out to see which one gives the original problem as its answer.

This method is more time consuming, but it will yield a correct answer if you get stumped.

#### What are the zeros of a quadratic expression, represented by the factors, (x + 5)and (x - 6)

The zeros of an expression are the points at which the corresponding y-values are 0.

Thus, the zeros of the expression, represented by the given factors, will occur at the x-values that have corresponding y-values of 0.

Setting each factor equal to 0 gives x + 5 = 0 and x - 6 = 0.

Solving for x gives x = -5 and x = 6.

Thus, the zeros of the expression are x = -5 and x = 6.

#### If 4x + 3x − 2(x + 5) = −9, then x = ?

The correct answer is 1/5. Evaluate the expression by first distributing the −2 through the parentheses and then combining like terms:

4x + 3x − 2x – 10 = −9

7x − 2x − 10 = −9

5x = 1

x = 1/5

#### David purchased new shoes that were on sale for $45.44. The original price was $60.59. What percentage discount was the sale price?

The correct answer is 25%. The percentage discount is the reduction in price divided by the original price. The difference between original price and sale price is:

$60.59 − $45.44 = $15.15
The percentage discount is this difference divided by the original price:

$15.15 ÷ $60.59 = 0.25

Convert the decimal to a percentage by multiplying by 100%:

0.25 × 100% = 25%

#### There are 1,000,000 kb in a GB. Guy has 34 GB of storage on his computer. He has a lot of picture files of about 82kb.

What is the maximum number of such pictures he can store on his computer?

There are 1,000,000 kb in a GB.

In 33GB there are 33,000,000kb.

Guy can store 33,000,000÷82 = 402,439.024.... pictures.

He can store 402,439 complete pictures

#### Which of these is true?

The symbol for square root is √.

The square roots of negative numbers are undefined.

#### A wage sheet of a small business shows one employee’s details. The employee is paid $60 an hour for overtime hours where they work more than their usual 28 hours.

For 26 hours they are paid 28×$30 = $840

The money they get for overtime is $1050 - $840 = $240.

The number of overtime hours is $240÷$60 = 4.

x is 4.

#### On a number line what is the distance between -3/7 and -2/3 ?

The distance between numbers can be found by using absolute values (|a| or abs(a)).

The distance between these numbers is abs(-3/7 − -2/3 )

= abs(-(3/7 -2/3))

= abs(3/7 -2/3)

= abs(9/21 - 14/21)

= abs(-5/21 )

=5/21

#### If the radius of the sphere were doubled by what factor would the surface area be enlarged?

Note: The formula for the surface area S of the sphere = 4 x (pi) x ²

If r = 1 then the surface area of the smaller sphere is 12.56......

If the radius is doubled the surface area is 50.26......

The factor is 50.26... ÷ 12.56.... = 4.

The surface area is enlarged by a factor of 4.

#### This pie chart shows Zia's monthly expenses. If Zia spent $210 on transportation in one month, how much did she spend on food in that month?

The correct answer is $350. One method for solving this problem is to recognize that the ratio of the amount Zia spends on food to the amount he spends on transportation will equal the ratio of the percent of his income spent on food to the percent spent on transportation. Expressed mathematically:

$Food/210 = 25/15

$Food x 15 = $210x25

$Food = ($210x25)/15 = $350

#### The graph below is part of the graph of the function T = (t + 1)(t - 3) for the temperature in a refrigerator for time t hours after midday.

For which set of t values is the temperature below 0?

Although T is negative for 1 < t < 3, when t= 3 T = 0.

T >= 0 for t >= 3

T > 0 for t < -1.

T < 0 or negative when -1< t < 3

#### 10 workers can make all the furniture for 5 days. If each worker makes as quickly as the others then how much of the furniture could 7 workers make in 5 days?

10 workers can make a furniture in 5 days.

Each worker makes 1/10 of the furniture in 5 days. In 5 days 7 worker would make 7 × 1/10 of the furniture.

In 5 days 7 worker would make 7/10 of the furniture.

#### One third of the candidates for a scholarship were 25 years old or younger. Two sevenths of the candidates were at least 50 years old. If 84 people applied for the scholarship, how many were between 25 and 50?

One third of 84 is 84 × 1/3 = 84÷3 = 28. 28 people 25 years old or younger applied for the scholarship.

Two seventh of 84 is 84 × 2/7= 2×84÷7 = 24.

24 people who were at least 50 years old applied for the scholarship. 84 - 28 - 24 = 32.

32 people applied for the scholarship who were between 25 and 50.

#### In the metric system of units: 1 meter = 100 centimeters and 1 meter:1 foot = 3.25:1

3.25 feet = 1 meter

1 foot = 1÷3.25 meters

21 feet = 21×1÷3.25 = 6.4615 meters

#### ABC is a triangle with coordinates (3, 1), (6, 1), and (1, 3). It is translated to points A′(−3, 3), B′( 0, 3), and C′(−5, 5). Find the rule for the translation.

The correct answer is 6 units left and 2 units up. The rule of translation is the rule, which when applied to the first set of points, yields the second set of points. The difference between the x values of the non-translated and translated points is:

(x2 − x1) = (−3 − 3) = (0 − 6) = (−5 − 1) = −6

This corresponds to a shift of 6 units to the left.

Likewise, for the y values:

(y2 − y1) = (3 − 1) = (3 − 1) = (5 − 3) = 2

#### Which of the following is a factor of 450 and multiple of 25?

It can be confirmed by division that (a), (b) and (c) are factors of 450, while 100 is not.

The multiples of 25 are 25, 50, 75,....

75 is both a factor of 450 and multiple of 25

#### Given the equation, 3/(y - 5) = 15/(y + 4) what is the value of y?

Rearranging the equation gives 3(y + 4) = 15(y - 5), which is equivalent to 15y - 3y = 12 + 75, or 12y = 87, and solving for y, y = 87/12 = 29/4