# TACHS Mathematics Practice Test

#### Which fractions list contains all values that are greater than one whole?

Explanation:

When a fraction has a numerator larger than its denominator, the total value is more than one whole. Fractions
like 3/3,5/5, and 7/7 are all equal to one whole. Fractions with numerators less than their denominators represent
values that are less than one whole. 5/3,7/5, and 3/2 are all improper fractions representing total values larger than one whole.

#### What is six times 1/3 of 90?

Explanation:

90/3 = 30, and 30 + 6 = 36.

#### Five red balls, three white balls, and two yellow balls belong to a kid. How many yellow balls are there in total?

Explanation:

Total no. of balls = 10, number of yellow balls = 2, so, 2/10 X 100 = 20%

#### As an improper fraction, express the mixed number 2 1/3.

Answer:
The correct answer is D: 7/3.
Explanation:

2 1/3 is equivalent to 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3.

This represents seven groups of 1/3, or as an improper fraction, 7/3

#### What number follows 116, 113, 107, 98, and so on in the series?

Explanation:

Each element of the series is a multiple of 3 less than the previous element. Starting with 116, the next element
is 1 × 3 less, or 116 – (1 × 3) = 113. The next element is 2 × 3 less, or 113 – (2 × 3) = 107. The next element is 3 × 3
less, or 107 – (3 × 3) = 98. So the next element will be 4 × 3 less, or 98 – (4 × 3) = 86.

#### A rectangle's length is twice its width, and its area is the same as a square with a side of 12 cm. What will the rectangle's perimeter be near the next whole number

Explanation:

Area of the square = 12 x 12 = 144cm. Let x be the width so 2x will be
the length of rectangle. The area will be 2 x 2 and the perimeter will be
2(2x + x) = 6x. According to the condition 2 x 2 = 144 then x = 8.48 cm.
The perimeter will be 6 X 8.48 = 50.88

= 51 cm.

#### What mixed number is 5/3 equivalent to?

Explanation:

The correct answer is A: 1 2/3.

5/3 can be thought of as 1/3+1/3+1/3+1/3+1/3.

We can combine three groups of 1/3 in order to create 3/3, or one whole.

There are still two thirds left, so our mixed number is 1 2/3

#### For every mile she runs, Carla intends to drink 14 quarts of water. How much water will she consume if she runs six miles?

Explanation:

The correct answer is c: 1 1/2 quarts of water.

If Kristina drinks 1/4 quart of water for every mile, she is essentially drinking 1/4+1/4+1/4+1/4+1/4+1/4 quarts of water.
The sum of this list of fractions is 1 2/4 or in simplest form, 1 1/2.

#### Marjorie put $5,000 into a savings account at the start of 2009. The account pays an annual interest rate of 4%. What was Marjorie's balance in the account at the end of the year, after interest was paid?

Explanation:

5000 X 4% = 200

5000 + 200 = $5200

#### In the following proportion, find the missing variable.

8/3 = x/9

Explanation:

Proportions are ratios that are equal to one another. We can solve
for the missing variable by using cross multiplication to develop
an equation.

8/3 x x/9 >br>
8x9 = x x 3

Simplify.

72 = 3x:

Divide both sides of the equation by 3.

72/3 = 3x/3

Solve.

x = 24

#### On a pair of dice, what is the chance of rolling a one?

Explanation:

In order to solve this problem, we need to discuss probabilities. A
probability is generally defined as the chances or likelihood of an
event occurring. It is calculated by identifying two components:
the event and the sample space. The event is defined as the
favorable outcome or success that we wish to observe. On the
other hand, the sample space is defined as the set of all possible
outcomes for the event. Mathematically we calculate probabilities
by dividing the event by the sample space:

P _ event: particular phenomenon we Wish to observe
/sample space: total number of possible outcomes

Let's use a simple example: the rolling of a die. We want to know
the probability of rolling a one. We know that the sample space is
six because there are six sides or outcomes to the die. Also, we
know that there is only a single side with a value of one; therefore,

P = 1/6

Now, let's convert this into a percentage:

1
— = 0.1666

6
0.1666 x 100% = 16.6%

#### Calculate the value of x.

x/4 + 12 = 22

Explanation:

In order to solve this problem we need isolate the variable on the
left side 0 the equation. We will do this by performing the reverse
of the operations that were done to the variable. It is important to
note that what is done to one side of the equation needs to be
done on the other.

Let's start by writing the equation.

x
— + 12 = 22

4
Subtract 12 from both sides of the equation.

x
—+12—12 = 22—12

x
— = 10

4
Multiply both sides of the equation by 4.

x
— x 4 = 10 x 4

4
Solve.

x = 40

#### Calculate the perimeter of a square with these side lengths:

s=5

Explanation:

Perimeters can be calculated by adding together the side lengths
of a polygon. A square has four sides that are all the same length,
therefore, we can write the following formula to solve for the
perimeter.

P = s + s + s + s

We can rewrite this equation as the following:

P = 4s

In these equations the variable, .s, represents side length.

Substitute the known side length and solve.

P = 4 x 5

P = 20

#### Solve the inequalities below: 10x+44>84

Explanation:

In algebra an inequality is a relationship that holds through
different values of a variable. An inequality is considered to be
solved when the variable is isolated to one side of the
inequality. We will do this by performing the reverse of the
operations that were done to the variable. It is important to note
that what is done to one side of the inequality needs to be done
on the other.

Let's start by writing the inequality.

10x + 44 > 84

Subtract 44 from both sides of the inequality.

10x + 44—44 > 84—44

10x > 40

Divide each side of the inequality by 10.

10x/10 > 40/10

Solve.

x > 4
The variable is greater than four.

#### Sarah is paid $1500 every week. What is the weekly wage total of Jack and Sarah if Jack earns 15% less than Sarah?

Explanation:

Start by finding out how much Jack makes. Since he makes
15% less than Sarah, we can write the following to find Jack's
weekly salary:

1500 — 0.15(1500) = 1275

Jack must make $1275 each week. Now, add together their
salaries to find the sum.

1500 + 1275 = 2775

#### Sam weighed 240 pounds when he began his diet. He had shed 112 pounds in the first month. He lost 10% of his residual weight in the second month. Sam's current weight is

Explanation:

Start by finding how much weight Steve lost after the first month.
Since he lost 1/12 of his starting weight of 240, he must have lost
20 pounds.

This means that at the end of his first month, he weighed

220 pounds.

Since he lost 10% of his remaining weight in the second month,
he must have lost 22 pounds from his 220 pounds.

Thus, Sam must weigh 198 pounds now.

#### Solve for x as follows:

5x+12=7x+2

Explanation:

5x + 12 = 7x + 2

Start by subtracting both sides by 5x.

12 = 2x + 2

Next, subtract both sides by 2.

2x = 10

Finally, divide both sides by 2.

x = 5

#### Which of the following is the least common multiple of 3 and 13?

Explanation:

Start by listing out multiples of 3:

3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39,42

Next, list out multiples of 13:

13 : 13,26,39, 52

Now, find the smallest number that is found in both lists. In this
case, the least common multiple must be 39.

#### What is the result of multiplying 5/6 and 3/8?

Explanation:

Since the question asks for the product, you will need to multiply
the two fractions. Recall that in multiplying two fractions, you will
multiply the numerators together and then multiply the
denominators together.

5/6 x 3/8 = 15/48 >br>
Next, reduce the fraction.

15/48 = 5/16

#### 325 volumes can be stored in a school library's shelves. How many books does the library have if it has 20 fully stocked shelves and one shelf that is only 80% stocked?

Explanation:

Start by finding out how many books the 20 full shelves can hold
by multiplying it by the number of books held per shelf.

20 X 325 = 6500

Next, find out how many books are held by the shelf that is not
completely full.

325 X 0.8 = 260

Now, add the two together to find how many books total are in
the library.

6500 + 260 = 6760

#### Ruby works as a science lab assistant at $12.50 per hour. How many 40-hour work weeks will she have to put in to cover the cost of a $3000 car?

Explanation:

Start by figuring out how much Rachel can earn in each week by
multiplying her hourly rate by the number of hours worked each
week.

Earning each week = 12.50 X 40 = 500

Now, divide the amount she needs to earn by the amount earned
each week to find how many weeks she will need to work to earn
that amount.

3000/500 = 6

Ruby must work for 6 weeks in order to earn enough for the car.

#### Amy wishes to wallpaper her room, which consists of four rectangular walls measuring 15 feet by 12 feet each. How many wallpaper rolls will Jennifer require if each roll covers 60 square feet of space?

Explanation:

Start by finding out the total square footage of wallpaper needed.
Find the area of one wall. Recall that in order to find the area of a
rectangle, you must multiply the length by the width.

Area of One Wall = 15 x 12 = 180

Since we have four identical walls,

Total Area of Walls = 4 x 180 = 720

Now divide this by the amount of square feet covered by each roll
of wallpaper to find how many rolls are needed.

Rolls of wallpaper needed = 720/60 = 12

#### Analyze:

15×8−12+25

Explanation:

In the order of operations, in the absence of grouping symbols,
multiplication takes precedence over addition and subtraction.
Multiply 15 by 8 first:

15 X 8 — 12 + 25

= 120 — 12 + 25

Addition and subtraction have equal precedence and are worked
in Ieft-to-right order. Subtract 120 and 12 next:

= 108 + 25

Now add:

= 133

#### Base on the scores below, give the median:

83, 87, 99, 90, 82, 84

Explanation:

To find the median of a group of scores, first, arrange the scores
from least to greatest:

{82, 83, {\color{Red} 84, 87}, 90, 99}

There are an even number of scores, so the median is the mean of
the two scores that fall in the middle, which are noted in red
above. Add the scores and divide by two:

84 + 87/ 2 = 171/2 = 85.5

#### Twenty bottles are chosen to see if a machine on an assembly line is filling bottles with the right amount of soda. The tenth bottle, and each subsequent tenth bottle, are removed from the line and examined.

Which kind of sampling is this an example of?

Explanation:

The sample in this scenario is selected from the population by
choosing obects that occur at regular intervals. That makes this
an example of systematic sampling.