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HSPT Math : HSPT Mathematics

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #517 : Arithmetic

$5\frac{5}{9} + 3 \frac{7}{9}$

Possible Answers:

$9\frac{1}{3}$

$9\frac{2}{3}$

$9\frac{1}{2}$

$8 \frac{1}{3}$

Correct answer:

$9\frac{1}{3}$

Explanation:

$5\frac{5}{9} + 3 \frac{7}{9}$

Add the whole numbers and fractions separately.

$(5 + 3) + \frac{5+7}{9}$

$8 + \frac{12}{9}$

$8 + 1\frac{3}{9} = 9 \frac{3}{9}$

Reduce to simplest form by dividing the numerator and the denominator by the greatest common factor of 3 and 9, which is 3.

$9\frac{3\div 3}{9\div 3} = 9\frac{1}{3}$

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Example Question #518 : Arithmetic

$\frac{3x-1}{4x-1} + \frac{x-2}{x+3}$

Possible Answers:

$\frac{8x^{3}-1}{(4x-1)(x+3)}$

$\frac{7x^{2}+x-1}{(4x-1) (x+3)}$

$\frac{7x^{2}-x-1}{(4x-1) (x+3)}$

$\frac{7x^{2}+x+1}{(4x-1) (x+3)}$

Correct answer:

$\frac{7x^{2}-x-1}{(4x-1) (x+3)}$

Explanation:

$\frac{3x-1}{4x-1} + \frac{x-2}{x+3}$

The method for solving the addition of an algebraic fraction with unlike denominators is the same as the method for fractions with unlike denominators; find the common denominator.

The common denominator is (4x-1) (x+3)

Using the FOIL Method, cross multiply:

$(3x-1) (x+3) = 3x^{2} +8x-3$ .

Using the FOIL Method, cross multiply: $(x-2) (4x-1) = 4x^{2} -9x +2$ .

$\frac{3x^{2}+ 8x-3}{(4x-1) (x+3)} + \frac{4x^{2}-9x +2}{ (4x-1)(x+3)} =$ $\frac{7x^{2}-x-1}{(4x-1) (x+3)}$

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Example Question #519 : Arithmetic

$\frac{4x}{1} +\frac{1}{(x-3)}$

Possible Answers:

$-\frac{8x +1}{x-3}$

$\frac{4x^{2}+12x+1}{x-3}$

$\frac{4x^{2}-12x+1}{x-3}$

$\frac{4x^{2}-12x-1}{x-3}$

Correct answer:

$\frac{4x^{2}-12x+1}{x-3}$

Explanation:

$\frac{4x}{1} +\frac{1}{(x-3)}$

The method for solving the addition of an algebraic fraction with unlike denominators is the same as the method for fractions with unlike denominators; find the common denominator.

The common denominator is (x-3)

$\frac{4x (x-3)}{x-3} + \frac{1}{x-3}$

$4x (x-3) = 4x^{2} - 12x+1$

$\frac{4x}{1} +\frac{1}{(x-3)} =$

$\frac{4x^{2}-12x+1}{x-3}$

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Example Question #1114 : Hspt Mathematics

The measurement of the base of an isosceles triangles is $1\frac{5}{6} cm$ . The sides measure $1\frac{2}{3}cm$ each. What is the perimeter of this triangle?

Possible Answers:

$3\frac{1}{6}cm$

$5\frac{1}{6}cm$

$3\frac{1}{2}cm$

$5\frac{1}{3}cm$

Correct answer:

$5\frac{1}{6}cm$

Explanation:

The formula for the perimeter of a triangle is P = a +b+c where each of the variables represents one of the measurements for each side of the triangle.

$1\frac{5}{6} + 1\frac{2}{3} + 1\frac{2}{3}$ Two sides of an isosceles triangle are equal.

Convert all mixed number (whole number and fraction), to improper fractions.

$1\frac{5}{6} = \frac{(6\times 1)+5}{6} = \frac{11}{6}$

$1\frac{2}{3} = \frac{(3\times 1)+2}{3} =\frac{5}{3}$

$\frac{11}{6} +\frac{5}{3} +\frac{5}{3}$

Because the denominators are not the same, create equivalent fractions with the same denominator. Find the least common multiple of LCM of 3 and 6.

Multiples of 3 are 3,6,9, and 12.

Multiples of 6 are 6,12, 18, 24, and 30.

The LCM which becomes the LCD or least common denominator of 3 and 6 is 6.

$\frac{5}{3} =\frac{10}{6}$

$\frac{11}{6} +\frac{10}{6} +\frac{10}{6} = \frac{11+10=10}{6} = \frac{31}{6}$

$\frac{31}{6} = 5\frac{1}{6}$

The perimeter of this isosceles triangle is $5\frac{1}{6}cm$ .

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Example Question #521 : Concepts

Two line segments have lengths of $2\frac{3}{4} inches$ and $2\frac{5}{6} inches.$ What is the total measurement of these two line segments?

Possible Answers:

$4\frac{2}{3} inches$

$5\frac{7}{12} inches$

$4\frac{11}{12} inches$

$4\frac{3}{4} inches$

Correct answer:

$5\frac{7}{12} inches$

Explanation:

$2\frac{3}{4} +2\frac{5}{6}$

Convert all mixed numbers to improper fractions.

$2\frac{3}{4} = \frac{(4\times 2)+3}{4} = \frac{11}{4}$

$2\frac{5}{6} = \frac{(6\times 2)+5}{6} = \frac{17}{6}$

$\frac{11}{4} +\frac{17}{6}$

Because the denominators are not the same, find the LCD of 4 and 6.

Multiples of 4 are 4,8,12, 16.

Multiples of 6 are 6 and 12.

The LCM or the LCD of 4 and 6 is 12. Then, create equivalent fractions.

$\frac{11}{4} = \frac{33}{12}$ Both numerator and denominator were multiplied by 3.

$\frac{17}{6} =\frac{34}{12}$ Both numerator and denominator were multiplied by 2.

$\frac{33}{12} +\frac{34}{12} = \frac{33+34}{12} =\frac{67}{12}$

$\frac{67}{12} = 5\frac{7}{12}$

The sum of the two line segments is $5\frac{7}{12} inches.$

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Example Question #521 : Arithmetic

What is a fraction form of .036?

Possible Answers:

$\dpi{100} \frac{9}{250}$

$\dpi{100} \frac{1}{4}$

$\dpi{100} \frac{36}{100}$

$\dpi{100} \frac{1}{36}$

Correct answer:

$\dpi{100} \frac{9}{250}$

Explanation:

The fraction form of .036 is $\dpi{100} \frac{36}{1000}$ . None of our answers match this fraction, so we must reduce it. The easiest way to do so is to divide the top and bottom by 2.

$\dpi{100} \frac{36}{1000}=\frac{18}{500}$

We can divide by 2 again:

$\dpi{100} \frac{18}{500}=\frac{9}{250}$

This is one of our answers (and also the fraction in its most reduced form).

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Example Question #522 : Arithmetic

$\dpi{100} 2\frac{1}{4}+5\frac{4}{5}=$

Possible Answers:

$\dpi{100} 8$

$\dpi{100} 7\frac{4}{9}$

$\dpi{100} 7\frac{4}{5}$

$\dpi{100} 8\frac{1}{20}$

Correct answer:

$\dpi{100} 8\frac{1}{20}$

Explanation:

First add the whole numbers.

$\dpi{100} 2+5=7$

Then add the fractions. In order to this, the fractions need to have a common denominator. The denominators are 4 and 5, so we need to find the least common multiple of 4 and 5. We can do this by finding all the multiples of the larger number (5) and try to divide each of them by 4.

5: No

10: No

15: No

20: Yes

So the least common multiple is 20. We can multiply $\dpi{100} 4\times 5$ to get 20, and $\dpi{100} 5\times 4$ to get 20.

$\dpi{100} \frac{1}{4}+\frac{4}{5}=\frac{5\times 1}{5\times 4}+\frac{4\times 4}{4\times 5}=\frac{5}{20}+\frac{16}{20}=\frac{21}{20}$

We convert $\dpi{100} \frac{21}{20}$ to $\dpi{100} 1\frac{1}{20}$ and add it to 7 to get $\dpi{100} 8\frac{1}{20}$ .

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Example Question #1 : Percentages

What is 32% of 2,000?

Possible Answers:

800

160

640

1,600

Correct answer:

640

Explanation:

Taking 32% of a number is the same as multiplying that number by 0.32. We therefore take the product:

$0.32 \cdot 2,000 = 640$

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Example Question #412 : Rational Numbers

Which of the following operations is equivalent to taking of a number?

Possible Answers:

Dividing the number by

Moving the decimal point one place to the left, then doubling the result

Dividing the number by

Moving the decimal point one place to the left, then tripling the result

Dividing the number by

Correct answer:

Dividing the number by

Explanation:

Let's just pick a number at random, for example 100 .

of this number is , which is 100 divided by .

We can also work by simplifying the fractional form of . A percent can be written as the number divided by 100 .

$=\frac{25}{100}$

We can simplify this fraction: $\frac{25}{100}=\frac{5}{20}=\frac{1}{4}$ .

Either way, we get the same answer.

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Example Question #2 : Percentages

What percent of 12,000 is 3,300?

Possible Answers:

27.5%

28.5%

26%

25%

24.5%

Correct answer:

27.5%

Explanation:

To find out what percent a part is of a whole , evaluate the expression

$\frac{P}{W} \cdot 100 = \frac{3,300}{12,000} \cdot 100 = 27.5$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #517 : Arithmetic

Example Question #518 : Arithmetic

Example Question #519 : Arithmetic

Example Question #1114 : Hspt Mathematics

Example Question #521 : Concepts

Example Question #521 : Arithmetic

Example Question #522 : Arithmetic

Example Question #1 : Percentages

Example Question #412 : Rational Numbers

Example Question #2 : Percentages

All HSPT Math Resources

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