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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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Example Question #1203 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

$18\div(5-2)$

Possible Answers:

Correct answer:

Explanation:

$18\div(5-2)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the division.

5-2=3

$18\div3=6$

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Example Question #1204 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

$16+3\times9+(42-10)$

Possible Answers:

Correct answer:

Explanation:

$16+3\times9+(42-10)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then addition.

42-10=32

$3\times9=27$

16+27+32=75

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Example Question #1 : Word Problems

Mark is three times as old as his son Brian. In ten years, Mark will be years old. In how many years will Mark be twice as old as Brian?

Possible Answers:

Correct answer:

Explanation:

In ten years, Mark will be years old, so Mark is 43-10 = 33 years old now, and Brian is one-third of this, or $33 \div 3 = 11$ years old.

Let be the number of years in which Mark will be twice Brian's age. Then Brian will be N + 11 , and Mark will be N + 33 . Since Mark will be twice Brian's age, we can set up and solve the equation:

2 (N + 11) = N + 33

2N + 22 = N + 33

2N + 22-N - 22 = N + 33 -N - 22

N = 11

Mark will be twice Brian's age in years.

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Example Question #1 : Word Problems

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?

Possible Answers:

Not enough information is given to determine the answer.

Correct answer:

Explanation:

Since Gary will be 37 in five years, he is 37 - 5 = 32 years old now. He is twice as old as Cathy, so she is $32 \div 2 =16$ years old, and in five years, she will be 16 + 5 = 21 years old.

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Example Question #81 : How To Solve Two Step Equations

A parking garage charges a minimum fee of $\$7$ to park in the garage. It also charges an additional fee of $\$2$ for every hour, or portion of an hour, in which a person parks in the garage. Cliff wants to pay a maximum of $\$20$ to park there. If he pulls into the garage at exactly $7\textup{:}00\textup { AM}$ , when must he leave at latest?

Possible Answers:

$12\textup{:}30\textup { PM}$

$1\textup{:}30\textup { PM}$

$2\textup{:}30\textup { PM}$

$1\textup{:}00\textup { PM}$

Correct answer:

$1\textup{:}00\textup { PM}$

Explanation:

Let be the number of hours that Cliff parks his car in the garage. Since he pays a flat fee of $\$7$ plus $\$2$ per hour or portion thereof, he pays 2X + 7 dollars. Since he does not want to spend more than $\$20$ ,

$2X + 7 \leq 20$

$2X + 7 - 7 \leq 20 - 7$

$2X \leq 13$

$2X \div 2 \leq 13 \div 2$

$X \leq 6.5$

Since a portion of an hour counts as much as an hour, must be a whole number.

$X \leq 6.5$

implies that

$X \leq 6$ .

Cliff can park in the garage for a maximum of 6 hours, and since he entered the garage at $7:00\textup { AM}$ , he must exit hours later:

7+ 6 - 12 = 1 ,

or $1:00\textup { PM}$ .

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Example Question #82 : How To Solve Two Step Equations

Solve the following:

$(12+13)\times2$

Possible Answers:

Correct answer:

Explanation:

$(12+13)\times2$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

12+13=25

$25\times2=50$

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Example Question #83 : How To Solve Two Step Equations

Solve:

$(34+17)\times2$

Possible Answers:

102

Correct answer:

102

Explanation:

$(34+17)\times2$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

34+17=51

$51\times2=102$

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Example Question #1 : How To Simplify Expressions

You are given that A,B,C are whole numbers.

Which of the following is true of AB +C if and are both odd?

Possible Answers:

AB +C is always odd.

AB +C is always odd if is even, and always even if is odd.

AB +C is always odd if is odd, and always even if is even.

None of the other statements are true.

AB +C is always even.

Correct answer:

AB +C is always odd if is even, and always even if is odd.

Explanation:

If is odd, then is odd, since the product of two odd whole numbers must be odd. When the odd number is added, the result, AB +C , is even, since the sum of two odd numbers must be even.

If is even, then is even, since the product of an odd number and an even number must be even. When the odd number is added, the result, AB +C , is odd, since the sum of an odd number and an even number must be odd.

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Example Question #1 : How To Simplify Expressions

Simplify the expression:

3x^2+9x+10x^2+5y+(-11x)

Possible Answers:

13x^2+2x-5y

15x^2+5y

13x^2-2x+5y

11x^2+5y

Correct answer:

13x^2-2x+5y

Explanation:

Combine all the like terms.

The x^2 terms can be combined together, which gives you 13x^2 .

When you combine the terms together, you get -2x .

There is only one term so it doesn't get combined with anything. Put them all together and you get

13x^2-2x+5y .

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Example Question #1 : How To Simplify Expressions

Simplify the following expression:

$\dpi{100} \small 2(4x-3x)-6t+5x$

Possible Answers:

$\dpi{100} \small 6x+11x$

$\dpi{100} \small 14x - 11xt$

$\dpi{100} \small 6t-7x$

$\dpi{100} \small 1x-6t+5$

$\dpi{100} \small 7x-6t$

Correct answer:

$\dpi{100} \small 7x-6t$

Explanation:

$\dpi{100} \small 2(4x-3x)-6t+5x$

First distribute the 2: $\dpi{100} \small 8x-6x-6t+5x$

Combine the like terms: $\dpi{100} \small 7x-6t$

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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1203 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #1204 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #1 : Word Problems

Example Question #1 : Word Problems

Example Question #81 : How To Solve Two Step Equations

Example Question #82 : How To Solve Two Step Equations

Example Question #83 : How To Solve Two Step Equations

Example Question #1 : How To Simplify Expressions

Example Question #1 : How To Simplify Expressions

Example Question #1 : How To Simplify Expressions

All HSPT Math Resources

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