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HSPT Math : Algebra

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Example Questions

Example Question #301 : Algebra

$f (x) = x^{2} + 4x - 10$ $\displaystyle f (x) = x^{2} + 4x - 10$

Evaluate: f (-3) $\displaystyle f (-3)$

Possible Answers:

$\displaystyle 11$

$\displaystyle -7$

$\displaystyle -31$

$\displaystyle -13$

Correct answer:

$\displaystyle -13$

Explanation:

$f (x) = x^{2} + 4x - 10$ $\displaystyle f (x) = x^{2} + 4x - 10$

$f (-3) = (-3)^{2} + 4(-3) - 10$ $\displaystyle f (-3) = (-3)^{2} + 4(-3) - 10$

$\displaystyle f (-3) =9-12 - 10$

$\displaystyle f (-3) =-13$

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Example Question #302 : Algebra

$2^{2}*3^{2}=$ $\displaystyle 2^{2}*3^{2}=$

Possible Answers:

$\displaystyle 5$

$\displaystyle 80$

$\displaystyle 13$

$\displaystyle 36$

Correct answer:

$\displaystyle 36$

Explanation:

First, solve the exponents:

$2^{2}=4$ $\displaystyle 2^{2}=4$

$3^{2}=9$ $\displaystyle 3^{2}=9$

Then, solve the equation:

4*9=36 $\displaystyle 4*9=36$

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Example Question #303 : Algebra

$5^{2}*4^2=$ $\displaystyle 5^{2}*4^2=$

Possible Answers:

400 $\displaystyle 400$

$\displaystyle 41$

$\displaystyle 13$

$\displaystyle 80$

Correct answer:

400 $\displaystyle 400$

Explanation:

First, solve the exponents:

$5^{2}=25$ $\displaystyle 5^{2}=25$

$4^{2}=16$ $\displaystyle 4^{2}=16$

Then, solve the equation:

$\displaystyle 25*16=400$

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Example Question #304 : Algebra

6r*11r= $\displaystyle 6r*11r=$

Possible Answers:

$66r^{2}$ $\displaystyle 66r^{2}$

$611r^{2}$ $\displaystyle 611r^{2}$

$17r^{2}$ $\displaystyle 17r^{2}$

$5r^{3}$ $\displaystyle 5r^{3}$

Correct answer:

$66r^{2}$ $\displaystyle 66r^{2}$

Explanation:

First, multiply the whole numbers.

Then, keep the variable the same and add an exponent totalling the number of variables in the equation:

$6r*11r=66r^{2}$ $\displaystyle 6r*11r=66r^{2}$

Answer: $66r^{2}$ $\displaystyle 66r^{2}$

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Example Question #305 : Algebra

$\displaystyle 21s*15s=$

Possible Answers:

$315s^{2}$ $\displaystyle 315s^{2}$

$300s^{2}$ $\displaystyle 300s^{2}$

$\displaystyle 6s$

315s $\displaystyle 315s$

Correct answer:

$315s^{2}$ $\displaystyle 315s^{2}$

Explanation:

First, multiply the whole numbers.

Then, keep the variable the same and add an exponent totalling the number of variables in the equation:

$21s*15s=315s^{2}$ $\displaystyle 21s*15s=315s^{2}$

Answer: $315s^{2}$ $\displaystyle 315s^{2}$

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Example Question #306 : Algebra

17r*7r= $\displaystyle 17r*7r=$

Possible Answers:

$24r^{2}$ $\displaystyle 24r^{2}$

10r $\displaystyle 10r$

119r $\displaystyle 119r$

$119r^{2}$ $\displaystyle 119r^{2}$

Correct answer:

$119r^{2}$ $\displaystyle 119r^{2}$

Explanation:

Multiply the whole numbers, and raise the variable's exponent by one:

$17r*7r=119r^{2}$ $\displaystyle 17r*7r=119r^{2}$

Answer: $119r^{2}$ $\displaystyle 119r^{2}$

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Example Question #918 : Concepts

Solve for $\displaystyle x$:

2x+4=-2 $\displaystyle 2x+4=-2$

Possible Answers:

x=-2 $\displaystyle x=-2$

x=-3 $\displaystyle x=-3$

x=-1 $\displaystyle x=-1$

x=0 $\displaystyle x=0$

Correct answer:

x=-3 $\displaystyle x=-3$

Explanation:

2x+4=-2 $\displaystyle 2x+4=-2$

$\displaystyle 2x+4-4=-2-4$

2x=-6 $\displaystyle 2x=-6$

$\frac{2x}{2}=\frac{-6}{2}$ $\displaystyle \frac{2x}{2}=\frac{-6}{2}$

x=-3 $\displaystyle x=-3$

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Example Question #919 : Concepts

Solve for $\displaystyle t$:

$-\frac{t}{4}+7=\frac{5}{2}$ $\displaystyle -\frac{t}{4}+7=\frac{5}{2}$

Possible Answers:

t=-38 $\displaystyle t=-38$

t=8 $\displaystyle t=8$

t=18 $\displaystyle t=18$

t=38 $\displaystyle t=38$

Correct answer:

t=18 $\displaystyle t=18$

Explanation:

$-\frac{t}{4}+7=\frac{5}{2}$ $\displaystyle -\frac{t}{4}+7=\frac{5}{2}$

$4(-\frac{t}{4}+7)=4(\frac{5}{2})$ $\displaystyle 4(-\frac{t}{4}+7)=4(\frac{5}{2})$

$\displaystyle -t+28=10$

$\displaystyle -t+28-28=10-28$

-t=-18 $\displaystyle -t=-18$

$\displaystyle -1(-t)=-1(-18)$

t=18 $\displaystyle t=18$

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Example Question #307 : Algebra

Solve for $\displaystyle x$:

4x+8=4 $\displaystyle 4x+8=4$

Possible Answers:

x=-2 $\displaystyle x=-2$

x=-1 $\displaystyle x=-1$

x=1 $\displaystyle x=1$

x=0 $\displaystyle x=0$

Correct answer:

x=-1 $\displaystyle x=-1$

Explanation:

4x+8=4 $\displaystyle 4x+8=4$

$\displaystyle 4x+8-8=4-8$

4x=-4 $\displaystyle 4x=-4$

$\frac{4x}{4}=\frac{-4}{4}$ $\displaystyle \frac{4x}{4}=\frac{-4}{4}$

x=-1 $\displaystyle x=-1$

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Example Question #117 : How To Find The Solution To An Equation

Solve for $\displaystyle n$:

$\frac{n}{3}-4=2$ $\displaystyle \frac{n}{3}-4=2$

Possible Answers:

n=2 $\displaystyle n=2$

n=12 $\displaystyle n=12$

n=6 $\displaystyle n=6$

n=18 $\displaystyle n=18$

Correct answer:

n=18 $\displaystyle n=18$

Explanation:

$\frac{n}{3}-4=2$ $\displaystyle \frac{n}{3}-4=2$

$\frac{n}{3}-4+4=2+4$ $\displaystyle \frac{n}{3}-4+4=2+4$

$\frac{n}{3}=6$ $\displaystyle \frac{n}{3}=6$

$(3)(\frac{n}{3})=(6)(3)$ $\displaystyle (3)(\frac{n}{3})=(6)(3)$

n=18 $\displaystyle n=18$

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HSPT Math : Algebra

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #301 : Algebra

Example Question #302 : Algebra

Example Question #303 : Algebra

Example Question #304 : Algebra

Example Question #305 : Algebra

Example Question #306 : Algebra

Example Question #918 : Concepts

Example Question #919 : Concepts

Example Question #307 : Algebra

Example Question #117 : How To Find The Solution To An Equation

All HSPT Math Resources

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