SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving SAT questions that focus on Factoring.
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SAT 2015 Test. $9a^4+12a^2b^2+4b^4$
Which of the following is equivalent to the expression shown above?
A) $(3a^2+2b^2)^2$
B) $(3a+2b)^4$
C) $(9a^2+4b^2)^2$
D) $(9a+4b)^4$
Answer:
Let's develop the expression in option A:
$(3a^2+2b^2)^2=$
$9a^4+2(3a^2)(2b^2)+4b^4=$
$9a^4+12a^2b^2+4b^4=$
Answer: A
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Friday, December 20, 2019
Monday, December 16, 2019
SAT Practice Test - Math - Interest Rate, and Profit Margin
SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving questions that focus on Interest Rate, and Profit Margin.
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SAT Practice Test 2015. The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns 120 dollars at a performance where 8 people attend.
The performer uses 43% of the money earned to pay the costs involved in putting on each performance. The rest of the money earned is the performer’s profit. What is the profit (in dollars) the performer makes at a performance where 8 people attend?
A) 51.60
B) 57.00
C) 68.40
D) 77.00
Answer:
If the performer uses 43% of the money to pay the costs, the profit will be 57%. Thus we just have to find what is 57% of 120 dollars:
$Profit=0.57(120)$
$Profit=68.4$
Answer: C
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SAT Practice Test 2015. Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was 100 dollars, and she uses the expression $100(x)^t$ to find the value of the account after t years.
What is the value of x in the expression?
Answer:
x is the interest rate, that is, x=1.02
Answer: 1.02
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SAT 2015 Test. Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was 100 dollars, and she uses the expression $100(x)^t$ to find the value of the account after t years.
Jessica’s friend Tyshaun found an account that earns 2.5 percent interest compounded annually. Tyshaun made an initial deposit of 100 dollars into this account at the same time Jessica made a deposit of 100 dollars into her account. After 10 years, how much more money will Tyshaun’s initial deposit have earned than Jessica’s initial deposit? (Round your answer to the nearest cent and ignore the dollar sign when gridding your response.)
Answer:
Jessica will have: $J=100(1.02)^{10}=121,90$
Tyshaun will have: $T=100(1.025)^{10}=128,01$
Tyshaun(-)Jessicas: $128,01-121,90=6.11$
Answer: 6.11
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SAT 2015 Test. Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?
A) $0.88p$
B) $\frac{p}{0.88}$
C) $(0.8)(1.08)p$
D) $\frac{p}{(0.8)(1.08)}$
Answer:
Let's call the original price R.
The price with a 20% discount, and before tax, is given by the formula: $R(0.8)$
The total amount she paid to the cashier is this value plus tax:
$p=R(0.8)(1.08)$
$\frac{p}{(0.8)(1.08)}=R$
Answer: D
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SAT Practice Test. A company’s manager estimated that the cost C, in dollars, of producing n items is $C=7n+350$. The company sells each item for 12 dollars. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?
A. $n<70$
B. $n<84$
C. $n>70$
D. $n>84$
Answer:
The total income for this company is: $12.n$
The company will make a profit when total income is greater than the total cost. Therefore,
$12n>7n+350$
$12n-7n>350$
$5n>350$
$n>70$
Answer: C
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SAT Practice Test 2015. The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns 120 dollars at a performance where 8 people attend.
The performer uses 43% of the money earned to pay the costs involved in putting on each performance. The rest of the money earned is the performer’s profit. What is the profit (in dollars) the performer makes at a performance where 8 people attend?
A) 51.60
B) 57.00
C) 68.40
D) 77.00
Answer:
If the performer uses 43% of the money to pay the costs, the profit will be 57%. Thus we just have to find what is 57% of 120 dollars:
$Profit=0.57(120)$
$Profit=68.4$
Answer: C
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SAT Practice Test 2015. Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was 100 dollars, and she uses the expression $100(x)^t$ to find the value of the account after t years.
What is the value of x in the expression?
Answer:
x is the interest rate, that is, x=1.02
Answer: 1.02
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SAT 2015 Test. Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was 100 dollars, and she uses the expression $100(x)^t$ to find the value of the account after t years.
Jessica’s friend Tyshaun found an account that earns 2.5 percent interest compounded annually. Tyshaun made an initial deposit of 100 dollars into this account at the same time Jessica made a deposit of 100 dollars into her account. After 10 years, how much more money will Tyshaun’s initial deposit have earned than Jessica’s initial deposit? (Round your answer to the nearest cent and ignore the dollar sign when gridding your response.)
Answer:
Jessica will have: $J=100(1.02)^{10}=121,90$
Tyshaun will have: $T=100(1.025)^{10}=128,01$
Tyshaun(-)Jessicas: $128,01-121,90=6.11$
Answer: 6.11
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SAT 2015 Test. Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?
A) $0.88p$
B) $\frac{p}{0.88}$
C) $(0.8)(1.08)p$
D) $\frac{p}{(0.8)(1.08)}$
Let's call the original price R.
The price with a 20% discount, and before tax, is given by the formula: $R(0.8)$
The total amount she paid to the cashier is this value plus tax:
$p=R(0.8)(1.08)$
$\frac{p}{(0.8)(1.08)}=R$
Answer: D
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SAT Practice Test. A company’s manager estimated that the cost C, in dollars, of producing n items is $C=7n+350$. The company sells each item for 12 dollars. The company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?
A. $n<70$
B. $n<84$
C. $n>70$
D. $n>84$
The total income for this company is: $12.n$
The company will make a profit when total income is greater than the total cost. Therefore,
$12n>7n+350$
$12n-7n>350$
$5n>350$
$n>70$
Answer: C
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Sunday, December 15, 2019
SAT Practice Test - Math - Modulus Function
SAT practice tests arranged by topic and difficulty level. In this section find tips and tactics for solving questions that focus on Modulus Functions.
Learn about Modulus Function
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SAT Practice Test 2015. Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to -1?
A) $y=|x|-2$
B) $y=x^2-2$
C) $y=(x-2)^2$
D) $y=x^3-2$
Answer:
Choice A and B are wrong, because for x=0, y=-2
Choice C is correct, because $y\geq0$, for any value of x.
Choice D is wrong, because y can take any value.
Answer: C
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SAT Practice Test 2015. For what value of n is $|n-1|+1$ equal to 0?
A) 0
B) 1
C) 2
D) There is no such value of n.
Answer:
$|n-1|+1=0$
$|n-1|=-1$
The modulus of any number gives us the magnitude of that number. Therefore the modulus is always positive.
Answer: D
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Learn about Modulus Function
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SAT Practice Test 2015. Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to -1?
A) $y=|x|-2$
B) $y=x^2-2$
C) $y=(x-2)^2$
D) $y=x^3-2$
Answer:
Choice A and B are wrong, because for x=0, y=-2
Choice C is correct, because $y\geq0$, for any value of x.
Choice D is wrong, because y can take any value.
Answer: C
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SAT Practice Test 2015. For what value of n is $|n-1|+1$ equal to 0?
A) 0
B) 1
C) 2
D) There is no such value of n.
Answer:
$|n-1|+1=0$
$|n-1|=-1$
The modulus of any number gives us the magnitude of that number. Therefore the modulus is always positive.
Answer: D
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