Good day students welcome to the accuplacer elementary algebra sample question review to get a copy of this document you can just go to the www.collegeboard.com website they have these questions and a lot of support materials to help you get ready for the test okay lets go ahead and take a look question 1 if a represents the number of apples purchased at 15 cents and b represents the number of bananas purchased at 10 cents which of the following represent the total value of purchases in cents so you just need to remember the equation for total price so basically the total the total price is given by total price is normally given by quantity multiplied by the unit price okay so lets look at we have two items here lets look at apples lets look at apples for example for apples the total for apples is going to be the quantity how many apples were bought A number of apples were bought and that will be multiplied by the unit price which is 15 okay this can be written as 15 A you normally write the number before the variable okay so there goes for apples and then we have bananas so for bananas the quantity is B multiplied by the unit price of bananas which is ten cents each alright so this is the total price of bananas that we can write as 10B okay so it asks for the total value of the purchases thats banana plus apples so total purchase total purchases is simply the sum of these two quantities right here which is going to be 15 A plus 10 B okay that is option letter D alright lets move on to question number two what is the square root of two times the square root of fifteen and this involves the use of property of radicals known as the product property so we have root a times root b these terms under the square root are known as the radicands anytime you are multiplying radicals of this nature all you have to do is multiply the radicands so its a times b which can be written as root ab okay so in this case what we are doing here we have the square root of two times the square root of 15. the radicands are two and fifteen so the product is simply going to be the square root of two times fifteen okay and that becomes the square root of thirty so our final answer is option b I am sorry lol the answer is option c moving along to question number 3 it says what is the value of the expression 2x^2+3xy-4y^2 when x is 2 and y equals -4 so what we are going to do here is substitute these values into this expression so we have two x squared plus three xy minus four y squared so x is two y is negative four. what does that mean it means anywhere we see x we replace that with two and anywhere we see y we replace it with negative four. anytime we substitute expressions into substitute values into an expression always make use of parenthesis okay so we are going to write two parenthesis two squared plus three times two for x and negative four for y minus four times y squared is negative four squared okay the reason why its always good to use parenthesis is because it prevents you from making mistakes associated with the signs alright so in this case we have we are going to use the order of operations to simplify this so we are going to do exponents first and then we will multiply then and or subtract okay so remember please excuse my dear aunt sally we don't have parenthesis here we are just dealing with exponents now alright lets evaluate the exponents so in this term right here we are going to square the two so two squared is two times four plus now when you are multiplying multiple terms you have to do two at a time okay so two times negative four is going to be times negative 8 okay and then we have that and then be careful here anytime you square a negative its a positive okay there is a trick for remembering how to multiply signs anytime the signs are the same you have a plus and if the signs are different you have a minus okay so you can also use the peace sign approach minus minus plus and there goes your peace sign well this basically tells us that when you multiply two minuses you get a plus if you multiply a minus and a plus you get a minus if you multiply a minus and a plus you get a a minus okay so there you have it let me make a nicer peace sign because i am going to be making multiple references to this mnemonic device. okay so just keep track of the nature of the signs as long as the signs are different the product of the signs will always be minus and if the signs are the same its going to be plus okay so minus times minus is plus so you can go this times this is that, that times that is that or minus time minus is plus plus times plus is plus and minus times plus is minus and plus times minus is minus alright so any of these tools that help you remember is good so this is minus minus four squared so minus four squared is minus four times minus four which is going to be positive so we have positive sixteen right here okay alright moving along so multiplying we are doing the multiplying portion of