Annie W.

Certified tutor at the University of Akron

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SAT

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Question:

If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?

Annie W.

Answer:

First, let's find k when they gave us values for x and y. Plug y = 24 and x = 6 into y = k x. We will get 24 = k * 6. Solving we can see k=4. Now that we know k is 4 and it does not change, let's use it to find a new value of y. Since 5 is our new value for x: y = k * x y = 4 * 5 y = 20 This is our answer! Not too bad, right?

PSAT

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Question:

What is the value of a if (2a + 3) − (4a − 8) = 7?

Annie W.

Answer:

To tackle this problem, we want the variable 'a' all by itself on one side of the = sign. STEP 1: Distribute Let's start with the distributive property. Looking at − (4a − 8) we need to distribute the − sign. If it helps you can think of this as −1 x (4a − 8). To distribute we need to take − 1 x 4a. (Negative times positive gives us a negative) We get − 4a. A popular mistake is to forget we also need to distribute the − 1 to the − 8. So − 1 x − 8. This gives us 8. (Negative times a negative gives us a positive) Let's rewrite the problem now. (2a + 3) − (4a − 8) = 7 becomes 2a + 3 − 4a + 8 = 7 STEP 2: Combine Like Terms 2a − 4a = −2a (Since 2a and − 4a are like terms) 3+8 = 11 (Since 3 and 8 are like terms) So we now have −2a+11 = 7 STEP 3: Solve for a −2a + 11 = 7 -11 -11 Subtract 11 from both sides to undo the addition of the 11 −2a + 0 = −4 ÷ -2 ÷ -2 Divide by -2 from both sides to undo -2 x a a = 2 Finally, we solved for a! You can check your answer by plugging in a=2 into the original equation. (2a + 3) − (4a − 8) = 7 (2*2 + 3) − (4*2 − 8) = 7 (4+3)-(8-8) = 7 7 - 0 = 7 7 = 7 This is a true statement so we are correct!

ACT

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Question:

When x =3 and y =5, by how much does the value of 3x^2 – 2y exceed the value of 2x^2 – 3y ?

Annie W.

Answer:

Okay, let's break this down. First, we will plug in x=3 and y=5 into the first expression, 3x^2 – 2y. The expression will now look like this: 3*3^2 – 2*5 We start with the exponents so the expression becomes: 3*9-2*5 Multiplication is next so we get: 27-10 Now we can subtract to get 17 So, when we plug in the x and y values for this expression, our answer is 17. Next, let's plug in x=3 and y=5 into the second expression, 2x^2 – 3y. Our expression now looks like 2*3^2 – 3*5. Simplifying we get 2*9-3*5 After multiplication: 18-15 After subtraction: 3 So, when we plug in the x and y values for this second expression, our answer is 3. Finally, we compare our two solutions (17 and 3) and see that the difference between then is 14. Therefore, when x =3 and y =5, 3x^2 – 2y exceeds 2x^2 – 3y by 14. Note: Don't forget to use your order of operations. (The acronym is PEMDAS. P stands for parentheses, E for exponents, M for multiplication, D for division, A for addition, S for subtraction. Some people remember this by using the mnemonic "Please excuse my dear aunt Sally". )

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