2021 WASSCE mathematics PAPER 1 Solutions/ can you solve these?

Welcome back, my lovely viewers. Today, let's discuss three questions that I've chosen. From the 2021 Paper One, the first question states: solve to raise the power of the square root of 2x. plus 1 equals 32. The options are a 13, b 24, c 12, and d 11. To solve this, this is actually Coming from indices, okay, and other indices, there are some laws that we can apply, so let's solve. this raised to the power of 2x plus 1 equals 32. First, let's make this less ambiguous—we all Know that the square root of x is the same thing as x to the power of 1 over 2. Okay, so let's write that. Here that means we can rewrite this as 2 to the power of what, 2x plus 1 raised to the power of Okay, now we can actually express this as 2 to the power of 2x plus 1. Raising to the power of half is equal to what? This 32 can be written as 2 to the power of 5. This is actually the first question; I have the second question here, and I have the third question. that we still solve, so stick around and enjoy the ride, okay? Let's continue whenever we are. when we solve anything regarding the indices and reach the point where the bases are equal, then just know that your powers are also equal, so since these bases are equal, that means that 2 to the power of x plus 1 raised to the power of half is equal to 5. Okay, now we don't have any another option here is to square both sides of this equation because when we square both sides From this equation, we'll be able to eliminate this half, so we have 2x plus 1 raised to the power of half. squared is equal to 5 squared, so these two will divide to give us one, yes, because x to the the power of a to the power of b is the same thing as x to the power of a times b, so half times two will give us one that means we have that this is 2x plus one equals five squared we give us 25 Okay, now um, we subtract one from both sides of this equation, and when we do that We have that 2x is equal to 25 minus 1, so 2x is equal to 24. When we divide both sides by two, we will have that x is equal to 12, which means that the solution to this question is is option C, which is what C is equal to 12, all right? That is for question one. Now let's If log₂(10) = m and log₃(10) = n, solve the following question. Find log₁₀ 24 in terms of m and n, given the following options: So let's do this: we are told that log base 10 of 2 is equal to m, and that log base 10 of 3 is equal to n, and we are asked to find log base 10 of 24 in terms of m and n, all right The first thing we need to know is that we need to factorize this in terms of two and three. Okay, factorize this 24 in terms of two and three, and when we do that, this is 24. If 2 divides 24, we'll have 12; if 2 divides 12, we'll have 6; if 2 divides 6, we'll have 3. Then 3 divides 3, we have 1; that means in terms of 2 and 3, we can express 24 as 2 times 2 times 2. 3 times 2 is the same as 2 to the power of 3. okay that means that the logarithm base 10 of 24 can be written as the logarithm base 10 of 2 to the power of 3, that is 2 times 2 times 2 times this 3, okay. All right, now there is this law of logarithms reading. which states that log a b log a b is the same thing as log a plus log b, okay that log of a times b equals log a plus log b, okay? Now let's incorporate this into what we just did. here that means we can express this as what logarithm to base 10 of 2 to the power of 3 plus log base 10 of 3. Now let's recall another law of logarithms which states that log a to the power of n can be expressed as n log a, which means the power can be brought down. Okay, all right, so log a to the power of n can be expressed as n log a. Now we can now write This one is log base 10 of 3 plus log base 10 of 2. Now this is the time we do substitution. recall that the logarithm base 10 of 2 is equal to m and the logarithm base 10 of 3 is equal to n, which means We can rewrite this as: 3 log base 10 of 2 is m, plus log base 10 of 3 is n. That means this is our solution: 3n plus 2. Now when we search for it here That means the solution is a, which is 3 m. These are the options: 3 m plus n. So these are the options. and this is what we got, which means a is our solution, a is our solution. All right, now let's Simplify: $ 2\sqrt{7} - 14\sqrt{7} $ plus 7 over root 7; if you are to solve this, we will understand what rationalization is all about To rationalize any denominator, the first thing we need to do is we need to multiply the the numerator and the denominator of that sword by whatever we have as our denominator—this is what I mean, now we are asked to simplify this: this is 2 root 7 minus 14 over root 7. Now this root 7 Here is a sword, and it's not supposed to be the denominator, which means we need to rationalize it. Okay, and to rationalize this, it's going to be times root 7 over root 7. All right, so this one is plus. 7 over root 21, we are going to rationalize the denominator here again since what we have as our is a sword, so to rationalize it we have to multiply the numerator and the denominator By the sword, so we go ahead and solve; this is equal to 2 root 7. minus 14 times root 7 gives you 14 root 7 over root 7 times root 7, which gives you 7 Okay, plus 7, excuse me, 7 times root 21. We give you 7 root 21 over root 21 times root 21. We give you You're 21, all right. In this case, 7 divides itself 1. If we divide 14, we get 2, which means the same applies here as well. 7 divided by itself is 1; if we divide 21, we get 3, which means we have 2 root 7 minus another 2 root 7. plus square root of 21 divided by 3, okay, but 2 times square root of 7 minus 2 times square root of 7 is 0, so we are left with only One option is what is root 21 over 3, and this is the answer. Now let's check our options. Root 21 over 3 is option C, and that is the last question. 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