CXC 2026 PREPARATION

Added: 2026-05-11

[00:00:02]All right, so simplify as a fraction.

[00:00:08]So the LCM would have been 12. 3 into 12 four times, and then we expand, right?

[00:00:13]So 4 * 2 8 4 * 3 12 12 into 4 into 12 three times, three times x 3x 3 times -4 -12 So we can see that this will cancel with itself. So we have 8x + 3x over 12, which is 11x over 12.

[00:00:42]For this one is a write the following statement as an algebraic expression.

[00:00:46]The sum, sum mean to add. So I'm going to have to add.

[00:00:49]And it's multiplicative inverse. How could it be y?

[00:00:56]This 1 over y equal 5 times a number. So that's 5y.

[00:01:37]Try well, guys. My light you bought.

[00:01:40]Okay.

[00:01:41]You know it's a flow, not fixed. Now I use my data, sir. You know it's a You know it's a digital You know it's a fixed light, good.

[00:01:48]I understand. Uh-uh, every time it just blink off and come on back same time.

[00:01:58]All right, one, guys. I I don't even know if you guys are catching the last part of it cuz I didn't realize.

[00:02:04]Yeah, so Y plus the inverse and that'll be 1 over Y. Yes, we did. We did, sir.

[00:02:12]>> Okay. Okay. Okay. Yeah.

[00:02:16]All right, so do these two and then So, it's a factorize completely X squared.

[00:02:30]Cuz these are very easy. You just find the square root of each, right?

[00:02:35]One a positive, one a negative.

[00:02:40]But this one now a little bit different.

[00:02:42]2X squared plus 5X First, we multiply A times C.

[00:02:48]So, it's A times C, which is 2X squared times minus 12.

[00:02:55]Which would give us minus 24. And then we have 1 times 24 2 times 12 3 times 8 and 4 times 6. So, which one can give us the five?

[00:03:15]I think it'll be three and eight.

[00:03:17]So, it would be 2X squared plus 8X minus 3X. And this is supposed to be positive five.

[00:03:26]This one can give us the five and then minus 12.

[00:03:31]Put two brackets.

[00:03:33]So, the highest common factor that'll be two and then X also common. So, 2X into that leaves X.

[00:03:39]2X into 8X leaves four.

[00:03:42]Put your minus and then the highest common factor three and 12 that'll be three.

[00:03:48]And then we divide. So, three into three goes one time.

[00:03:53]Negative into negative positive, so that's positive four. So, it's x + 4, which is this in another bracket here, and then 2x - 3.

[00:04:06]That would have been the final answer for that one.

[00:04:09]And I get four marks for that.

[00:04:17]The formula of the volume of a cylinder is V = πr² h. Make R What I am going to do? Make R the subject of the formula.

[00:04:34]All right, so V is equal to πr² h. And we want to make R the subject, so that means we are going to get rid of everything including the pi, the square, and the h. All right? So, first I'm going to get rid of the pi and the h.

[00:04:49]Since they are times, we're going to divide by those. So, I'm going to divide by pi h.

[00:04:55]Anything I do to one side I do to the next side. So, this cancel, this cancel.

[00:05:00]So, we leave with V over pi h = r². Now, the opposite of square is square root, so I find the square root.

[00:05:10]And there you have it. It's the square root of V over pi h.

[00:05:16]That's our answer.

[00:05:22]All right, given that x² + ax = bx, work out the values of a and b.

[00:05:44]So, basically they only want us to just expand this one.

[00:05:48]Cuz they say all of this equal this. So we can expand the bracket.

[00:05:58]So x * x that's x squared.

[00:06:01]x * 2 2x and then we use 2 * all of this again. So 2 * x 2x 2 * 2 4 So these are the only like terms that would be 4x plus one. But you remember they said that A is here, all right?

[00:06:29]And this is x squared. So that means that A equal to 4 and B equal to 1.

[00:06:47]All right, so given that f of x is 4x minus 7 and g of x is 3x plus 1 over 2, determine the values of g 2 plus g 0 plus g 5. So first one is 0.

[00:07:05]This is 0 plus 1 over 2, which will go to a half.

[00:07:09]And for g 5 it will be 3 * 5 plus 1 over 2. So that's 15 plus 1 which will go to 8. So add a half plus 8 and that's 8 and a half.

[00:07:26]So you made a mistake. It will go to 16.

[00:07:28]15 plus 1 equals 16.

[00:07:32]No man, the final answer are 8, right?

[00:07:35]Yeah man, 8 and a half is the final, but when you add this up here, so you don't get 8. No man, because I divide it.

[00:07:43]Oh, you just divide it. Okay. Yeah.

[00:07:45]Yeah. Yeah.

[00:07:53]I try FG 5.

[00:07:55]Oh, we need to go up really.

[00:08:13]All right. So, FG 5. So, let me work out FG first, now. And the rule says the last function, write it down first.

[00:08:20]So, we have 3x + 1 over 2. This becomes our x in f. So, we are going to write back f, which is 4x - 7.

[00:08:31]And then we just work it out. Consider this all over 2. All right?

[00:08:36]Make it easier for you. So, 4 * 3 12. 4 * 1 4. And then - 7.

[00:08:44]So, it would be 12x - 3 over 2.

[00:08:48]Now, we can plug in our substitute 5 where for x.

[00:08:53]So, x equal to 5.

[00:08:57]So, 12 * 5 - 3 over 2.

[00:09:02]It is 60 - 3 over 2. So, that's 57 over 2.

[00:09:08]Our functions, we can leave it like that.

[00:09:11]All right?

[00:09:13]All right. Let's stop here, guys. But, tomorrow I'll give you about 3 hours.

[00:09:17]So, we'll do 3 hours tomorrow.

[00:09:21]Sir.

[00:09:23]Yes, Marshall.

[00:09:26]Um g5, right?

[00:09:31]f of g5?

[00:09:33]Yeah.

[00:09:35]Didn't we find it and it um, eight and a 16 over two and we 16 over two? No, it wasn't G5, you know.

[00:09:46]It was We found G0 + G5.

[00:09:49]Mhm. This is a composite function, so they wanted you to combine both functions and then put in five.

[00:09:57]Oh, because I just didn't use, um, what I got. Oh, no.

[00:10:02]>> that I got for G5.

[00:10:04]All right, scroll it over and let me write it up, please.

[00:10:12]And they wanted you to combine both functions.