Pass GCE Mathematics Paper 1 2026 With These Questions #maths

Added: 2026-06-04

[00:00:00]Ladies and gentlemen, good morning, good afternoon, and good evening wherever and wherever you are watching this video from. Welcome to my YouTube channel.

[00:00:10]Now, guys, in this video, we are going to solve together these questions, okay?

[00:00:17]These mathematics questions as we prepare for the final exam. Paper one, our focus will be is on paper one, all right? So, we have five questions. The first one, this is under algebra. Uh this is under indices. This is algebra.

[00:00:34]This is coordinate geometry, and this is set operation under sets, all right? So, without wasting much of the time, let's solve together.

[00:00:44]The first one is saying "Factorize completely." Factorize completely, and this question is just the two marks. All right? So, solutions.

[00:00:57]Solution one, we are asked to factorize completely. We have three x squared minus 30 27, rather.

[00:01:07]Minus 27. Now, when factorizing, okay? This is what you should know.

[00:01:15]When factorizing two terms, we have one, two, two terms.

[00:01:20]Make sure you look for what is common. That's the first step. Look for what is common, all right? Common factor. Is three Can three go into 27? Yes, all right? So, we can factor out three. Three into three x squared, you just remain with x what?

[00:01:40]Squared. Three into negative 27, it is negative nine. Now, when you have what is inside here, this is called difference of two squares. This is a difference of what? This is a difference of two squares, my friends. So, this is what you do. This nine is a perfect square of three. So, you can just write it three squared like this. All right? Which gives us the final answer to be three open bracket.

[00:02:14]So, here we have two x's, right? It's what it means. We have x to the power two. We So, we just write one of the two what? x's. Then we just add a plus. Then here we also do the same. Just write one of the threes.

[00:02:28]Then open bracket. The remaining x, see?

[00:02:30]Bring it here. This time around just change the sign the signs, okay? The other one should be positive, the other one negative. Then you write the remaining what? Three. And this is the answer. Two marks. Simple, right?

[00:02:43]Good. Mhm.

[00:02:45]Now, let's solve the second um the second question. All right?

[00:02:53]Question two here.

[00:02:56]We're asked to solve for x. This is what we call equations involving indices.

[00:03:02]Equations involving indices and this is how you solve it. Let's write the question. It is two the equation two x two to the power x minus four is equals to zero. Let's take this four is a constant. Let's take it to the right hand side so that you just remain with what? Two to the power x minus one is equals to four. Is there a way Is there a what? A way you can make these bases equal or the same?

[00:03:32]Yes.

[00:03:34]How? Because this four is the same as two to the power Very good. Two to the power two.

[00:03:42]So, we have two to the power x minus one is equals to two to the power two. When bases are the same, you just get the powers.

[00:03:51]When bases are the same, just get the Very good. The powers. So, bases are the same, let's get the powers. We're going to say x - 1 x - 1 is equals to the power here is two. Let's solve for x. So, x is equals to two, then uh this positive negative one across the cosine becomes positive what? Positive one. Therefore, x is just three.

[00:04:20]Three. Simple [clears throat] mathematics.

[00:04:27]Yes. This is we go to number three.

[00:04:30]Number three we have two questions.

[00:04:32]And uh whether you like it or not, you will have a question on simplifying algebraic expressions. Okay?

[00:04:42]Now, a, we are given four open bracket x + 2y close bracket open Oh, we have a minus here. Minus open bracket 3x 8y. What do you do when you're given such a question?

[00:05:01]You can do nothing but you solve. Just you solve. So, here this is what you do.

[00:05:06]4 * x is 4 x. 4 * 2 is 8. 8 what? 8y.

[00:05:15]Remember, when you have a negative here, you distribute using what? A negative. You multiply using a negative. Negative times negative Negative times three is just negative three x. Negative times negative it is positive 80y. Simple.

[00:05:33]What do you do here?

[00:05:35]Very good. You collect like terms. So, here we have 4x - 3x + 8y + 8y Yes, yes, yes, yes. What is Now, here 4x - 3x just concentrate on the coefficients, numbers in front of the variable.

[00:05:58]4 - 3 is 1, so just have x.

[00:06:03]What is 8 + 8? 16. 16y and this is the answer. Two marks for parking off in later. The exam work. Simple. Guys, if you have [clears throat] If you're enjoying up to question three A, why can't you subscribe? If you haven't subscribed, like the video and give us a comment. All right?

[00:06:30]Number B, 3B.

[00:06:33]3B is a similar question. We have 2a plus open bracket b - a close bracket - 2b. What do you do here?

[00:06:46]Mhm. Look at the brackets.

[00:06:49]What number on the right side is in front of the brackets? There's a positive one. So, let's use that invisible positive one or positive two remove the brackets. Positive times b it's just positive b. Positive times negative positive times negative is negative a - 2b. You don't need to use this. Don't use this. Use what is in this side on the right side. Here, we can collect like terms. So, this is um like to this and then this one with this one. So, it'll be 2a a + b - 2b. What is 2 - 1? It's just remaining a. That's one.

[00:07:36]Because this is the same as 2 - there's an invisible one. Then what you have a common variable which is A.

[00:07:42]What What is 1 - 2? It's negative 1, which is negative B.

[00:07:48]And this is the answer. All right.

[00:07:52]Simple.

[00:07:53]Let's solve question four, which is under coordinate geometry.

[00:08:01]Coordinate geometry. And this question is uh asking us to find the distance between Oh, this is supposed to be P.

[00:08:11]The distance between P and Q.

[00:08:15]Mhm.

[00:08:17]Now, what do you do when you're finding distance between two points? This is the formula, don't worry. As long as you know the formula, it is easy to find distance between two points. So, this is the distance between two points.

[00:08:28]This PQ.

[00:08:30]So, we're going to write PQ is equals to the square root of the difference in X axis, which is X2 - X1 squared plus the difference in Y axis between the two points. So, it'll be Y2 - Y1 close brackets squared.

[00:08:56]Simple. This is X1, this is Y1, this is X2, this is Y 2.

[00:09:05]Simple. Let's solve.

[00:09:08]So, PQ [clears throat] is equals to the square root of open bracket. What is X2? X2 is -4 minus this minus here. X1 is -7.

[00:09:22]Okay, you have to be very careful. This negative is on the formula. This one is here on the question.

[00:09:30]All right.

[00:09:31]Squared plus What is Y2? Y2 is 5 minus y1 one squared. All right. So, PQ is equals to the square root of What is negative as negative here? It is positive. So, inside here we have -4 + 7.

[00:09:55]What is -4 + 7? It is positive three.

[00:09:59]So, it will be just three squared.

[00:10:02]Right. Very good.

[00:10:05]Plus 5 - 1 is four. Just a four squared.

[00:10:10]Okay. Even without [clears throat] putting in the brackets, this there's no problem here.

[00:10:15]All right. Now, what is three squared? It's nine.

[00:10:20]Four squared? 16.

[00:10:23]This gives us This gives us 25 inside. 25 and 25 the square root of 25.

[00:10:33]Now, remember the square root can either be positive or negative.

[00:10:37]Take note. We are finding distance. So, length can never be negative. Unless otherwise, but here we just get the positive number. So, square root of five, it is just 5D units.

[00:10:53]What are the units? We don't know.

[00:10:55]Can either be in centimeters, meters, or kilometers.

[00:10:58]I mean, not come out. Who knows?

[00:11:01]Number five.

[00:11:03]Number five, we can Yeah, so you can copy. Pause the video, copy. Otherwise, in any food.

[00:11:11]Great. Number five, describe the shaded region using the set using set notation.

[00:11:18]So, when you When you give me such a question, it is two marks. Yes.

[00:11:22]The first thing you're supposed to do is identify the set or sets which are not shaded completely.

[00:11:30]We have set B and C not shaded completely, and this is union, B union C. So, you can say this is B union C.

[00:11:43]B union C. Okay?

[00:11:46]B union C, then is we can put this one in brackets. B union C, look at this. This is not shaded, so it's B union C complement.

[00:11:58]Are you following?

[00:12:00]Very good. It's not shaded, B union C complement, meaning do not shade set B and C.

[00:12:10]Just shade set A. This is This is what is shaded.

[00:12:14]Mhm.

[00:12:16]This is the answer.

[00:12:18]Okay? That's simple as this, two marks.

[00:12:20]Guys, if you have enjoyed this video, consider subscribing. We are still revising. In the next video, we'll look at more questions. Thank you so much.