LEAKED WAEC 2026 Mathematics Objective Questions 😱 | Most Expected OBJ Questions & Answers

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[00:00:00]Don't enter the hall tomorrow morning for your mathematics white examination if you don't watch this video to the end. Now we're going to be solving around 40 questions that you should be expecting in your mathematics white exam tomorrow. You might not see them exactly word forward, but if you watch it to the end, you will be able to solve the questions in your exam tomorrow without stress. Let's get down to business.

[00:00:30]Question number one says as shown on the screen it says find we have 101 all raised to power two in base two. Find this value and express the answer in base two. Now this is from the topic called number basis. So quickly we're going to express or expand since the square term. It means we're going to be having 101 in base 2 times 101 in base 2. Quickly we can easily convert the values to a base 10 number and multiply and then convert back to base 2 in split second quickly. Now your normal conventional way is to have 012 here. But we can skip that. Let's try a new pattern. Now the number here is one.

[00:01:18]The base is two. We are doing number time base plus number time base till you get the last number. So let's go. 1 * 2 gives you two. 2 + 0 still gives you two. 2 * 2 gives you 4. 4 + 1 gives you 5. So this is five. And this also is five. So this becomes 25 in base 10. We convert that value back to base two. So our answer becomes in base two. So 2 and 25 will go 12 times remaining one. 2 in 12 6 remaining zero. 2 in 6 3 remaining zero. Two in three one remaining one.

[00:01:57]And two in one you cannot go. You write down the one back and you read your answers upward. So the answer should be 1 one 0 01 in this two.

[00:02:09]Number two says if three children share 10.5 NRA among themselves in the ratio 6 ratio 7 ratio 8 how much is the largest share quickly we have 6 ratio 7 and ratio 8. So obviously the largest share should be the one for eight. So the largest share is going to be 8 / what's the sum of the ratio? 8 + 6 is 14. 14 + 7 21 times they are sharing 10.5 NRA. We're going to solve that with our calculator quickly. We have 8 / 21 * 10.5 and the answer should be 4 NRA. So the largest shape should be 4 naira. Question three says, express this number in standard form. Quickly, let's work with that.

[00:03:04]We're going to count the zeros. Okay? 1 2 3 4. Now you stop after the first number. So you have 8.34 * 10^ because we counted towards the right having a negative exponent. Okay?

[00:03:20]And we move one 2 3 four times. to have this as the answer in standard form.

[00:03:26]Question number four says, simplify this decimal. Quickly, let's convert this guy to a fraction. We have 1 2 3 that is 27 / a,000 all raised to the power of -13.

[00:03:42]You're going to apply the laws of indices because you have a negative power here. We can swap the fraction to be 1,00 / 27 all raised to power 1 / 3.

[00:03:53]Then express the numbers in index form.

[00:03:55]Now 1,00 also means 10 to the^ 3 and 27 means 3 to the^ 3 all the power what?

[00:04:02]Now 1 / 3. We're going to apply a law I call the lawian. The law says inside that power another power d inside. So when you have something like this, use the power inside. So multiply the powers outside. Let's go. We're going to have 10 ^ 3 * 1 / 3 / 3 ^ 3 * 1 / 3. Then we're going to apply what I call base.

[00:04:28]Let's cancel the values. 3 cancels 3. 3 cancel 3. Answer should be 10 / 3 in fraction.

[00:04:36]Number five says given that this equals that, find the value of a log. Let's make sure the bins are the same. Over here we have log a to be two. And here we can convert this guy to a number that has two and four as well that has two.

[00:04:54]This becomes log four is 2^ 2 and 8 is 2^ 3. Okay. Now quickly remember for logarithm the num the powers of the number and the base must always go to the back. So here we have log a b 2 becoming we have 2 / 3 and then we have log 2 b 2. Now quickly we know log 2 b 2 is equal to 1. So we have log a base 2 = 2 / 3. Since we are finding a the logarithm says the log number is equal to the log base raised to power the answer. So we can say a should be equal to 2^ 2 / 3. Now this also means 2^ 2 or^ 1 / 3 and that can be 4^ 1 / 3 as our answer.

[00:05:50]Number six sorry by selling some crates of soft drinks for 600 naira a dealer makes a profit of 50%. How much the dealer pay for the drink? Quickly the formula we applying should be profit percent equals to selling price minus cost price over cost price* 100. But because it's an objective question apply my shortcut. Selling price equals to cost price times shortcut. Now what is the shortcut? It depends on the question. If it is profit you're going to convert the profit to decimal and do one plus the value. If it is lost, you do one minus the value. Let's apply the formula. Now, the selling price was 600 naira. We have 600 naira. We are finding the cost price. Now, since he made profit or 50%. 50% means 50 over 100 and that's 0.5. Remember profit means you are gaining. We're going to do 1 + this value for the short. I'm going to have 1.5 over here. So our CP should be 600 divided by 1.5. Let's see that in our calculator. We have 600 / 1.5 and that should give you 400 naira. So the cost price was actually 400 naira. Question number seven says find the nth term of the AP. This is the AP. Find the end. Recall formula for n term t cn = a + in brackets n -1 d. Now our first term in this series or sequence rather is 11 and our common difference 4 - 11 that should be around -7. So our common difference is - 7.

[00:07:36]Okay. And our first is 11. So let's do that. So our n 10 although they they use u n in their options. Let's use n. Okay.

[00:07:44]That's un. So un should be first term is 11 plus n -1 common difference is 7 open a bracket here we have n term= to 11 plus we have - 7 + - 7 n + 7 okay we have nth term to be that is 17 - sorry not 17 18 - 7 n that should be the n term okay number eight says if r equals that and s= that find arrow union s. Now union of a set means write out all the elements in each set without repeating a value. So this going to be just equal to we have one, we have two, we don't have three, but we have four, we don't have five, we have six, we have seven and we have eight. This will be the answer to the question number nine says 16 over 9x1 y. This is a GP and we have to find the product X and Y. We're going to apply my personal formula. call it Einstein's formula. Okay, the shortcut.

[00:08:45]Now, quickly to get X and Y, if we notice a GP, if know the common ratio of this sequence, we can find the the the terms that follow. So, quickly common ratio for my shortcut is just basically N minus one root of L / A. Now, I'm going to give you something. Your L should be the last term that you know. And the last here is Y. We don't know why. So, use the one you know, which is one. Okay? So, and this n is the position of the last term you are picking. So, what's the point of one? That's three. We're going to be saying 3 - one root of 1 / first term is this guy that's 16 over 9. Okay. So, this should arrow should become square root okay of 9 / 16 and that should be square root of 9 3 and this should be four. Now, we've got an arrow. We can find the next guy. So x is going to be 16 / 9 * 3 / 4. So 4 into 16 is 4. 3 into this guy is 3. So x is 4 3. We can find y. y should be 1 * the common ratio. Again, that's also 3 4. So we're finding the product of x as x * y. That should be 4 3 * 3 4. And that should just give us one as the answer. Okay. In question number 10 diagram below the shaded portion is dash. Let's check where was shaded. Now arrow was shaded but none of P was shaded. So we must have a P complement first of all. Okay.

[00:10:19]And now P complement basically refers to Q and arrow. But now the entire of arrow was shaded except the one entering P. So I can say P complement intersecting arrow should be the answer to this question. The best answer to the question. Number 11 says find the values of x for which the expression is undefined. And when you hear undefined forget top look at bottom. Now forget the top the bottom concerns us. For you to be undefined your bottom must always be equal to zero. We're going to solve this as equation. Let's see what can put as x gave you zero. Let's factoriize the equation quickly. All the times to get minus1 but how to get four. That should be five and minus1. So we have five and minus1. Quickly swap the signs. You're going to have -5 and one as your answers.

[00:11:11]Question number 12 says, solve the inequality. Now, quickly you times both of the equation. You're going to have 2x - 1 less than 5 * 3 gives you 15. You have 2x less than 15 + 1. You have 2x less than 16. So into that you have x less than 8 as your answer. Number 13.

[00:11:33]What's the smallest value of x in this expression? Let's find the values of x first. Okay. From here, when I go to times to get two, but how to get -3?

[00:11:43]That should be -2 and -1. Right now, you're going to swap, you're going to get 2 and one. The smaller value is obviously one. Question 14 says, factoriize the expression quickly. We have a minus c here, but we have c minus a here. Let's try to make here look like here. Okay, I'm going to do something here. Let's bring out the minus value here. Bring minus value. You're going to have minus here. Then here's minus and here's plus. This becomes a minus c.

[00:12:10]Same thing we have here. You can bring it out now. So we have a minus c into x - y as your answer. Number 15. We have this expression. We as to find the value of y when x is 2. From the number 15, we asked to find the value of y when x= 2.

[00:12:28]From this expression quickly from the way it relates we can see that y is inverse to x. So you can see y1 x1 2 = y2 and x2. Quickly put the values given to get the answer. y1 was 4 and x1 was 3. 3² is 9. Y2 is unknown and x2 is 2. 2 is 4. 4 cancels four. Therefore y2 should just be nine.

[00:12:55]Number 16 says find the value of x. Now quickly what will you times okay let's see that first 54 what will you times to get 54 but how to get sorry4 but how to get 25 quickly I think that should be 27 and two right 27 and two we're going to say 27 and minus2 as the factors now quickly shortcuts again slap the signs we're going to have minus 27 and then two but that's not all remember the term x² has a number three. Divide the answers by that number three. So the answer should become this should be - 9 and 2 over 3 as your answers. Number 17 says solve for x. Quickly we're going to equate each brackets to zero. So x + 2 = 0 and x - 7 = 0. Meaning x = -2 and x =7. These are the answers to the question number 18 says solve the sim question and hence find 2y plus x. Let's find x and y in this equation first. Now quickly from the equation we can use we can multiply all three by two. Take out the fraction. So 2 * x is 2x + 2 y = 3.

[00:14:13]And then we have 2x - 2 y = 5. Now quickly from here 2x = 3 - 2 y. So transfer this guy into here as 2x. So we have 3 - 2 y - 2 y = 5. That means 3 - 4 y = 5. Okay, that means 3 - 5 = 4 y.

[00:14:39]This is this is - 2. So - 2 + 4 y and y should be -1 / 2. And then we can find x because we all know that 2x = 3 - 2 y and y is - 1 / 2. So - 6 becomes + 2 here that's 1. So we have 2x = 3 + 1 and 2x = 4 meaning x = 2. We asked to find 2 y + x. So 2 * -1 / 2 + 2. This -1 + 2 and the answer should be 1. Number 19 says which of the following gives this graph in the option. Now quickly let's see the graph is a straight line so it should be in the form y= mx + c but it's an inequality so it should either be less than or greater than or equal to quickly but already we know that we shaded below the line so it should be less than okay or equal because it's a thick line equal to there. Now quickly next thing is to find the gradient and this this intercept on the y ais. Now c y can be shown from the graph. The graph cost the y at 3. So already we know that c y = 3. Now we can find m. m is change in y over change in x. Now quickly the change in y this is something like this. So 3 minus one.

[00:16:06]Okay. Or since we're going from here towards here the final y value is 0.

[00:16:12]Initial is 3. So we have 0 - 3 / we have 1 - 0. So we have - 3 1 - 3. So we can say y is less than = - 3x + 3 and this should be the inequality. Number 20 says what's the minimum value of y. Now from the graph on your screen if you look closely the minimum value of y falls between -5 and -10. And in the options, the only one that is around that range is option A, minus 7. So minus 7 should just be the answer. Number 21 says, find the root of the equation. Now that's the graph on your screen again. Look closely the root at the point where the the graph cuts through the x-axis. So negative and positive side. Now look at the graph very cut through negative part between -1 and minus2 but beyond minus 1.5. So that should be around - 1 something. Let's say - 1.7. And the only option close to that A. So answer should be 1.4 and minus 1.7. The diagonals of rhombus are given as 16 and 12. Find the area. Quickly the area for rhombus is D1 D2 / 2. D1. These are diagonals. So we have 16 * 12 / 2. So 2 here 8. 8 * 2 16 carry one. The answer should be 96 96 cm squared. Option A. Part 23. We asked to find the surface area of the cylinder there as shown on the diagram on the screen right now. Now quickly for a cylinder the CSA for the cylinder area should be the area of the top and bottom which is 2 pi r² plus the curve area which is 2 pi r. Quickly we can just say this is 2 pi r into r + h. Now let's quickly put our values there. Sorry 2 * 52 7 the radius was given as let's see yes said seven we have seven then 7 + the height is five now don't mistake the diagram although seven but they say in the question that the radius is cm 7 takes out 7 we have 44 into 12 what's 44 * 12 let's see 5 gives you 44 * 12 let's see we have 44 sorry * 12 and this should give you 528 as the total surface area number 24 says the position of two countries P and Q are given as that find the difference in latitude now in the the coordinates we see that the north is having 15 and 65 but the east are the same so quickly when you have the the values in the same coordinate you're going to subtract so quickly The angle the answer will be 65 - 15 and that should be 50°. Option A number 25. The locus of a point which equidistance from two given fixed points is dash. Now we have two fixed point let's say point A.

[00:19:18]Sorry matter is gone.

[00:19:22]We have let's say point A and point B.

[00:19:24]The locus of a point that has equal distance from these two fixed points is going to be a perpendicular bis sector of the line joining the two points and that should be option D. Number 26. What is the mode of the numbers? We have 8 10 9 10 again 8 11 8 10 98. I think eight appeared more. We have eight appearing 1 2 3 four times. Nine appearing three times. Okay. So, A should be the mode option A. Number 27. From a bus containing two red ball, six white and five black balls. A ball is picked as random. What's probability that the ball is black? Now, we have five black balls there. So, five over there. 2 + 6 8 + 5 13. So, we have 5 over 13 as our answer.

[00:20:15]Number 28. We start using table. Anyway, find the value of this. Now quickly you can pick a in the exam but let's just solve it with the way we solve it. Now remember from trigonometry s and cosine are complmentary when their angles sum up to 90. So it means sin 20 and cos 70 are the same thing. So this will give you one and the same way this also the same one the answer is two. Number 29 says that two f ds together find the probability that the sum of the outcome is at least 10. Quickly going to draw a sum table for our dice. 1 2 3 4 5 6 1 2 3 4 5 6. And then we're going to add the outcomes together to get our sum outcome table. So quickly, I'm not going to waste time over here.

[00:21:05]1 + 1 is 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6 7 8 9 5 6 7 8 9 10 6 7 8 9 10 11 7 8 9 10 11 12 and they said the sum of at least 10. At least 10 mean 10 and above. So we have these values here. We have 1 2 3 4 5 6. So the answer should be 6 over 36 and that is 1 / 6 as the answer. Number 30 says the bearing of two points Q and arrow from a point P are 30° and one point respectively. PQ is 12 P is 5.

[00:21:46]Find QR. Quickly let's draw our diagram.

[00:21:48]Okay. So from P we have from P this should be P 30° this is P should be Q. Q is over here.

[00:22:01]and then 120 should be arrow. So yes 30 but everything from here to here is 120.

[00:22:11]Okay. Now quickly remember we can do connect these dots. Okay. Let's see what we can do from here. We have 30 over here and we have from here to here as 120. So if look at what we have here. If here is 30 and yet to here is 120. What should be inside here? 120us 30 should be 90. This is a right angle triangle obviously and then we're giving PQ as 12 and P as 5. So this is the hypotenus and remember triangles of three when you have five and 12 what should be missing is what? 13. to the answer to the question you just get