Category: Math

Pupils in primary or basic 5 write the National Common Entrance Examination (NCEE). It is important that your child is well-prepared and passes the exam before proceeding to the secondary school of his/her choice. One of the areas of preparation is quantitative aptitude. I will try as much as possible to lay the foundation to help pupils in primary 5 do well in this section.

Quantitative questions are used to test your skills in numbers. In this context, you must be skillful in the use of addition, multiplication, subtraction, and division of numbers.

For this content, all the sample questions are BECE past questions. So, be rest assured that I won’t go out of the syllabus.

Samples

The series of problems below are based on quantitative reasoning. Before answering the questions, study the sample that precedes each set and use it to solve the problems in that set.

To solve this question, check the sample and think through it without wasting time. The approach to solving it will be given below.

(2^2 + 3^2) = 4 + 9 = 13.

(1^2 + 6^2) = 1 + 36 = 37

(4^2 + 0^2) = 16 + 0 = 16

The results I got are the numbers on the image. You can now use the same concept to solve the questions beneath.

In the above sample, there are two circles. You will add all the numbers on the big circle and square the number on the small circle.

(2+3+4) = (3^2) = 9

(3+0+1) = (2^2) = 4

(7+5+4) = (4^2) = 16

For this question, the differences between the top numbers must be the same with the ones below.

(15-10) = (25-20) = 5

(9-7) = (18-16) = 2

(9-4) = (5-0) = 5

The first sample is addition while the second one is subtraction. Also, check the sign so as to avoid mistake.

For the first question, (50+20)/(30-20) = 70/10 = 10. So, B is the answer.

For this question, if you multiply the number on the left side of the “Z” it must be equal to that on the right side.

(16*3) = (6*8) = 48

(9*1) = (3*3) = 9

(25*2) = (10*5) = 50

This is the solution

(3^2 – 1^2) = 9 -1 = 8

(10^2 – 5^2) = 100 – 25 = 75

(7^2 – 6^2) = 49 – 36 = 13.

So, if you have any questions you can drop in the comment section.

One of the JAMB subjects that candidates are a little bit afraid of is Mathematics. The primary reason is that JAMB mathematics has some basic further mathematics in the question. And if you are not so sound in it, you are already at a disadvantage.

However, there are some hidden facts that you need to understand in JAMB mathematics that will enable you to score high in it. For this reason, I have decided to shed some light on hidden facts in JAMB mathematics.

Read: 5 steps to get a good mark in maths

 What to Know

1. Learn differentiation, integration, matrix, permutation & combination, and polynomials at the foundation level

The topics I just mentioned are simple because they have already made formulas that will enable you to solve any question on them. Don’t let anyone scare you since JAMB will only bring out simple questions from these topics.

2. Make sure you master logarithms & indices, surd, circle geometry, probability, set, number base, mean, median and mode well

These are essential topics you need to work more on to increase your chance of scoring high in JAMB mathematics. They are simple and easy to solve if can practice them as many times as possible

3. Work on your speed

JAMB mathematics is different from other subjects being that it can waste your time if you don’t know how to manage your time. Most times I do advise candidates who aren’t fantastic in mathematics to make it the last subject to answer. However, you can find some JAMB online CBT on math that you can practice with before the exam day. Using this approach will help increase your speed.

4. Anybody can score high in it

Some candidates believe that only science students can score high in mathematics, but this assertion is false. A social science student can do well in this subject if he/she prepares well and follow the first 3 points that I give above.

Question and Answer

Question 1

Tanθ = 5/4, find sin²θ – cos²θ

A. 41/9     B. 9/41     C. 1       D. 5/4

Answer

Recall,

Tanθ = opposite/adjacent

Opposite = 5

Adjacent = 4

Also,

(Hypotenuse)² = (opposite)² + (adjacent)²

(Hypotenuse)² = 5² + 4² = 25 + 16 = 41

sin²θ = (opposite)²/(hypotenuse)² = 25/41

cos²θ = (adjacent)²/(hypotenuse)² = 16/41

sin²θ – cos²θ = 25/41 – 16/41 = 9/41

Question 2

In triangle XYZ, <XYZ = 15^o, <XZY = 45^o, |XY| = 7cm, find |YZ|

A. 7√2 cm    B. 7cm    C. 14√2 cm       D. 7/2 √6 cm

Answer

To calculate, use sine rule

|XY|/sine (<XZY) = |YZ| / sine (<YXZ)

Note,

<YXZ + <XZY +  <XYZ = 180 (sum of angles in a triangle)

<YXZ = 180 – 15 – 45 = 120

7/sine 45 = |YZ| / sine 120

sine 45 = 1/√2

sine 120 = √3 /2

7√2 = 2 |YZ| / √3

7√6 / 2 = |YZ|

|YZ| = 7/2 √6 cm

Question 3

The mean of the numbers 3, 6, 4, x, and 7 is 5. Find the standard deviation

A. 2         B. 3    C. √3   D. √2

Answer

Mean = (3 + 6 + 4 + x + 7) /5

5 = (3 + 6 + 4 + x + 7) /5

25 = 20 + x

X = 5

To calculate standard deviation,

((3-5)² + (6-5)² + (4-5)² + (5-5)² + (7-5)²)/5 =  (4 +1+1+0+4) /5 = 10/5 = 2

Then, find the square root

S.D = √2

Question 4

A cinema hall contains a certain number of people. If 22 ½ % are children, 47 ½% are men and 84 are women. Find the number of men in the hall.

A. 133      B. 113     C. 63      D. 84

Answer

Percentage of children + men + women = 100

Let x be the percentage of women

22 ½ % + 47 ½%  + x = 100

X = 100 – 70 = 30%

Let the total number of people in the cinema hall be Y

30% of Y = 84 for women

i.e.

30/100 x Y = 84

8400/30 = Y

Y = 280

Number of men,

47 ½% of 280

95/200 x 280 = 133

Recommended: JAMB MATHEMATICS PAST QUESTIONS AND ANSWERS

Question 5

Find the derivative of y = sin²(5x) with respect to x

A. 2sin5xcos5x       B. 5sin5xcos5x   C. 10sin5xcos5x   D. 15sin5xcos5x

Answer

Y = (sin(5x))²

Let u = sin5x

Let a = 5x

Da/dx = 5

U = sina

Du/da = cos a

Du/dx = da/dx x du/da = 5 x cosa = 5cosa = 5cos5x

Y = u²

Dy/du = 2u

So,

Dy/dx = dy/du x du/dx = 5cos5x x 2u = 10ucos5x

Since u = sin5x

Dy/dx = 10sin5xcos5x

Quantitative Reasoning measures a person’s ability to use mathematical or analytical skills to solve problems. This is to help those in primary schools to understand the logic behind solving any of the given questions in their textbooks. The examples that I solved in this article were obtained from the books recommended for pupils in Nigeria. Here, I will solve some examples for primary 3, 4, and 5 pupils.

Example 1

Solution

One good thing about quantitative reasoning is that it helps you think deeply to generate the right answer.

The technique used in the above example follows this pattern;

(2*3) – 5 = 1

(16*3) – 5 = 43

(27*3) – 5 = 76

(40*3) – 5 = 115

Use this format to solve the remaining question

(10*3) – 5 = 25

(15*3) – 5 = 40

(33*3) – 5 = 94

(54*3) – 5 = 157

Example 2

Solution

The format to solve this particular question is discussed below;

139 * 3 = 417

258 * 2 = 516

To solve the first question,

113 * 5 = 565

Therefore, 6 will be in the box

Example 3

Solution

(9*4) divided by square root of 9 = 36/3 = 12

(36*5) / square root of 36 = 180/6 = 30

(64*2)/ square root of 64 = 128/8 = 16

Example 4

Solution

The numbers in COLUMN must be the same in the ROW

For ROW 1, the numbers are 1, 2, 3, 0, 1

For COLUMN 1, the numbers are 1, 2, G, 0, T

The G is 3

The T is 1

So, use the same method for the rest.

Example 5

Solution

For the first sample question, take the 2 and 2 in the square boxes to be 22 and multiply the 3 and 6 in the triangle boxes. then subtract i.e. 22-(6*3) = 4 in the circular box

2nd sample: 18-(2*5) = 8

sample 3: 22-(7*3) = 1

Use this approach to solve questions 6-10 of the diagram

Example 6

Solution

From the samples given, adding the first two columns together will give the third column.

1st example, 4118 + 5420 = 9538

2nd example, 1257 + 3482 = 4739

Also, subtracting the first column from the second column will give you the fourth column.

sample 1, 5420 – 4118 = 1302

sample 2, 3482 – 1257 = 2225

Use this same method to solve questions 1-5 of the diagram

Example 7

Solution

If you look at the first example, add the left-hand side together (7+5+4+3 = 19) and the right-hand side (9+12+15+21 =57). So if you multiply the sum of the left-hand side, which is 19 x 3, you will get the sum of the right-hand side, which is 57

The same for the second example, the left-hand side is 12+5+13+8 = 38, and the right-hand side is 24+36+15+39 = 114. if you multiply the 38 x 3 = 114

In summary, if you add the numbers on the left-hand side and multiply by 3, you will get the sum of the numbers on the right-hand side.

Example 8

solution

Example 9

Solution

(34/2) + 6 = 23

(49/2) + 6 = 30 1/2

(62/2) + 6 = 37

(76/2) + 6 = 44

Maths is a subject I love so much and getting good marks in it hasn’t been difficult for me. What helped me back then was that I took some smart steps to make sure I got good marks in maths.

I got motivated to start aiming for a high score in mathematics when I was in grade 4 (Senior Secondary School 1). It happened when the first time exam results came out; one of my classmates had 98/100 in maths. This got me thinking and I was convinced that it is possible to consistently do well in mathematics.

That said, another reason why I take the subject as my delight is because it helps to enhance my analytical and logical skills. And this can only be possible through perseverance and persistence in the subject.

Now I will discuss the smart steps I used to get high marks in maths.

Steps

1. Love the subject

Loving mathematics is the first step to getting your desired grade in the subject. I love it because it makes me think through a problem for a long time and by so doing I become more alert mentally. It will be difficult to give your best to a subject you don’t love.

2. Practice with a lot of questions

There are many textbooks on mathematics for each grade, therefore, lay your hands on those recommended by your school and the ones you like the author(s). For every topic you are taught in class, go to your textbooks look for related questions, and solve them. By so doing, you are building the mental capacity to address any questions in maths.

3. Never jump steps when answering theory questions in maths

The easiest way to be marked down in mathematics is when you jump steps to arrive at your answer. Each of them has a mark attached to it which contributes to the overall mark you will score. This will show the examiner that you understand the question and are not gambling.

4. Have a shortcut when answering objective questions

Some exams are purely objective and need you to complete the whole question in the shortest time. This is not a time to start showing long workings; you have to be as fast and accurate as possible.

It then means that when practicing try to devise a shortcut approach to solving different questions.

5. Don’t rush when solving problems in mathematics

It is easy to make a mistake when you are in haste when answering questions in mathematics. You must be meticulous for you to have good marks in maths.  For you to have an excellent grade, you have to understand the question and solve it step by step.

Recommended: Hidden facts about JAMB Mathematics