Mathematics Lesson 15 - Foundations Review Set | Dataplexa

Foundations Review Set

This lesson is a complete revision of everything you learned in the Foundations section (Lessons 1–14). It is designed to strengthen understanding, improve speed, and build confidence.

If you can solve this lesson comfortably, you are fully ready to move into Algebra.

What This Review Covers

This review includes mixed questions from all foundation topics. Each question tests understanding, not just calculation.

Number systems
Fractions & percentages
Exponents & roots
Order of operations
Equations & inequalities
Ratios & proportions
Sequences & patterns
Geometry basics
Coordinate plane
Units, estimation, word problems

Section A – Concept Check (Very Important)

These questions test whether you truly understand the ideas. Do not rush — think before answering.

Q1. Which number system includes negative numbers?

Integers

Q2. What does the equal sign (=) actually mean?

Both sides have the same value

Q3. When do we reverse an inequality sign?

When multiplying or dividing by a negative number

Section B – Calculations & Skills

These questions test calculation accuracy and rule application.

Q4. Simplify: 3 + 2² × 4

2² = 4 → 4 × 4 = 16 → 3 + 16 = 19

Q5. Solve: x + 7 = 15

x = 8

Q6. Simplify the ratio 24 : 36

Divide by 12 → 2 : 3

Section C – Fractions, Percentages & Estimation

These problems test practical math used in daily life.

Q7. Convert 3/5 into a percentage.

3/5 = 0.6 = 60%

Q8. Estimate: 498 + 302

500 + 300 = 800

Section D – Sequences & Patterns

Pattern recognition is heavily tested in exams. Focus on the logic, not guessing.

Q9. Find the next term: 2, 6, 18, ___

Multiply by 3 → Next term = 54

Q10. Find the missing number: 1, 4, 9, __, 25

Square numbers → Missing number = 16

Section E – Geometry & Coordinate Plane

These questions test visual understanding. Always draw a quick sketch in exams.

Q11. What is the area of a rectangle with length 6 cm and width 4 cm?

Area = 6 × 4 = 24 cm²

Q12. In which quadrant does the point (−3, 5) lie?

Quadrant II

Section F – Units & Word Problems

These problems connect math to real life. Always check units carefully.

Q13. Convert 2500 m into kilometers.

2.5 km

Q14. A pen costs ₹12. How much will 9 pens cost?

9 × 12 = ₹108

Final Confidence Check

If you can solve most of these questions:

You understand mathematical foundations
You are exam-ready at the basics level
You are prepared to learn Algebra

If some questions were difficult, revisit the related lessons — that is how strong foundations are built.

Quick Recap – Foundations Completed

Numbers, operations, and rules mastered
Logical thinking improved
Math connected to real life
Confidence built step by step

🎉 Congratulations! You have completed the Foundations of Mathematics.

Next up: Algebra & Functions — where math becomes even more powerful.

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