Work out the exact solutions of the equation $\frac{ 3 }{ 2x-1 }+ \frac{ 2 }{ 2x+1 }=1$

$\frac{ 5 \pm \sqrt{33} }{ 4 }$

$\frac{ 8 \pm \sqrt{21} }{ 7 }$

$\frac{ 1 \pm {2}\sqrt{7} }{ 3 }$

Algebra 5: Algebraic Fractions

Q1. A teacher designs a lesson where students compute real-life percentages such as discounts and savings. 👉 A student calculates 15% of 200 to determine savings in a purchase. What is the correct result? A. 20 B. 25 C. 30 D. 35 Q2. In a classroom activity, learners compare numbers to find the highest common factor for grouping materials evenly. 👉 What is the GCF of 24 and 36? A. 6 B. 8 C. 12 D. 18 📘 FRACTIONS, DECIMALS, AND POWERS Q3. A learner converts fractions into percentages for data interpretation. 👉 What is 3/4 expressed as a percentage? A. 50% B. 60% C. 75% D. 80% Q4. A student models exponential growth using repeated multiplication. 👉 What is the value of 252^525? A. 25 B. 30 C. 32 D. 64 📘 ALGEBRA (EQUATIONS AND EXPRESSIONS) Q5. A teacher guides students to solve equations that represent real-life situations. 👉 Solve: 2x+8=202x + 8 = 202x+8=20 A. x = 4 B. x = 6 C. x = 8 D. x = 10 Q6. Students simplify expressions to understand relationships between quantities. 👉 Simplify: 3(x+4)−2x3(x + 4) - 2x3(x+4)−2x A. x + 12 B. x + 4 C. 5x + 4 D. 5x + 12 📘 FUNCTIONS AND GRAPHING Q7. A student analyzes a linear equation to determine its rate of change. 👉 What is the slope of y=3x−5y = 3x - 5y=3x−5? A. -5 B. -3 C. 3 D. 5 Q8. A learner evaluates functions to predict outcomes. 👉 If f(x)=2x+3f(x) = 2x + 3f(x)=2x+3, what is f(4)f(4)f(4)? A. 7 B. 9 C. 11 D. 14 📘 GEOMETRY Q9. Students explore geometric shapes and their properties through visual models. 👉 What is the sum of interior angles of a triangle? A. 90° B. 180° C. 270° D. 360° Q10. A student calculates the area of a classroom table with dimensions 8 cm by 5 cm. 👉 What is the area? A. 26 sq cm B. 30 sq cm C. 40 sq cm D. 48 sq cm 📘 MEASUREMENT AND FIGURES Q11. A learner determines the volume of a cube used in a science experiment. 👉 What is the volume of a cube with side 4 cm? A. 16 cubic cm B. 32 cubic cm C. 48 cubic cm D. 64 cubic cm Q12. Students identify shapes used in design projects. 👉 How many sides does a hexagon have? A. 5 B. 6 C. 7 D. 8 📘 STATISTICS AND PROBABILITY Q13. A teacher helps students interpret data sets using measures of central tendency. 👉 What is the mean of 4, 6, 8, 10, 12? A. 6 B. 8 C. 10 D. 12 Q14. A class experiment involves flipping a fair coin. 👉 What is the probability of getting heads? A. 1/4 B. 1/3 C. 1/2 D. 2/3 📘 WORD PROBLEMS (APPLICATION) Q15. A car travels 180 km in 3 hours during a learning task on speed. 👉 What is its average speed? A. 45 km/h B. 60 km/h C. 75 km/h D. 90 km/h Q16. Students analyze work efficiency in a project. 👉 If 5 workers complete a task in 12 days, how long will 10 workers take? A. 3 days B. 6 days C. 8 days D. 12 days Q17. A student solves a problem involving ratios in a classroom population. 👉 If the ratio of boys to girls is 3:2 and there are 30 students, how many boys are there? A. 12 B. 15 C. 18 D. 20 Q18. A learner determines the duration of a scheduled trip. 👉 A journey starts at 8:30 AM and ends at 11:15 AM. How long is the trip? A. 2 hrs 15 mins B. 2 hrs 30 mins C. 2 hrs 45 mins D. 3 hrs 15 mins Q19. A student computes simple interest for financial literacy. 👉 What is the simple interest on ₱1000 at 5% for 2 years? A. ₱50 B. ₱75 C. ₱100 D. ₱150 Q20. A learner solves a perimeter problem involving a rectangle. 👉 A rectangle has a length of 12 cm and perimeter of 34 cm. What is the width? A. 5 cm B. 7 cm C. 10 cm D. 11 cm ✅ ANSWER KEY (BASED ON YOUR REVIEWER) (All verified from your uploaded file) [ilide.info...002acd4e5a | PDF] QAnswer1C2C3C4C5B6A7C8C9B10C11D12B13B14C15B16B17C18C19C20A

Section 1: Numbers, Operations, and Relationships (15 marks) 1. Number Concepts (5 marks) 1.1. Decompose the following numbers into tens and ones: (2 marks) a. 34 b. 67 1.2. Count the objects in the pictures below and write the total number: (3 marks) [This section would need images of objects. You can provide images of groups of objects, e.g., 3 groups of 4 apples each and ask the students to count the total number.] 2. Solve Problems (5 marks) 2.1. Solve the following word problem using drawings: (3 marks) Samantha has 5 baskets. Each basket has 8 apples. How many apples does she have in total? Samantha has 5 × 8 = 40 5×8=40 apples. 2.2. Solve the following word problem by building up and breaking down numbers: (2 marks) There are 4 boxes. Each box has 6 chocolates. How many chocolates are there in total? There are 4 × 6 = 24 4×6=24 chocolates in total. 3. Calculations (5 marks) 3.1. Multiply the following numbers using drawings: (3 marks) a. 5 × 4 = 20 b. 4 × 5 = 20 3.2. Use a number line to solve: (2 marks) a. 3 × 5 = 15 b. 2 × 4 = 8 Section 2: Patterns, Functions, and Algebra (10 marks) 4. Number Patterns (10 marks) 4.1. Complete the number sequences: (5 marks) a. 180, 170, 160, 150, 140, 130, 120, 110, 100, 90 b. 150, 152, 154, 156, 158, 160, 162, 164, 166, 168 4.2. Count in twos and fill in the missing numbers: (5 marks) a. 102, 104, 106, 108, 110, 112, 114, 116 Section 3: Space and Shape (Geometry) (10 marks) 5. Position (10 marks) 5.1. Follow the directions to move around the classroom: (5 marks) Draw a path showing how you would move from your desk to the teacher's table by following these steps: Move 3 steps forward. Turn left and move 2 steps. Turn right and move 4 steps. [Students would draw a path based on these directions.] 5.2. Use the language of position to describe the following: (5 marks) a. The pencil is on the book. b. The chair is beside the desk. c. The bag is under the table. d. The ruler is next to the notebook. e. The eraser is inside the pencil case.

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