**NECTA Standard Seven Exams Mathematics Questions and Answers, Mastering Mathematics (Hisabati) for NECTA Standard Seven: Importance of Solving Past Papers and Exam Tips,**

Mathematics, or **Hisabati**, is a subject that requires consistent practice and understanding of concepts to excel. For students in Standard Seven preparing for the **Primary School Leaving Examination (PSLE)**, mastering Mathematics is critical for success. One of the most effective ways to achieve this is by solving **NECTA past papers**. Past exam papers give students a sense of the types of questions they can expect and help build confidence for the real exam.

### Importance of Solving Past Papers

Solving past papers is a crucial aspect of exam preparation for several reasons:

**Familiarity with Exam Structure**:

Past papers help students understand the structure of the exam, the types of questions that frequently appear, and the time allocation for each section.**Identify Knowledge Gaps**:

By working through previous papers, students can identify the areas where they need to focus more attention. It highlights topics they may have overlooked during revision.**Boost Time Management**:

Practicing under timed conditions helps students improve their ability to complete the exam within the allotted time. It reduces the chances of running out of time during the actual exam.**Improve Problem-Solving Skills**:

Past papers often include challenging problems. By solving these, students enhance their critical thinking and problem-solving abilities, which are essential for excelling in Mathematics.**Build Confidence**:

Familiarity with the types of questions and constant practice builds the studentâ€™s confidence. They feel more prepared and less anxious on the day of the exam.

### Tips to Pass Mathematics Exams

To do well in Mathematics exams, students should follow these useful tips:

**Understand the Concepts**:

Rote memorization wonâ€™t help in Mathematics. Make sure to understand the concepts and practice different types of problems related to each topic.**Practice Regularly**:

Consistent practice is key to mastering any subject, especially Mathematics. Set aside time each day to practice different topics and questions.**Focus on Weak Areas**:

Identify the topics or question types that are most challenging for you and work on those. Donâ€™t just practice what you already know.**Review Mistakes**:

Every mistake you make during practice is an opportunity to learn. Review the solutions carefully and ensure you understand where you went wrong.**Manage Time**:

Time management during the exam is crucial. Practice solving past papers within the set time to ensure you can complete all the questions during the real exam.**Use Simple Methods**:

Sometimes, simpler methods can solve problems more efficiently. Avoid over-complicating answers, and stick to straightforward solutions that get you the correct result.

## 50 Technical Mathematics Questions for NECTA Standard Seven Exams

### 1. **Arithmetic (Addition, Subtraction, Multiplication, Division)**

**Q1**: If you subtract 456 from 1,234, what is the result?

**A**: 1,234 – 456 = **778**

**Q2**: Multiply 376 by 48.

**A**: 376 Ã— 48 = **18,048**

**Q3**: Divide 7,812 by 42.

**A**: 7,812 Ã· 42 = **186**

**Q4**: What is the sum of 1,250 and 3,756?

**A**: 1,250 + 3,756 = **5,006**

**Q5**: If a student divides 3,600 shillings equally among 9 friends, how much does each friend get?

**A**: 3,600 Ã· 9 = **400 shillings**

### 2. **Fractions and Decimals**

**Q6**: Simplify the fraction 18/27.

**A**: 18/27 = **2/3** (after dividing both numerator and denominator by 9).

**Q7**: Convert 0.45 into a fraction.

**A**: 0.45 = **9/20**

**Q8**: Add 2/5 and 3/4.

**A**: 2/5 + 3/4 = **23/20** = **1 3/20** (Convert to the same denominator and add).

**Q9**: Subtract 1/3 from 5/6.

**A**: 5/6 – 1/3 = **3/6** = **1/2** (Convert to the same denominator and subtract).

**Q10**: Multiply 2.5 by 1.2.

**A**: 2.5 Ã— 1.2 = **3.0**

### 3. **Percentages**

**Q11**: Find 35% of 840.

**A**: 35% of 840 = 0.35 Ã— 840 = **294**

**Q12**: A student scored 75 marks out of 100. What percentage did the student get?

**A**: (75/100) Ã— 100 = **75%**

**Q13**: A shirt that was originally priced at 20,000 shillings is now being sold for 15,000 shillings. What is the percentage discount?

**A**: (20,000 – 15,000) / 20,000 Ã— 100 = **25%**

**Q14**: Increase 480 by 12%.

**A**: 480 + (12/100) Ã— 480 = **537.6**

**Q15**: Decrease 900 by 15%.

**A**: 900 – (15/100) Ã— 900 = **765**

### 4. **Geometry**

**Q16**: Find the perimeter of a rectangle with a length of 15 cm and a width of 8 cm.

**A**: Perimeter = 2(L + W) = 2(15 + 8) = **46 cm**

**Q17**: A triangle has a base of 12 cm and a height of 7 cm. What is its area?

**A**: Area = 1/2 Ã— base Ã— height = 1/2 Ã— 12 Ã— 7 = **42 cmÂ²**

**Q18**: Calculate the circumference of a circle with a radius of 14 cm (use Ï€ = 22/7).

**A**: Circumference = 2Ï€r = 2 Ã— (22/7) Ã— 14 = **88 cm**

**Q19**: What is the volume of a cube with a side length of 6 cm?

**A**: Volume = sideÂ³ = 6Â³ = **216 cmÂ³**

**Q20**: If the perimeter of a square is 64 cm, what is the length of one side?

**A**: Perimeter of square = 4 Ã— side, so side = 64 Ã· 4 = **16 cm**

**Q21**: Calculate the area of a rectangle with length 12 cm and width 8 cm.

**A**: 96 cmÂ².

**Q22**: Find the perimeter of a square with a side length of 7 cm.

**A**: 28 cm.

**Q23**: What is the area of a triangle with a base of 10 cm and a height of 6 cm?

**A**: 30 cmÂ².

**Q24**: The circumference of a circle is 44 cm. What is the diameter? (Use $Ï€=722â€‹$).

**A**: 14 cm.

**Q25**: A right-angled triangle has legs measuring 6 cm and 8 cm. Find the hypotenuse.

**A**: 10 cm.

**Q26**: Calculate the volume of a cube with a side length of 5 cm.

**A**: 125 cmÂ³.

**Q27**: Find the area of a parallelogram with base 15 cm and height 8 cm.

**A**: 120 cmÂ².

**Q28**: If the radius of a circle is 7 cm, calculate the area of the circle ($Ï€=722â€‹$).

**A**: 154 cmÂ².

**Q29**: Find the surface area of a cuboid with dimensions 4 cm by 3 cm by 2 cm.

**A**: 52 cmÂ².

**Q30**: The height of a cylinder is 10 cm, and the radius of the base is 7 cm. Find the volume of the cylinder ($Ï€=722â€‹$).

**A**: 1,540 cmÂ³.

#### 4. **Algebra**

**Q31**: Solve for $x$: $3x+5=20$.

**A**: $x=5$.

**Q32**: If $2yâˆ’3=9$, find $y$.

**A**: $y=6$.

**Q33**: Simplify: $5(xâˆ’2)+3x$.

**A**: $8xâˆ’10$.

**Q34**: Solve for $x$: $4xâˆ’7=2x+5$.

**A**: $x=6$.

**Q35**: If $3a+2=17$, find $a$.

**A**: $a=5$.

**Q36**: What is the value of $y$ if $y+8=3yâˆ’4$?

**A**: $y=6$.

**Q37**: Solve for $x$: $7xâˆ’2=5x+4$.

**A**: $x=3$.

**Q38**: Simplify the expression: $2(3xâˆ’4)âˆ’5(x+1)$.

**A**: $xâˆ’13$.

**Q39**: Find $x$ if $2x+3=9$.

**A**: $x=3$.

**Q40**: Simplify: $4(x+5)âˆ’3(xâˆ’2)$.

**A**: $x+26$.

### 5. **Word Problems**

**Q21**: A farmer has 50 cows. If each cow eats 5 kilograms of grass per day, how much grass do all the cows eat in 7 days?

**A**: Total grass = 50 Ã— 5 Ã— 7 = **1,750 kilograms**

**Q22**: John has 2,400 shillings. If he buys 3 notebooks for 200 shillings each, how much money will he have left?

**A**: Total cost = 3 Ã— 200 = 600, so John will have 2,400 – 600 = **1,800 shillings** left.

**Q23**: A shop sells 12 pens for 3,600 shillings. What is the price of one pen?

**A**: Price per pen = 3,600 Ã· 12 = **300 shillings**

**Q24**: If it takes 8 workers 4 hours to build a wall, how many hours would it take 4 workers to build the same wall?

**A**: (8 workers Ã— 4 hours) = 32 worker-hours. So, 4 workers will take 32 Ã· 4 = **8 hours**.

**Q25**: A car travels 240 km in 4 hours. What is the car’s speed in km/h?

**A**: Speed = distance Ã· time = 240 Ã· 4 = **60 km/h**

**Q41**: A car covers 120 km in 3 hours. What is its speed in km/h?

**A**: 40 km/h.

**Q42**: A man has 360 apples and sells 75% of them. How many apples are left?

**A**: 90 apples.

**Q43**: A water tank holds 500 liters. If 40 liters are used each day, how many days will the water last?

**A**: 12.5 days.

**Q44**: A worker earns 240,000 shillings per month. If 20% is deducted for taxes, how much is left?

**A**: 192,000 shillings.

**Q45**: If the price of 6 pencils is 1,200 shillings, what is the price of one pencil?

**A**: 200 shillings.

**Q46**: A bus travels 60 km in 90 minutes. What is its speed in km/h?

**A**: 40 km/h.

**Q47**: If 3 bags of rice weigh 150 kg, how much does 1 bag weigh?

**A**: 50 kg.

**Q48**: A bookshop sold 150 books in 5 days. What is the average number of books sold per day?

**A**: 30 books per day.

**Q49**: The cost of 8 mangoes is 2,400 shillings. What is the cost of 3 mangoes?

**A**: 900 shillings.

**Q50**: If a piece of cloth is 12 meters long and is cut into pieces of 1.5 meters each, how many pieces are there?

**A**: 8 pieces.

### 6. **Ratios and Proportions**

**Q26**: The ratio of boys to girls in a class is 3:4. If there are 24 girls, how many boys are there?

**A**: Let the number of boys be 3x and the number of girls be 4x. Since 4x = 24, x = 6. Therefore, the number of boys = 3 Ã— 6 = **18 boys**.

**Q27**: Divide 600 shillings in the ratio 3:5.

**A**: Total ratio = 3 + 5 = 8. So, the first part = (3/8) Ã— 600 = 225 shillings, and the second part = (5/8) Ã— 600 = **375 shillings**.

**Q28**: A recipe requires 3 cups of sugar for every 5 cups of flour. How many cups of sugar are needed if you use 15 cups of flour?

**A**: 3/5 = x/15, solving for x, x = 9 cups of sugar.

**Q29**: The ratio of teachers to students in a school is 1:20. If there are 500 students, how many teachers are there?

**A**: Let the number of teachers be x. Therefore, x/500 = 1/20, solving for x = **25 teachers**.

**Q30**: Simplify the ratio 45:60.

**A**: Simplified ratio = 45 Ã· 15 : 60 Ã· 15 = **3:4**

### 7. **Measurements**

**Q31**: Convert 7.5 kilometers to meters.

**A**: 7.5 km = 7.5 Ã— 1,000 = **7,500 meters**

**Q32**: How many liters are there in 3,200 milliliters?

**A**: 3,200 milliliters = 3.2 liters

**Q33**: A rope is 1.8 meters long. Convert it into centimeters.

**A**: 1.8 meters = 1.8 Ã— 100 = **180 centimeters**

**Q34**: If 1 kg equals 1,000 grams, how many kilograms is 7,500 grams?

**A**: 7,500 grams = 7,500 Ã· 1,000 = **7.5 kilograms**

**Q35**: Convert 24 hours into seconds.

**A**: 24 hours = 24 Ã— 60 Ã— 60 = **86,400 seconds**

### 8. **Miscellaneous Questions**

**Q36**: Find the next number in the sequence: 3, 6, 12, 24, __?

**A**: The pattern is multiplying by 2. The next number is 24 Ã— 2 = **48**

**Q37**: Solve for x: 5x = 60.

**A**: x = 60 Ã· 5 = **12**

**Q38**: What is the square root of 196?

**A**: âˆš196 = **14**

**Q39**: If x + 7 = 15, what is the value of x?

**A**: x = 15 – 7 = **8**

**Other calculation**

#### . **Distance, Speed, and Time**

**Q1**: A cyclist covers 90 kilometers in 3 hours. What is the cyclistâ€™s average speed in kilometers per hour?

**A**: Average speed = $hourskmâ€‹=30km/h$.

#### 2. **Cost Calculation**

**Q2**: A bag of sugar costs 5,000 shillings. How much will 6 bags of sugar cost?

**A**: Total cost = $6Ã—5,000=30,000shillings$.

#### 3. **Work and Time**

**Q3**: If 4 workers can complete a task in 8 days, how long will it take 2 workers to complete the same task, assuming they work at the same rate?

**A**: Time taken = $4workersÃ—8days=32worker-days$.

For 2 workers: $232â€‹=16days$.

#### 4. **Area and Cost**

**Q4**: A rectangular plot of land measures 20 meters by 15 meters. If the cost to fence the land is 200 shillings per meter, how much will it cost to fence the entire plot?

**A**: Perimeter = $2Ã—(20+15)=70meters$.

Cost = $70Ã—200=14,000shillings$.

#### 5. **Savings**

**Q5**: Jane saves 500 shillings each week. How much will she have saved in 6 months if each month has 4 weeks?

**A**: Total savings = $500Ã—4Ã—6=12,000shillings$.

#### 6. **Profit Calculation**

**Q6**: A shopkeeper buys an item for 4,500 shillings and sells it for 5,200 shillings. What is the profit?

**A**: Profit = $5,200âˆ’4,500=700shillings$.

#### 7. **Travel Time**

**Q7**: A bus leaves at 8:00 AM and travels for 5 hours and 30 minutes. What time does the bus arrive at its destination?

**A**: Arrival time = $8:00AM+5hours30minutes=1:30PM$.

#### 8. **Ratio**

**Q8**: The ratio of boys to girls in a class is 3:4. If there are 24 girls, how many boys are in the class?

**A**: Let the number of boys be $3x$ and the number of girls be $4x$.

If $4x=24$, then $x=6$.

So, the number of boys is $3x=18boys$.

#### 9. **Percentage Increase**

**Q9**: A farmer had 150 cows, and the number increased by 20%. How many cows does the farmer have now?

**A**: Increase = $10020â€‹Ã—150=30$.

Total cows = $150+30=180cows$.

#### 10. **Simple Interest**

**Q10**: If you invest 10,000 shillings at an interest rate of 5% per year, how much interest will you earn in 2 years?

**A**: Interest = $1005â€‹Ã—10,000Ã—2=1,000shillings$.

#### 11. **Division Problem**

**Q11**: A group of 6 friends shares 540 shillings equally. How much does each friend get?

**A**: Each friend gets $6540â€‹=90shillings$.

#### 12. **Total Cost**

**Q12**: If 4 notebooks cost 1,200 shillings, how much do 10 notebooks cost?

**A**: Total cost = $4,â€‹Ã—10=3,000shillings$.

#### 13. **Average**

**Q13**: Find the average of the numbers 45, 55, 60, and 40.

**A**: Average = $4+++â€‹=50$.

#### 14. **Fuel Consumption**

**Q14**: A car uses 8 liters of fuel to travel 120 kilometers. How many liters of fuel will it use to travel 300 kilometers?

**A**: Fuel consumption = $1208â€‹=0.0667liters/km$.

For 300 km = $300Ã—0.0667=20liters$.

#### 15. **Discount**

**Q15**: A jacket costs 2,500 shillings but is sold at a 15% discount. What is the sale price?

**A**: Discount = $10015â€‹Ã—2,500=375shillings$.

Sale price = $2,500âˆ’375=2,125shillings$.

#### 16. **Rate of Work**

**Q16**: If 3 painters can paint a house in 12 days, how many days will it take 6 painters to paint the same house, assuming they work at the same rate?

**A**: $3Ã—12=36painter-days$.

For 6 painters: $636â€‹=6days$.

#### 17. **Perimeter**

**Q17**: A rectangular garden has a length of 18 meters and a width of 12 meters. What is the perimeter of the garden?

**A**: Perimeter = $2Ã—(18+12)=60meters$.

#### 18. **Profit Percentage**

**Q18**: A trader buys a bicycle for 120,000 shillings and sells it for 150,000 shillings. What is the percentage profit?

**A**: Profit = $150,000âˆ’120,000=30,000shillings$.

Percentage profit = $,,â€‹Ã—100=25%$.

#### 19. **Dividing an Amount**

**Q19**: A sum of 1,200 shillings is to be shared between two friends in the ratio 2:3. How much does each friend get?

**A**: The total number of parts is $2+3=5$.

The first friend gets $52â€‹Ã—1,200=480shillings$.

The second friend gets $53â€‹Ã—1,200=720shillings$.

#### 20. **Time and Distance**

**Q20**: A car travels at 60 km/h. How long will it take to travel 300 kilometers?

**A**: Time = $km/hkmâ€‹=5hours$.

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