Math Problems for 10th Class
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Questions and Answers

The cost of 3 stools and 5 desks is $360. The cost of 6 stools and 15 desks is $900. What is the cost of 1 desk? (Round off the answers to the nearest $10).

70

A roll of string is cut into three pieces in the ratio of 7 : 2 : 3. The shortest piece is 44 cm. What is the length of the longest piece of the string?

154

ABCD is a rhombus. ∠BAC = 52°. What is the sum of ∠x and ∠y?

180

Mrs Tan bought a dress for $140. She paid the cashier in $10 and $5 notes. If there were fifteen dollar notes altogether, how many $10 notes were there?

<p>10</p> Signup and view all the answers

A large tank contained 6l of water. The graph below shows the amount of water left in a tank at the end of each day. What is the total amount of water used on Day 2 and Day 4.

<p>3</p> Signup and view all the answers

What percentage of the students are in Dance Club and Brownies?

<p>25</p> Signup and view all the answers

The ratio of the number of students in Dance Club to the number of students in Brownies is 3 : 2. How many students are in Brownies?

<p>72</p> Signup and view all the answers

The figure below shows an empty container. All edges meet at right angles. When the tap is turned on, water flows into the container at rate of 2.01 litres per minute. How much time is needed to fill the container completely?

<p>60</p> Signup and view all the answers

The distance between Town C and Town D is 1680 km. Train X travels from Town C to Town D at 8.00 a.m. at an average speed of 230 km/h. At the same time, Train Y travels from D to Town C at an average speed of 190 km/h. (a) What time did they meet?

<p>11:00 a.m.</p> Signup and view all the answers

The distance between Town C and Town D is 1680 km. Train X travels from Town C to Town D at 8.00 a.m. at an average speed of 230 km/h. At the same time, Train Y travels from D to Town C at an average speed of 190 km/h. (b) How far would each train have travelled when they meet on the way?

<p>Train X: 690 Train Y: 570</p> Signup and view all the answers

There were 45 soccer balls, 30 basketballs and 68 netballs in the PE room. After 80 balls were added, the number of soccer balls increased by 40% and the number of netballs increased by 25%. What was the percentage increase in the number of basketballs?

<p>50</p> Signup and view all the answers

Both Tammy and Adam left their houses at the same time to go to the water theme park. Tammy travelled 20 km from her house to the park at an average speed of 30 km/h. Adam travelled from his house at an average speed of 42 km/h and reached the park 15 minutes later than Tammy. What was the distance between Adam's home and the park?

<p>28</p> Signup and view all the answers

The figure below is not drawn to scale. ABEF is a parallelogram and BCDE is a trapezium. BE // CD, AB // FD and BC // AD, DF is a straight line. ZADF = 42° and ∠DAF = 68°. (a) Find ∠BCD.

<p>110</p> Signup and view all the answers

There were a total of 2120 students in the school field at first. After 536 boys and 1/4 of the girls left, the ratio of the number of boys to the number of girls became 4 : 9. How many more girls than boys were there at the school field in the end?

<p>340</p> Signup and view all the answers

Bottles A, B and C contain 7.35 litres of paint altogether. 1/5 of the paint in Bottle A is transferred to Bottle B. After that, 1/5 of the paint in Bottle B is transferred to Bottle C. Now, Bottle A has twice the amount of paint in Bottle B and Bottle B has twice the amount of paint in Bottle C. (a) How much paint was transferred from Bottle A to Bottle B?

<p>1.47</p> Signup and view all the answers

Bottles A, B and C contain 7.35 litres of paint altogether. 1/5 of the paint in Bottle A is transferred to Bottle B. After that, 1/5 of the paint in Bottle B is transferred to Bottle C. Now, Bottle A has twice the amount of paint in Bottle B and Bottle B has twice the amount of paint in Bottle C. (b) How much pain was in Bottle C at first?

<p>0.49</p> Signup and view all the answers

Gary is playing a mobile game on his phone. On his first win, he obtains 3 points. For every subsequent win, he will receive 2 additional points more than his previous win. (a) Gary gets 6 wins in a row. What will be his score for the 6th win?

<p>13</p> Signup and view all the answers

Gary is playing a mobile game on his phone. On his first win, he obtains 3 points. For every subsequent win, he will receive 2 additional points more than his previous win. (b) How many times must he win the game in a row for him to achieve 98 points?

<p>7</p> Signup and view all the answers

The figure below is made up a quadrant and a circle overlapping each other. The quadrant touches the circle at points F and G. The circle, with centre O, has a diameter of 24 cm. Find the area of the shaded part. (Take π = 3.14)

<p>113.04</p> Signup and view all the answers

Mr Chan received $6120 from selling some shoes and some shirts. He received $3240 more for the shoes than the shirts. 4 times as many shoes as shirts were sold. Each shirt cost $15 more than each shoe. (a) How much did Mr Chan receive for the shoes?

<p>4680</p> Signup and view all the answers

Mr Chan received $6120 from selling some shoes and some shirts. He received $3240 more for the shoes than the shirts. 4 times as many shoes as shirts were sold. Each shirt cost $15 more than each shoe. (b) How many shirts did Mr Chan sell?

<p>60</p> Signup and view all the answers

Abu, Bob, Cheryl and Donna shared a sum of money equally at first. Abu gave 2/3 of his money to Bob. (a) What fraction of the sum of money did Abu have in the end?

<p>1/3</p> Signup and view all the answers

Abu, Bob, Cheryl and Donna shared a sum of money equally at first. Abu gave 2/3 of his money to Bob. (b) Bob then gave 1/5 of his money to Cheryl. Cheryl then gave 3/8 of her money and an additional $55 to Donna. Donna had $595 in the end. How much was the sum of money they shared?

<p>2400</p> Signup and view all the answers

Flashcards

Problem 1

The cost of 3 stools and 5 desks is $360. The cost of 6 stools and 15 desks is $900. Find the cost of 1 desk.

Problem 2

A roll of string is cut into three pieces in the ratio of 7 : 2 : 3. The shortest piece is 44 cm. Find the length of the longest piece of string.

Problem 3

In a rhombus ABCD, ∠BAC = 52°. Find the sum of ∠x and ∠y.

Problem 4

Mrs Tan bought a dress for $140. She paid the cashier in $10 and $5 notes. If there were fifteen dollar notes altogether, how many $10 notes were there?

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Problem 5

A large tank contained 6ℓ of water. The graph shows the amount of water left in a tank at the end of each day. Find the total amount of water used on Day 2 and Day 4.

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String

A series of characters, like letters, numbers, or symbols, that are considered as a single unit.

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Pie Chart

A visual representation of data using sectors of a circle, where the size of each sector is proportional to the amount of data it represents.

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Brownies Ratio

The ratio of the number of students in Dance Club to the number of students in Brownies is 3 : 2. How many students are in Brownies?

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Right Angles

All edges meet at right angles.

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Volume

A quantity that describes the amount of space occupied by a three-dimensional object.

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Problem 8 (a)

The distance between Town C and Town D is 1680 km. Train X travels from Town C to Town D at 8.00 a.m. at an average speed of 230 km/h. At the same time, Train Y travels from D to Town C at an average speed of 190 km/h. What time did they meet?

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Train X distance

The distance traveled by Train X when it meets Train Y.

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Train Y distance

The distance traveled by Train Y when it meets Train X.

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Parallelogram

A four-sided figure with two pairs of parallel sides.

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Trapezium

A four-sided figure with only one pair of parallel sides.

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Problem 11 (a)

ABEF is a parallelogram and BCDE is a trapezium. BE // CD, AB // FD and BC // AD, DF is a straight line. ∠ADF = 42° and ∠DAF = 68°. Find ∠BCD.

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Problem 11 (b)

ABEF is a parallelogram and BCDE is a trapezium. BE // CD, AB // FD and BC // AD, DF is a straight line. ∠ADF = 42° and ∠DAF = 68°. Find ∠ABE.

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Problem 11 (c)

ABEF is a parallelogram and BCDE is a trapezium. BE // CD, AB // FD and BC // AD, DF is a straight line. ∠ADF = 42° and ∠DAF = 68°. Find ∠BEF.

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Problem 13 (a)

Bottles A, B and C contain 7.35 litres of paint altogether. 1/5 of the paint in Bottle A is transferred to Bottle B. After that, 1/5 of the paint in Bottle B transferred to Bottle C. Now, Bottle A has twice the amount of paint in Bottle B and Bottle B has twice the amount of paint in Bottle C. How much paint was transferred from Bottle A to Bottle B?

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Problem 13 (b)

Bottles A, B and C contain 7.35 litres of paint altogether. 1/5 of the paint in Bottle A is transferred to Bottle B. After that, 1/5 of the paint in Bottle B transferred to Bottle C. Now, Bottle A has twice the amount of paint in Bottle B and Bottle B has twice the amount of paint in Bottle C. How much paint was in Bottle C at first?

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Problem 14 (a)

Gary is playing a mobile game on his phone. On his first win, he obtains 3 points. For every subsequent win, he will receive 2 additional points more than his previous win. What will be his score for the 6th win?

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Problem 14 (b)

Gary is playing a mobile game on his phone. On his first win, he obtains 3 points. For every subsequent win, he will receive 2 additional points more than his previous win. How many times must he win the game in a row for him to achieve 98 points?

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Quadrant

A region enclosed by a curved boundary.

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Problem 16 (a)

Mr. Chan received $6120 from selling some shoes and some shirts. He received $3240 more for the shoes than the shirts. 4 times as many shoes as shirts were sold. Each shirt cost $15 more than each shoe. How much did Mr. Chan receive for the shoes?

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Problem 16 (b)

Mr. Chan received $6120 from selling some shoes and some shirts. He received $3240 more for the shoes than the shirts. 4 times as many shoes as shirts were sold. Each shirt cost $15 more than each shoe. How many shirts did Mr. Chan sell?

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Problem 17 (a)

Abu, Bob, Cheryl, and Donna shared a sum of money equally at first. Abu gave 2/3 of his money to Bob. What fraction of the sum of money did Abu have in the end?

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Combined-cost problem

A mathematical problem where you need to figure out the price of a single item using information about the prices of multiple bundles of those items.

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Ratio division

A way to represent a ratio by dividing a whole into parts, where the size of each part represents the proportion of the ratio.

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Rhombus properties

In a rhombus, the diagonals bisect each other at right angles, forming four congruent right triangles.

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Currency problem

A technique to solve problems involving multiple denominations of currency, usually by setting up equations to represent the total value and the number of each type of note.

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Water usage calculation

The amount of water used is equal to the difference between the starting amount and the remaining amount at the end of each day.

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Percentage calculation

Finding the proportion of students in a specific category by dividing the number of students in that category by the total number of students and then multiplying by 100.

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Ratio problem

A technique for solving problems involving a known total and a ratio between two quantities, where you can use the ratio to find the actual values of each quantity.

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Volume of a rectangular prism

The volume of a rectangular prism is calculated by multiplying its length, width, and height.

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Filling time calculation

Calculating the amount of time needed to fill a container at a constant rate of water flow, by dividing the container's volume by the flow rate.

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Distance calculation

The distance traveled by an object is equal to its speed multiplied by the time it travels.

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Meeting time calculation

The meeting time of two objects traveling towards each other is determined by finding the time it takes for them to cover the total distance between them.

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Percentage increase calculation

Calculating the percentage increase of a quantity by finding the difference between the final and initial values, dividing that difference by the initial value, and then multiplying by 100.

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Relative speed concept

The time it takes for a faster object to reach a certain point is less than the time it takes for a slower object to reach the same point.

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Angle sum property of a triangle

The sum of all the interior angles of a triangle is always 180 degrees.

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Corresponding angles

The angles formed when two parallel lines are intersected by a transversal are equal.

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Part-to-part ratio

A ratio that is used to determine the relative size of different quantities in a set.

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Combined ratio

A combination of two or more ratios, where you can find the actual values of each quantity using the information provided in the problem.

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Transfer problem

Solving a problem involving multiple transfers between containers by tracking the amount of liquid in each container after each transfer.

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Total revenue calculation

Finding the total amount of money that a person receives by selling items, given the quantity of each item sold and its selling price.

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Arithmetic sequence

A sequence where each term is calculated by adding a constant value to the previous term.

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Area of a shaded region

Finding the area of a shaded part within a complex shape by subtracting the area of the unshaded region from the area of the larger shape.

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Quantity sold calculation

Calculating the number of items sold given the total revenue and the price of each item.

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Equal sharing

A situation where multiple individuals share a certain amount of money equally.

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Money transfer problem

A complex word problem involving multiple individuals and their actions regarding money, where you need to track each individual's money after each transfer.

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Study Notes

Question 1

  • The cost of 3 stools and 5 desks is $360
  • The cost of 6 stools and 15 desks is $900
  • Find the cost of 1 desk (rounded to the nearest $10)

Question 2

  • A string is cut into three pieces in the ratio 7:2:3
  • The shortest piece is 44 cm
  • Find the length of the longest piece

Question 3

  • ABCD is a rhombus
  • ∠BAC = 52°
  • Find the sum of 2x and y

Question 4

  • Mrs Tan bought a dress for $140
  • She paid with $10 and $5 notes
  • There were 15 notes in total
  • Find the number of $10 notes

Question 5

  • A large tank initially contained 6 liters of water
  • The graph shows the amount of water left each day
  • Find the total amount of water used on Day 2 and Day 4

Question 6a

  • The pie chart shows the CCAs of 300 students
  • Find the percentage of students in Dance Club and Brownies

Question 6b

  • The ratio of Dance Club students to Brownies is 3:2
  • Find the number of students in Brownies

Question 7

  • An empty container has dimensions of 85 cm, 42 cm, 24 cm, and 20 cm
  • Water flows in at 2.01 litres/min
  • Find the time needed to fill the container completely

Question 8a

  • The distance between Town C and Town D is 1680 km
  • Train X travels from C to D at 230 km/h
  • Train Y travels from D to C at 190 km/h
  • Both trains start at 8:00 a.m.
  • Find the time they meet

Question 8b

  • Find the distance each train traveled when they met

Question 9

  • 45 soccer, 30 basketball, and 68 netballs
  • 80 balls are added
  • Soccer balls increased by 40%
  • Netballs increased by 25%
  • Find the percentage increase in basketballs

Question 10

  • Tammy travels 20 km at 30 km/h
  • Adam travels at 42 km/h, and arrives 15 minutes later than Tammy
  • Find the distance between Adam's home and the park

Question 11a

  • ABEF is a parallelogram
  • BCDE is a trapezium
  • BE // CD, AB // FD, BC // AD
  • ∠ADF = 42°, ∠DAF = 68°
  • Find ∠BCD

Question 11b

  • Find ∠ABE

Question 11c

  • Find ∠BEF

Question 12

  • 2120 students initially
  • 536 boys left, 1/4 of girls left
  • Ratio of boys to girls became 4:9
  • Find the difference in number of girls and boys

Question 13a

  • Bottles A, B, and C contain 7.35 liters
  • 1/5 of A's paint is transferred to B
  • 1/5 of B's paint is transferred to C
  • Bottle A has twice the amount of paint in B
  • Bottle B has twice the amount of paint in C
  • Find the amount transferred from A to B

Question 13b

  • Find the initial amount of paint in Bottle C

Question 14a

  • Gary scores 3 points on first win
  • Subsequent wins add 2 more points than previous
  • Gary wins 6 games in a row
  • Find his score for the 6th win

Question 14b

  • Find the number of wins to get 98 points

Question 15

  • Quadrant and circle overlap
  • Circle diameter = 24 cm
  • π = 3.14
  • Find the area of the shaded part

Question 16a

  • Mr. Chan received $6120 from selling shoes and shirts
  • $3240 more for shoes than shirts
  • 4 times as many shoes as shirts
  • Shirts cost $15 more than shoes
  • Find the amount received for the shoes

Question 16b

  • How many shirts did Mr. Chan sell?

Question 17a

  • Abu, Bob, Cheryl, and Donna share money equally
  • Abu gives 2/3 of his share to Bob
  • Find the fraction of the total Abu has left

Question 17b

  • Bob gives 1/5 to Cheryl
  • Cheryl gives 3/8 to Donna and additional $55
  • Donna received $595
  • Find the starting total amount shared

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Description

Test your understanding of mathematics with this quiz designed for 10th class students. Covering topics from geometry to ratios and percentage calculations, this quiz will challenge your problem-solving skills. Ideal for exam preparation and practice.

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