Easy Maths For YEAR 10

Question 1

Basic Algebra: 3x + 5 = 20

Answer 1

x = 5

Question 2

Pythagoras Theorem: find the missing side a right angled triangle has sides of 3cm and 4cm. What is the hypotenuse?

Answer 2

5cm

Question 3

Convert 0.75 into a fraction

Answer 3

3/4

Question 4

Find 20% of 150

Answer 4

30

Question 5

A ladder leans against a wall. The angle between the ladder and the ground is 30°. The ladder is 10 m long. Find the height it reaches up the wall.

Answer 5

5m. Opposite / hypotenuse
sin(30*) = h/10

Since sin(30*) = 0.5 we substitute
0.5 = h/10

Multiply 10 on both sides h = 5m

Question 6

Find the Mode: In the dataset {4, 7, 2, 4, 9, 4, 6, 7}

Answer 6

4

Question 7

Bimodal Dataset: What are the modes in {5, 8, 5, 3, 8, 2, 9, 8, 5}?

Answer 7

Modes = 5 and 8, since both appear most frequently.

Question 8

Does the dataset {1, 3, 5, 7, 9} have a mode?

Answer 8

No mode, since all numbers appear only once.

Question 9

Grouped Data Mode: If a class scored {65, 70, 75, 70, 85, 90, 70, 85} on a test, what is the mode?

Answer 9

Mode = 70, since it appears most frequently.

Question 10

Real-World Mode Question: A shop records daily sales of apples as {14, 18, 22, 18, 22, 18, 25} over a week. What is the mode?

Answer 10

Mode = 18, since it occurs most often.

Question 11

Algebra: Solve for x
4x − 7 = 21

Answer 11

x = 7

Question 12

Pythagoras’ Theorem: Find the missing side A right-angled triangle has sides 5 cm and 12 cm, what is the hypotenuse?

Answer 12

a2 + b2 = c2
Given a = 5 and b = 12
5 squared + 12 squared = c2
25 + 144 = 169
169 divided by 13 = 13

Question 13

Fractions & Ratios: A recipe calls for 3 parts flour to 2 parts sugar. If you have 600g of sugar, how much flour do you need?

Answer 13

900g

Question 14

Percentage Increase: A jacket costs £50. After a 20% increase, what is the new price?

Answer 14

£60

Question 15

Trigonometry (SOHCAHTOA): In a right-angled triangle, the opposite side is 8 cm, and the hypotenuse is 10 cm. Find the angle.

Answer 15

53.1 degrees using Sin?

Question 16

What is mode?

Answer 16

The most frequently occurring value in a dataset.

Question 17

What is the mean?

Answer 17

The average value. You find it by adding up all the numbers and dividing by the total count.

Question 18

What is the median?

Answer 18

The middle value when numbers are sorted in order. If there’s an even count, take the average of the two middle values.

Question 19

What is range?

Answer 19

Range is the difference between the largest and smallest values in a dataset.

For the numbers {3, 7, 10, 15}, Range = 15 - 3 = 12