Random Math

Question 1

In age comparison problems, what stays the same over time?

Answer 1

The difference in ages between two people remains constant.

Question 2

Mrs Robert is 36 and her daughter is 24 years younger. What is their age difference?

Answer 2

36 − 12 = 24 years.

Question 3

If ‘4 units’ represents a 24‑year difference, what is 1 unit?

Answer 3

24 ÷ 4 = 6 years.

Question 4

When the daughter was 6 (1 unit), how old was Mrs Robert?

Answer 4

5 units × 6 years/unit = 30 years.

Question 5

How many years ago was Mrs Robert five times as old as her daughter?

Answer 5

36 − 30 = 6 years ago.

Question 6

How do you turn the phrase ‘7 more than a number x’ into an algebraic expression?

Answer 6

x + 7.

Question 7

Solve for x: 2x - 5 = 11.

Answer 7

2x = 16 ⇒ x = 8.

Question 8

What’s the first step to solve1/3x + 4 = 10?

Answer 8

Subtract 4 from both sides: \frac{1}{3}x = 6.

Question 9

How do you check your solution to an equation?

Answer 9

Substitute it back into the original equation to see if both sides match.

Question 10

If 3(x + 2) = 15, what is x?

Answer 10

Divide both sides by 3: x + 2 = 5 ⇒ x = 3.

Question 11

How do you add 2/5 + 1/3

Answer 11

Find common denominator 15: 6/15+5/15=11/15

Question 12

What’s the reciprocal of 7/8

Answer 12

8/7

Question 13

How do you multiply 3/4 times 2/5?

Answer 13

Multiply numerators and denominators: 6/20= 3/10.

Question 14

How do you divide 5/6 by 2/3

Answer 14

Flip the second fraction and multiply: 5/6 times 2/3 = 15/12 = 5/4

Question 15

How can you tell which of 4/7 and 5/8 is larger?

Answer 15

Cross-multiply: 4×8 = 32 vs. 5×7 = 35; since 35>32, 5/8 is larger.

Question 16

Convert 45% to a fraction and a decimal.

Answer 16

45/100=9/20 0.45

Question 17

What is 20% of 150?

Answer 17

0.20 × 150 = 30.

Question 18

If a price rises from $80 to $100, what is the percent increase?

Answer 18

Increase = $20; \frac{20}{80}×100\%=25\%.

Question 19

How do you express 3/4 as a percentage?

Answer 19

3/4=0.75=75%.

Question 20

A quantity decreases by 10%. What fraction remains?

Answer 20

90% remains = \frac{90}{100}=\frac{9}{10}.

Question 21

Simplify the ratio 12 : 18.

Answer 21

Divide both by 6 → 2 : 3.

Question 22

Share $120 in the ratio 3 : 5. How much does the smaller share get?

Answer 22

Total units = 3+5=8; one unit = $15; smaller = 3×15=$45.

Question 23

If the ratio of boys to girls is 4 : 7 and there are 28 girls, how many boys?

Answer 23

One ‘girl’ unit = 28/7=4; boys = 4×4=16.

Question 24

Express 3 : 4 as a fraction of the whole.

Answer 24

3/(3+4)=3/7.

Question 25

Write the formula linking speed, distance, and time.

Answer 25

Speed = Distance/Time

Question 26

A car travels 180 km in 3 h. What is its average speed?

Answer 26

180 ÷ 3 = 60km/h.

Question 27

How long to cover 150 km at 50 km/h?

Answer 27

150 ÷ 50 = 3h

Question 28

If a runner’s speed is 5 m/s, how far in 2 min?

Answer 28

5×120 = 600\text{ m}.

Question 29

What is the relationship between diameter d and radius r?

Answer 29

d = 2r.

Question 30

Write the formula for circumference.

Answer 30

C = 2pi r or pi d.

Question 31

Write the formula for the area of a circle.

Answer 31

A = pi r^2.

Question 32

If r=7 cm, what’s C?

Answer 32

2×\pi×7 ≈ 14\pi cm.

Question 33

If d=10 cm, what’s A?

Answer 33

r=5; A=25\pi cm².

Question 34

What’s the first step in the supposition method for a missing‑value problem?

Answer 34

Assume a convenient value for the unknown.

Question 35

After assuming, what do you do with the given conditions?

Answer 35

Adjust your result (add/subtract) to match the real scenario.

Question 36

Why is supposition useful?

Answer 36

It turns a complex 'change‑over‑time' problem into a simpler assumed case.

Question 37

In 'excess and shortage' problems, what do the two comparisons represent?

Answer 37

One shows how much you have extra, the other how much you lack.

Question 38

How do you find the actual amount using units?

Answer 38

Treat excess and shortage as different numbers of units of the same size; find unit value then compute.

Question 39

Give a one‑line definition of 'shortage.'

Answer 39

When the available amount is less than required.

Question 40

Give a one‑line definition of 'excess.'

Answer 40

When the available amount is more than required.

Question 41

Sum of interior angles of a triangle?

Answer 41

180°.

Question 42

Sum of interior angles of a quadrilateral?

Answer 42

360°.

Question 43

In a right‑angled triangle, what is the Pythagorean theorem?

Answer 43

a^2 + b^2 = c^2.

Question 44

How do you find the perimeter of a polygon?

Answer 44

Add all side lengths.

Question 45

How do you find the area of a rectangle?

Answer 45

length × width.

Question 46

What is a tessellation?

Answer 46

A tiling of the plane by shapes with no gaps or overlaps.

Question 47

Name three regular polygons that tessellate.

Answer 47

Equilateral triangle, square, regular hexagon.

Question 48

Why can a regular pentagon not tessellate by itself?

Answer 48

Its interior angle (108°) does not divide 360° evenly.

Question 49

Give an example of a semi‑regular tessellation.

Answer 49

Pattern combining squares and octagons.

Question 50

How many faces does a cube have?

Answer 50

Six.

Question 51

How many distinct nets can a cube have?

Answer 51

11.

Question 52

What does a cube net consist of?

Answer 52

Six squares connected edge‑to‑edge.

Question 53

In any cube net, how many squares touch the central square?

Answer 53

Four.