Algebra, Geometry & Mensuration — Practice

Question 1

Solve for $x$: $5x - 9 = 2x + 15$.

Accepted Answer

Collecting terms: $5x-2x=15+9$, so $3x=24$, giving $x=8$. Check: $5(8)-9=31$ and $2(8)+15=31$.

Answer: $x=8$.

Question 2

If $a=3$ and $b=6$, evaluate $2a^2 + b - 4$.

Accepted Answer

$2(9)+6-4=18+6-4=20$.

Answer: 20.

Question 3

Find the area and perimeter of a rectangle with length 20 cm and breadth 13 cm.

Accepted Answer

Area $=20	imes13=260$ cm². Perimeter $=2(20+13)=66$ cm.

Answer: Area = 260 cm², Perimeter = 66 cm.

Question 4

Two angles of a triangle are 38° and 97°. Find the third angle.

Accepted Answer

$180-38-97=45°$.

Answer: 45°.

Question 5

Find the area and perimeter of a square with side 11 cm.

Accepted Answer

Area $=11^2=121$ cm². Perimeter $=4	imes11=44$ cm.

Answer: Area = 121 cm², Perimeter = 44 cm.

Question 6

Four angles around a single point are $x$, $2x$, $3x$ and $4x$. Find the value of $x$ and each angle.

Accepted Answer

Angles around a point sum to 360°: $x+2x+3x+4x=360 \Rightarrow 10x=360 \Rightarrow x=36$. The angles are $36°, 72°, 108°, 144°$.

Answer: $x=36°$; angles 36°, 72°, 108°, 144°.

Question 7

A triangle's angles are in the ratio 5:6:7. Find each angle.

Accepted Answer

Total parts $=5+6+7=18$. One part $=180\div18=10°$. The angles are $50°, 60°, 70°$.

Answer: 50°, 60°, 70°.

Question 8

A right-angled triangle has legs of 10 cm and 24 cm. Find its area.

Accepted Answer

Area $=\frac{1}{2}	imes10	imes24=120$ cm² (the two legs serve directly as base and height).

Answer: 120 cm².

Question 9

Find the circumference and area of a circle with radius 21 cm (use $\pi=\frac{22}{7}$).

Accepted Answer

Circumference $=2	imes\frac{22}{7}	imes21=132$ cm. Area $=\frac{22}{7}	imes21^2=\frac{22}{7}	imes441=1{,}386$ cm².

Answer: Circumference = 132 cm, Area = 1,386 cm².

Question 10

Find the volume of a cube with side 7 cm.

Accepted Answer

$7^3=343$ cm³.

Answer: 343 cm³.

Question 11

Find the volume of a cylinder with radius 14 cm and height 5 cm (use $\pi=\frac{22}{7}$).

Accepted Answer

$V=\frac{22}{7}	imes14^2	imes5=\frac{22}{7}	imes196	imes5=22	imes28	imes5=3{,}080$ cm³.

Answer: 3,080 cm³.

Practice — Algebra, Geometry & Mensuration