KS3 Mathematics Practice Questions and Solutions
Indices
1. Question: Simplify \(w^4 \times w^4\).
Solution: When multiplying terms with the same base, add the powers: \(4 + 4 = 8\). Hence \(w^4
\times w^4 = w^8\).
2. Question: Simplify \(a^6 \div a^3\).
Solution: When dividing terms with the same base, subtract the powers: \(6 - 3 = 3\). Hence \(a^6
\div a^3 = a^3\).
Circumference and Area of Circles
1. Question: A circle has radius 9 cm. Calculate its circumference (use \(\pi \approx 3.14\) and give
your answer to 1 dp).
Solution: \(C = 2\pi r = 2 \times 3.14 \times 9 \approx 56.55\;\mathrm{cm}\). Rounded to 1 dp:
56.5 cm.
2. Question: A circle has radius 3 cm. Calculate its area, giving your answer in terms of \(\pi\).
Solution: \(A = \pi r^2 = \pi \times 3^2 = 9\pi\;\mathrm{cm}^2\).
Interior and Exterior Angles of Polygons
1. Question: Each interior angle of a regular polygon is \(156^\circ\). How many sides does the polygon
have?
Solution: Exterior angle = \(180^\circ - 156^\circ = 24^\circ\). \(360^\circ \div 24^\circ = 15\) sides.
2. Question: In a regular polygon, each interior angle is 5 times its exterior angle. How many sides
does the polygon have?
Solution: Let exterior angle be \(e\). Then interior = \(5e\). \(5e + e = 180^\circ \Rightarrow e =
30^\circ\). \(360^\circ \div 30^\circ = 12\) sides.
Angles of a Triangle
1. Question: Two angles of a triangle are \(45^\circ\) and \(70^\circ\). Find the third angle.
Solution: \(180^\circ - (45^\circ + 70^\circ) = 65^\circ\).
2. Question: The angles in a triangle are in the ratio 1 : 2 : 3. Find the size of each angle.
Solution: Let the angles be \(x, 2x, 3x\) so \(6x = 180^\circ\) and \(x = 30^\circ\). The angles are 30°,
60°, 90°.