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First Round Challenge: A 90 minute, 25 multiple choice question first round Challenge aimed at students year 13 or below. The problems on the Senior Maths Challenge are designed to make students think. Stimulating problems for both beginners and experienced problem-solvers.
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When completed correctly, the cross number is filled with four three-digit numbers. What digit is * ?
In the diagram, the outer hexagon is regular and has an area of 216. What is the shaded area?
What is the value of 99 x (0.(49) − 0.(4))?
0.(49) = 0.49494949...
0.(4) = 0.4444444...
In 2021, a first-class postage stamp cost 85p and a second-class postage stamp cost 66p. To spend an exact number of pounds and buy at least one of each type, what is the smallest total number of stamps that should be purchased?
A sequence begins 2023, 2022, 1, . . . . After the first two terms, each term is the positive difference between the previous two terms. What is the value of the 25th term?
Three points P, Q, and R are placed on the circumference of a circle with centre O. The arc lengths PQ, QR, and RP are in the ratio 1:2:3. In what ratio are the areas of the sectors OPQ, OQR, and ORP?
How many lines of three adjacent cells can be chosen from this grid, horizontally, vertically or diagonally, such that the sum oft he numbers in the three cells is a multiple of three?
The sum of four consecutive primes is itself prime. What is the largest of the four primes?
Three circles with radii 2, 3 and 3 touch each other, as shown in the diagram.
What is the area of the triangle formed by joining the centres of these circles?
The positive integer x is a solution of the equation (x ÷ 12) ÷ (15 ÷ x) = 20. What is the sum of the digits of x?
The diagram shows two symmetrically placed squares with sides of length 2 and 5. What is the ratio of the area of the small square to that of the shaded region?
In 2016, the world record for completing a 5000m three-legged race was 19 minutes and6 seconds. It was set by Damian Thacker and Luke Symonds in Sheffield.
What was their approximate average speed in km/h?
The diagram shows two congruent regular pentagons and a triangle. The angles marked G° are equal. What is the value of G?
The figure shows a regular hexagon. How many parallelograms are there in the figure?
The base of a triangle is increased by 20% and its height is decreased by 15%. What happens to its area?
The sequence of primes rounded to the nearest ten begins 0, 0, 10, 10, 10, 10, 20, 20. How many terms are equal to 40?
When the expression (2² − 1) × (3² − 1) × (4² − 1) × (5² − 1) / (2 × 3) × (3 × 4) × (4 × 5) × (5 × 6) is simplified, which of the following is obtained?
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