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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The base of a triangle is increased by 20% and its height is decreased by 15%. What happens to its area?
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?
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?
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?
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?
What is the value of 99 x (0.(49) − 0.(4))?
0.(49) = 0.49494949...
0.(4) = 0.4444444...
When completed correctly, the cross number is filled with four three-digit numbers. What digit is * ?
How many of the numbers 6, 7, 8, 9, 10 are factors of the sum 2^2024 + 2^2023 + 2^2022?
Wenlu, Xander, Yasser and Zoe make the following statements:
Wenlu: “Xander is lying.”
Xander: “ Yasser is lying.”
Yasser: “Zoe is telling the truth.”
Zoe: “Wenlu is telling the truth.”
What are the possible numbers of people telling the truth?
The greatest power of 7 which is a factor of 50! is 7^k (n! = 1×2×3×4×. . .× (n − 1) × n). What is k?
PQRST is a regular pentagon. The point U lies on ST such that ∠QPU is a right angle. What is the ratio of the interior angles in triangle PUT?
The points P (d, −d) and Q (12 − d, 2d − 6) both lie on the circumference of the same circle whose centre is the origin. What is the sum of the two possible values of d?
In Bethany’s class of 30 students, twice as many people played basketball as played football. Twice as many played football as played neither. Which of the following options could have been the number of people who played both?
G and H are midpoints of two adjacent edges of a cube. A trapezium-shaped cross-section is formed cutting through G, H and two further vertices, as shown. The edge-length of the cube is 2√2. What is the area of the trapezium?
The number M = 124563987 is the smallest number which uses all the non-zero digits once each and which has the property that none of the pairs of its consecutive digits makes a prime number. For example, the 5th and 6th digits of M make the number 63 which is not prime. N is the largest number which uses all the non-zero digits once each and which has the property that none of the pairs of its consecutive digits makes a prime number.
What are the 5th and 6th digits of N?
How many solutions are there of the equation 1 + 2 sin X − 4 sin2 X − 8 sin3 X = 0 with 0° < X < 360°?
The expression (7n + 12) / (2n + 3) takes integer values for certain integer values of n. What is the sum of all such integer values of the expression?
Triangle LMN represents a right-angled field with LM = r, LX = p and XN = q. Jenny and Vicky walk at the same speed in opposite directions along the edge of the field, starting at X at the same time. Their first meeting is at M. Which of these expressions gives q in terms of p and r?
Triangle PQR is equilateral. A semicircle with centre O is drawn with its diameter on PR so that one end is at P and the curved edge touches QR at X. The radius of the semicircle is √3. What is the length of QX?
The length of a rectangular piece of paper is three times its width. The paper is folded so that one vertex lies on top of the opposite vertex, thus forming a pentagonal shape. What is the area of the pentagon as a fraction of the area of the original rectangle?
A square has its vertices on the edges of a regular hexagon. Two of the edges of the square are parallel to two edges of the hexagon, as shown in the diagram. The sides of the hexagon have length 1. What is the length of the sides of the square?
What is the area of the part of the xy-plane within which x3y2 − x2y2 − xy4 + xy3 ≥ 0 and 0 ≤ x ≤ y?
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