Sevenoaks School — 13+ Maths Entrance Exam 2020 (Interactive)

Q1: Work out the value of 57 of 63.

Q2: Simplify 5x - 6y - x + 3y.

Q3(a): Simplify w^8 ÷ w^2.

Q3(b): Simplify 5c^2d × 3c.

Q4: By rounding each number to 2 significant figures, estimate the answer to (24.3 × 14.93) / 123.

Q5(a): Expand and simplify 4c(d - 5).

Q5(b): Expand and simplify 3x - (2x - 3).

Q6(a): A function diagram shows: 4 → [+6] → [×8] → ? Complete the missing output number.

Q6(b): A function diagram shows: 14 → [÷ ?] → [+4] → 11. Find the missing number in the ÷ operation.

Q6(c): A function diagram shows: ? → [×3] → [-5] → 13. Find the missing input number.

Q7(a): Given that a - b = 5, work out the value of 3(a - b).

Q7(b): Given that a - b = 5, work out the value of b - a.

Q8: A 3×3 grid must be completed so that the product of the three numbers in every row, column and diagonal equals 1. The given numbers are: Row 1: 10, ?, 12. Row 2: 120, ?, 20. Row 3: 2, 5, ?. Find the three missing numbers. Give your answer as three values separated by commas in reading order (Row 1 middle, Row 2 middle, Row 3 right). (Refer to original PDF for figure.)

Q9: There are 24 boys, 45 girls and 281 adults in a badminton club. 50 more children join the club. The number of girls is now 18% of the total number of members. How many of the 50 children were boys?

Q10(a): A football team has P points. P = 3W + D, where W is the number of wins and D is the number of draws. A team gets 0 points for losing. A team has won 5 games, drawn 3 games and lost 1 game. How many points does the team have?

Q10(b): A football team has P points where P = 3W + D (W = wins, D = draws, 0 points for a loss). After 33 games a different team has 53 points. 11 games were draws. How many games has this team lost?

Q11: BCD is a straight line. Triangle ABC is equilateral. CE = DE. Angle DEC = 28°. Work out the size of angle x, where x is angle ACE. (Refer to original PDF for figure.)

Q12: AB is parallel to CD. A transversal crosses both lines. At line AB the angle between the transversal and AB is 2x°. At line CD the angles between the transversal and CD are 5x° and x°. Calculate the value of x. (Refer to original PDF for figure.)

Q13: Nicola thinks of a number. She doubles it, adds 4 to the answer, and then divides the result by 7. The number she now has is 2. Find the number she first thought of.

Q14(a): A rectangle has width x cm and length (3x - 2) cm. Form a simplified expression for the perimeter of this rectangle. (Refer to original PDF for figure.)

Q14(b): The perimeter of the rectangle (with width x cm and length (3x - 2) cm) is 124 cm. Calculate the value of x.

Q15: Here are five cards: 1, 5, 7, 9, 11. One of the cards is removed. The mean of the remaining four cards is 6. Which card was removed? You must show your working.

Q16: The range of a set of numbers is 15 14. The smallest number is -2 78. Work out the largest number. Give your answer as a mixed fraction.

Q17(a): A sequence has term-to-term rule 'multiply by 8 and then add 11'. The first term is -1. Work out the third term.

Q17(b): The sequence from part (a) is -1, 3, 35. The order of the three terms is reversed to make a new sequence: 35, 3, -1. Work out the term-to-term rule for this new sequence.

Q18: Find the value of x given that 12 : 23 = x : 1.

Q19: A solid has a uniform cross section. The cross section is a rectangle and a semicircle joined together. The rectangle has width x cm and height 2x cm, with the semicircle sitting on top (diameter = x cm). The depth of the solid is x cm. Work out an expression, in cm^3, for the total volume of the solid. Give your answer in terms of pi. (Refer to original PDF for figure.)

Q20: The minute hand of a clock is missing. The angle between the hour hand and twelve o'clock is 137°. How many minutes have passed since the last full hour? (Refer to original PDF for figure.)