Alleyns School 13 Plus Maths Sample Paper Online Quiz view all papers Welcome to your Alleyn's School 13+ MATHS SAMPLE EXAMINATION PAPER 11. How much larger is the 9 than the 5 in the number 690753? A. 8950 B. 90050 C. 8995 D. 89950 E. 89500 None 2. 3 + 4 × 5 – 1 = A. 34 B. 28 C. 19 D. 22 E. 24 None 3. Estimate the value of \[\frac{584.3+43.27}{5.24×22.64}\] A. 50 B. 25 C. 20 D. 10 E. 5 None 4. A regular polygon has interior angles of 162°. How many sides does the polygon have? A. 45 B. 9 C. 20 D. 18 E. 24 None 5. How many sides does a heptagon have? A. 6 B. 7 C. 8 D. 9 E. 10 None 6. Write the ratio 1.6m : 480cm in its simplest form A. 1 : 3 B. 1.6 : 480 C. 1 : 300 D. 40 : 12 E. 1600 : 48 None 7. 6 – 2(x – 1) simplifies to A. 4x – 4 B. 4 – 2x C. 8 – 2x D. 2x + 5 E. 2x + 8 None 8. Which of these is the same as \[\frac{3}{7}\] ? A. \[\frac{13}{17}\] B. \[\frac{1}{2}\] + \[\frac{2}{5}\] C. \[\frac{5}{12}\] - \[\frac{2}{5}\] D. \[\frac{13}{14}\] - \[\frac{1}{2}\] E. \[\frac{33}{70}\] None 9. What would be the most appropriate units in which to measure the mass of an apple? A. g B. mg C. kg D. m E. cm None 10. The two shorter sides of a right-angled triangle are 5cm and 12cm. What is the length of the third side? A. 10.9cm B. 15cm C. 169cm D. 17cm E. 13cm None 11. Work out: (a) 576.02 + 34.523 610.543 600.543 921.250 811.250 61.0543 None (b) 36.84 × 20.3 747.852 74.7852 184.20 7478.52 747842 None 12. Work out the following, giving your answers in lowest terms: (a) \[5\frac{2}{9} − 2\frac{5}{6}\] 2 7/18 30/3 3 7/18 2 5/7 1 6/15 None (b) \[\frac{12}{15} ÷ \frac{18}{35}\] 1 5/9 3 5/3 1 6/9 2 4/5 1 9/5 None (c) \[1\frac{1}{2} + 2\frac{1}{2}\ × 3\frac{4}{5}\] 11 22/4 38/5 76/5 none of the above None 13. (a) (−4) × (−5.2) = 20.8 0.20 2.08 both a&b none of the above None (b) 7 − 2(3 + (−2)) = 5 45 25 -5 15 None (c) \[\frac{(−3)+3×(−8)}{(−5)+(−1) }\] 4.5 -4.5 3.5 2.5 1.5 None (d) (−11) − (−3) + (−5) = -13 13 -19 -9 9 None 14. (a) Work out 16% of £545. £87.20 £86.20 £85.70 £86.10 £84.50 None (b) A holiday was offered in a 20% discount sale for £1088. What was its cost before the sale? £1360 £136 £1250 £1000 £1400 None 15. Find the next two terms in each sequence, and also the formula for the nth term. (a) 2, 5, 8, 11, ....... 14,17, 3n-1 15,16, n-1 14,18, n-2 12,14, n-1 14,17, 3n+1 None (b) 3, 6, 11, 18, 27 38,51, n2+2 38,51, n+2 38,51, n2-2 28,40, n+1 18,36,2n-1 None 16. The following pattern of squares is made out of matchsticks: (a) The next shape in this pattern is made up of 4 squares. How many matchsticks are needed to make this new 4-square shape? 17 18 15 16 19 None (b) Let m stand for the number of matchsticks and s for the number of squares. Write an equation for m in terms of s. 4s+1 4s-1 2s+1 2s-1 none of the above None (c) How many matches are needed for a pattern with 15 squares? 61 64 59 60 65 None (d) How many squares can be made using 201 matches? 50 5.5 55 800 none of the above None 17. Solve the following equations, showing your working. (a) 3a − 7 = 20 a=9 a=4.2 a=81 a=8 a=10 None (b) 3(3 − 5d) = 45 d=-2.4 d=2.4 d=0.8 d=24 d=-3.6 None (d) \[\frac{2x}{3} + 1 = 11\] x=15 x=18 x=6.6 x=8 x=16 None (e) 2(3x + 1) = 6 − 4(7 − x) x=-12 x=10 x=14 x=16 x=8 None 18. Here are the handspans of 13 girls from Year 9, measured in centimetres. 18, 22, 17, 19, 19, 22, 22, 23, 18, 19, 21, 21, 19 (a) What is the mean handspan? 20 2 1.8 19 21 None (b) What is the median handspan? 19 22 21 18 17 None (c) What is the range of the girls’ handspans? 6 5 4 14 16 None 19. (a) What is the circumference of a bicycle wheel if the radius is 32 cm? Give your answer correct to 1 decimal place. 201.1 20.11 2.011 201.0 201.6 None (b) How many complete revolutions does the wheel make in a journey of 5 km? 2486 2286 2480 2280 2400 None (c) If it takes 20 minutes to cycle 8 km, what is the speed in kilometres per hour? 24km/h 0.4km/h 14km/h 16km/h 2.5km/h None (d) What is this speed in metres per second? Give your answer correct to 2 decimal places. 6.67m/s 66.7m/s 6.66m/s 240m/s None of the Above None 20. The following four cards are shuffled and placed face down. Jacob then selects two of the cards randomly. (a) List all the possible pairs of cards. 2&3, 2&6, 2&7, 3&7, 6&7 2&2, 2&6, 2&7, 3&7, 6&7 2&3, 2&6, 2&7, 3&3, 6&7 2&3, 2&6, 2&7, 3&7, 6&6 None of the Above None (b) Find the probability that the total for the two cards is 9. 1/3 1/6 2/3 1/4 1/5 None (c) Find P(both even). 1/6 1/8 1/4 1/2 1/10 None 21. Here is a net for a cube. (a) Which face will be opposite to the one marked B? E A B C D None (b) Which face will be opposite to the one marked C? F E D C B None 22. (a) Calculate the volume of the following prism. 476.16cm3 4761.6cm3 47.616cm3 958.32cm3 4721.6cm3 None (b) Calculate the surface area of the prism. 493.68cm2 4936.8cm2 49.368cm2 4.9368cm2 490.68cm2 None 23. Find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) for 108 and 630. HCF=18 & LCM=3780 HCF=90 & LCM=3780 HCF=108 & LCM=3780 HCF=12 & LCM=3780 HCF=18 & LCM=1890 None 24. The shape shown is formed of two semicircles and a rectangle. Find the perimeter and area for the shape. Give your answers correct to 1 decimal place. Perimeter=42.8cm & Area=123.8cm2 Perimeter=4.28cm & Area=123.8cm2 Perimeter=42.8cm & Area=12.38cm2 Perimeter=42.8cm & Area=113.8cm2 Perimeter=40.8cm & Area=123.8cm2 None 25. Anne, Bilal and Colin share £3800 in the ratio 8 : 5 : 7. Work out how much each one receives. Anne £1520, Bilal £950, Colin £1330 Anne £1150, Bilal £950, Colin £1130 Anne £1520, Bilal £9450, Colin £1430 Anne £8720, Bilal £950, Colin £1330 Anne £1720, Bilal £1050, Colin £1230 None 26. Describe fully the transformation of triangle A onto triangle B. enlargement by a factor of 2 with centre(7,0) enlargement by a factor of 0.5 with centre(7,0) enlargement by a factor of 2 with centre(6,0) enlargement by a factor of 2 with centre(0,7) enlargement by a factor of 4 with centre(7,0) None 27. Calculate the shaded area for the following shape. Give your answer to 1 decimal place. The radius of the outer circle is 15cm. 157.1cm2 15.71cm2 155.1cm2 150.1cm2 147.1cm2 None Time's up
