Oundle School — 13+ Maths Academic Scholarship Preliminary 2020 (Interactive)

Q1(a): Work out 74 + 19

Q1(b): Work out -13 - (-17)

Q1(c): Work out 8 × 23

Q1(d): Work out 8 ÷ 23

Q1(e): Work out 2000 × 0.0005

Q1(f): Work out 0.4 ÷ 0.08

Q1(g): Work out 1 34 + 1 13

Q1(h): Work out 12 - 4 ÷ 12 + 6 ÷ (1 - 4)

Q1(i): Work out 10% of 30% of 3000

Q1(j): Work out the cube root of 8, i.e. ∛8

Q1(k): Work out ∛8000000 (the cube root of 8,000,000)

Q1(l): Work out √(6² + 8²)

Q1(m): Work out 3 × 2⁰

Q1(n): Work out (3 × 2)⁰

Q2(a): If d = 2, e = -3 and f = -14, find the value of d - e + f

Q2(b): If d = 2, e = -3 and f = -14, find the value of (d × e) / f

Q2(c): If d = 2, e = -3 and f = -14, find the value of 2def

Q2(d): If d = 2, e = -3 and f = -14, find the value of d² / f²

Q2(e): If d = 2, e = -3 and f = -14, find the value of (ef)^d

Q3(a): Insert the correct sign (+, -, × or ÷) to make the statement true: 23 ☐ 1.5 = 49

Q3(b): Insert the correct sign (+, -, × or ÷) to make the statement true: 34 ☐ 3 = 2 14

Q3(c): Insert the correct signs (+, -, × or ÷) in the three boxes to make the statement true: 38 ☐ 34 ☐ (112 ☐ 14) = 16

Q4(a): Find the next two terms in the sequence: 8, 2, -4, -10, ...

Q4(b): Find the next two terms in the sequence: 20, 10, 5, 2.5, ...

Q4(c): Find the next two terms in the sequence: 1, 4, 9, 16, ...

Q4(d): Find the next two terms in the sequence: -1, 2, 1, 3, 4, 7, ...

Q4(e): Find the next two terms in the sequence: 27, 314, 521, 728, ...

Q5(a): Find the fraction that is halfway between 15 and 16. The numerator and denominator of your answer must both be whole numbers.

Q5(b): Find the fraction that is halfway between 1/a and 1/b. Give your answer as a single fraction in terms of a and b.

Q6(a): Remove brackets and simplify: 2(5 - x)

Q6(b): Remove brackets and simplify: 3x(x + 3) - (1 - x)

Q6(c): Remove brackets and simplify: (4x + 1)²

Q7(a): Factorise fully: 8y - 16

Q7(b): Factorise fully: xy² - 2xy

Q7(c): Factorise fully: 8y - 16 + xy² - 2xy

Q8(a): Solve for x: 6x + 1 = -2

Q8(b): Solve for x: 5 - 2(x + 3) = 4 - x

Q8(c): Solve for x: 4 - x/3 = 72

Q8(d): Solve for x: (9x + 2)/(9x - 2) = 2

Q9: John takes 40 minutes to walk to school and then to run home. When he runs both ways, it takes him 24 minutes. He has one constant speed whenever he walks, and another constant speed whenever he runs. How long would it take him to walk both ways?

Q10(a): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 45² - 15²

Q10(b): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 736² - 264²

Q10(c): You are told that x² - y² = (x + y)(x - y). Use this result (and NOT long multiplication) to find the value of 1007 × 993

Q11: Asif is shopping for a new outfit for a special occasion. He needs a shirt, a pair of trousers and a pair of shoes. If he doesn't buy the shirt, he can get the other items for £115. If he doesn't buy the trousers, he can get the other items for £100. If he doesn't buy the shoes, he can get the other items for £75. How much will he have to pay for all of them?

Q12: In a bag, there are 180 marbles, of which n are red and the others green. A marble is to be drawn randomly from the bag. If 10 more red marbles were added to the bag, the probability of drawing a red would be doubled. Write down and solve an equation in n to work out how many red marbles were originally in the bag.

Q13: A solid cuboid has dimensions 3 cm by 5 cm by 6 cm. A spider at point S (bottom corner of the 6 cm edge on the front face) needs to crawl on the outside of the cuboid to reach a fly at point F (top corner diagonally opposite, at the back of the top face). What is the shortest distance the spider can travel to reach the fly? (Refer to original PDF for figure.)

Q14: A rectangle ABCD has a diagonal line from a point on the top edge (1 cm from corner A along the top) to corner C. The length along the bottom from D is split as 1 cm and 4 cm, making DC = 5 cm. The shaded region consists of a vertical strip on the left of width 1 cm (full height) and the triangle below the diagonal in the remaining portion. Express the shaded area as a fraction of the whole rectangle ABCD. (Refer to original PDF for figure.)

Q15: A rectangular piece of card ABCD has AB = 12 cm and AD = 16 cm, where A is the bottom-left corner, B is top-left, C is top-right, and D is bottom-right. If the card is folded so that C is on top of A, how long is the crease? (Refer to original PDF for figure.)