ABC Education · 11+ Practice

Week 54 · Maths Practice Paper

16 questions · 64 marks · Suggested time: 1 hour.

Question 1

[6 marks]

Calculate the answers to the following sums:

(a)

53.84 + 27.156

(b)

462.7 − 69.238

(c)

4172 × 367

(d)

78,624 ÷ 24

(e)

8⅜ − 4⅗ (as a mixed number)

(f)

4⅙ ÷ 6⅔

Question 2

[3 marks]

Fill in the blank squares with a number to make these sums correct:

(a)

3 59 + ___ = 8 27

(b)

___ × 24 = 157,248

(c)

(18 × 17) + ___ = 428

Question 3

[2 marks]

Margaret thinks of a number. She divides this number by 13 and then adds 17. Her answer is 100. What was her original number?

Question 4

[3 marks]

An isosceles triangle has a perimeter of 84 cm. One of the sides is 30 cm. What are the lengths of the other two sides? (NOTE: there are two possible answers to this)

Question 5

[4 marks]

(a)

A shape has vertices at (1,5), (3,6) and (2,3). Reflect it in the horizontal line y = 3. Give the reflected coordinates.

(b)

A shape has vertices at (2,7), (2,4) and (4,5). Rotate it 90° clockwise about the point X(2,2). Give the new coordinates.

Question 6

[3 marks]

Sort the numbers 19, 20, 21, 22, 23 and 24 by whether each is prime or not prime, a multiple of 3 or not, and odd or even.

Prime, not a multiple of 3, odd:

Not prime, not a multiple of 3, even:

Not prime, a multiple of 3, odd:

Not prime, a multiple of 3, even:

Question 7

[8 marks]

Add the next two numbers to each of the following sequences:

(a)

38, 71, 104, 137, ___, ___

(b)

4, 9, 19, 39, ___, ___

(c)

15, 11, 7, 3, ___, ___

(d)

2.47, 4.18, 5.89, 7.60, ___, ___

Question 8

[6 marks]

A coaching course overview: Course 101 (5 total hrs, no practical, no assignment, $20 fee, no accreditation fee); Course 1 (12 hrs, 10h practical, 4h assignment, $60 fee, no accreditation); Course 2 (20 hrs, 35h practical, 8h assignment, $90 fee, $18 accreditation); Course 3 (45 hrs, 80h practical, 15h assignment, $130 fee, $25 accreditation); Course 4 (90 hrs, 140h practical, 18h assignment, $220 fee, $28 accreditation).

(a)

How many hours in total will it take to complete courses 2 and 3, including the practicals and the assignments?

(b)

What is the total participation fee to complete all 5 levels?

(c)

A large sports firm wants all 13 of its coaches fully and totally trained — all levels plus coach accreditation at all levels. How much will it cost them?

Question 9

[3 marks]

A woodlouse moves away from its starting point, reaching a distance of 8m after 6 seconds (moving at a steady pace). It then stays still from 6s to 11s. It then moves back toward the start at a steady rate, reaching its starting point again at 15s.

(a)

Explain the shape of the graph immediately between the 6th and the 11th second.

(b)

What is the woodlouse's average speed, in metres per second, over the first 6 seconds?

(c)

How long from the start of the experiment before the woodlouse returns to its starting point?

Question 10

[2 marks]

One angle of a quadrilateral is 66°. The other three angles are all the same. How large is each of the other three angles?

Question 11

[3 marks]

Peter is building an extension. He purchases 36 kg of sand. He uses a third of this in building the foundation. He then uses 8 further kilograms on a patio area, and finds he only needs another three quarters of the remaining sand. How much sand will be wasted?

Question 12

[4 marks]

What is:

(a)

38% of 650 m?

(b)

87½% of £824?

Question 13

[6 marks]

The results of a maths test taken by a group of students are: 0-10 marks: 2 students, 10-20: 3 students, 20-30: 5 students, 30-40: 3 students, 40-50: 2 students.

(a)

How many students scored between 10 and 20 marks?

(b)

How many students are there in this class in total?

(c)

If any student scoring between 10 and 20 was given 1 gold star, between 20 and 30 was given 2 gold stars, between 30 and 40 was given 3 gold stars, and scoring more than 40 was given 5 gold stars, how many gold stars were the group awarded in total?

Question 14

[4 marks]

Paul runs a marathon. He manages the first 4 miles in 30 minutes. The next 6 miles take an average of 9 minutes each. He then has a pain in his side, so stops for 18 minutes. The remainder of the run takes 2 hours and 47 minutes. How long does it take Paul in total to complete the marathon?

Question 15

[3 marks]

32 children are going on a school trip. The trip costs £6.25 including lunch. However the students may pay only £3.85 and bring their own packed lunch if they wish. The total cost of the trip is £178.40. How many of the students took a packed lunch?

Question 16

[4 marks]

Find the area of this shape:

m²