ABC Education · 11+ Practice

Week 6 · Maths Practice Paper

13 questions · 75 marks · Suggested time: 45 minutes.

Question 1

[14 marks]

Mental Arithmetic. Work out the answers to these sums. Show your working out.

(a)

34 + 521 + 298

(b)

3142 - 1867

(c)

789 × 6

(d)

376 × 42

(e)

1288 ÷ 8

(f)

1508 ÷ 13

Question 2

[6 marks]

Decimal Operations. Work out the answers to the following sums:

(a)

(18.6 + 7.4) ÷ 4 =

(b)

7.2 × 5 - 4.8 =

(c)

9 × 1.6 + 16 × 0.9 =

Question 3

[5 marks]

Percentages.

(a)(i)

10% of 140 =

(a)(ii)

5% of 140 =

(a)(iii)

1% of 140 =

(b)

Use your answers to part (a) to find 47% of 140. Show your working out.

Question 4

[5 marks]

Shapes. A shape is made by joining unit squares edge-to-edge in a single connected chain with no loops (so every new square is attached along exactly one edge). Such a shape's perimeter is always (2 × area) + 2.

(a)

A shape made this way has a perimeter of 12. What is its area?

(b)

A different shape, made the same way, has an area of 16 squares. What is its perimeter?

(c)

A rectangle (which does have an enclosed interior, unlike the loop-free shapes above) has an area of 12 and a perimeter of 16. What are its dimensions?

Question 5

[13 marks]

Factors.

46   28   62   84   66   90   96   63   82   48

(a)

From the list above, circle the one number that is: a 2-digit number with both digits even, where the tens digit is greater than the ones digit, the ones digit is not a multiple of 3, the tens digit is not double the ones digit, AND the digit sum is a multiple of 5.

(b)

Write down the factors of 24.

(c)

Write down the factors of 40.

Venn: only 24, only 40, both

Using your two lists, sort them into the Venn diagram above.

(d)

What is the highest common factor of 24 and 40?

(e)

Using the method 'multiply the two numbers together, then divide by the highest common factor', find the lowest common multiple of 24 and 40.

Question 6

[5 marks]

Clock angles. The hour and minute hands of a clock make an angle, and its size depends on the time shown.

(a)

What is the obtuse angle between the hands at 8 o'clock?

(b)

Give one time when the angle between the hands will be exactly 90°.

(c)

The angle between the hour and minute hand is exactly 60°. What time could the clock be showing?

(d)

At 11 o'clock the angle between the hands is exactly 30°. What is the next time when the angle between the hands will again be exactly 30°?

Question 7

[2 marks]

Number detective. Follow the clues to find the mystery number from the list below.

The number has two digits. Both digits are even. The tens digit is greater than the ones digit. The ones digit is not in the three times table. The tens digit is not double the ones digit. The sum of the two digits is a multiple of 5.


46	28
62	84
66	90
96	63
82	48

The mystery number is:

Question 8

[3 marks]

Four bags. Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any TEN numbers from the bags above so that their total is 38.

Which ten numbers?

Question 9

[4 marks]

Sticky triangles. I was exploring a puzzle in which headless matchsticks had to be moved to make a different number of triangles. I made one small triangle (3 matches), then made it into 4 small triangles by adding 6 matches (9 matches in total, arranged as 2 rows).

1 row, 3 matches

2 rows, 9 matches

I added another row to make the next shape in the pattern. How many small triangles are in the next shape?

How many matches are in the next shape in the pattern?

Question 10

[5 marks]

Equations. Solve these equations to find the number represented by each letter.

(a)

16s = 112

(b)

6t + 14 = 86

(c)

n3 - 4 = 17

Question 11

[6 marks]

Odd Sums. This sum is made using odd numbers: (5 × 7) - 3 - 1 = 31. Complete the following using the numbers 1, 3, 5 and 7 exactly once each, with any of +, -, ×, ÷, ( ):

(a)

1 3 5 7 = 31

(b)

1 3 5 7 = 16

(c)

1 3 5 7 = 43

Question 12

[3 marks]

Twenty divided into six. Priya had a pack of twenty cards numbered 1 to 20. She arranged the cards into six unequal piles (not all the same size), and the numbers on the cards in each pile added to the same total. What was the total, and how could this be done?

Total and one valid grouping:

Question 13

[4 marks]

Multiplication square. In a 2×2 example, the boxes at the end of each row and foot of each column give the product of the two numbers in that row/column: rows (6,7)=42 and (4,3)=12; columns (6,4)=24 and (7,3)=21. The 3×3 square below works the same way, using the row products (right) and column products (bottom). The numbers 1-9 may be used once each. Work out the arrangement of digits.

The 3×3 arrangement (row by row):