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SAT Practice: Non-Calculator Questions 1 (2013/Level 6)

In this worksheet students practise answering questions similar to those found in past non-calculator extension SATs papers at level 6.

'SAT Practice: Non-Calculator Questions 1 (2013/Level 6)' worksheet

Key stage:  KS 2

Curriculum topic:  Practice Papers

Curriculum subtopic:  SAT Non-Calculator

Difficulty level:  

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Worksheet Overview

QUESTION 1 of 10

This worksheet contains 20 questions similar to those found in past non-calculator extension SATs papers at level 6.

This is not a test paper, but a collection of questions for you to practise your maths at this level.

You may need some paper to carry out your working.

What is 50% of a tenth?

Write your answer as a decimal.

 

Choose the fraction which is exactly half-way between:

 

5/13 and 3/7

4/10

2/5

37/91

4/7

15/37

Match each expression on the left with its simplified version on the right.

 

Column A

Column B

2(w + 3)
2w - 1
2(w - 3)
2w - 6
(w + 3) + (w - 4)
7
(w + 3) - (w + 4)
2w + 6
(w + 3) - (w - 4)
-1

What percentage of 20 is 13?                                                  

 

% 

(Just write the number)

Jack makes a sequence of numbers.

 

His rule is:

Add the same amount to each number.

 

Select the three missing numbers in his sequence.

 

- 3                        17

-1

2

5

7

12

15

16

The diagram shows a square divided into three unequal parts.

 

(Not drawn to scale)

 

Part P is 1/3 of the area of the whole square.

Part Q is 2/9 of the area of the whole square.

 

What fraction of the area of the whole square is part R?

 

(Write the fraction in its lowest terms in the form a/b)

Two numbers are in the ratio 2 : 5.

One of the numbers is 0.1.

 

Select all the possible answers for the other number.

0.04

0.2

0.25

0.4

0.5

Solve this equation to find the value of m.                               

 

46 - 5m = 2m - 3

m =

(Just write the number)

A bicycle originally costs £150.

 

 

It is reduced to £120 in the sale.

 

By what percentage has the price of the bicycle been reduced in the sale?

 

% 

(Just write the number)

Write down the missing number.

 

= 0.1
120

Work out the mean, mode, median and range of the following set of numbers:

 

4,  4,  6,  7,  4,  -4,  0

Column A

Column B

mean
4
mode
4
median
11
range
3

Work out:

 

3 - 3
4 9

 

  

(Write your answer as a fraction in its lowest terms in the form a/b)

Select the two decimals which are closest in value to each other.

 

0.3      0.03      0.33      0.1      0.01

0.3

0.03

0.33

0.1

0.01

Look at this equation.

 

a - 3b = 20

 

When b = 15, what is the value of a?               


a =

(Just write the number)

Look at this equation.

 

a - 3b = 20

 

When a = 14, what is the value of b?               


b =

(Just write the number)

There are 10 balls in a bag.

The probability of picking a blue ball from the bag is 0.4

A blue ball is removed from the bag and not replaced.

 

What is now the probability of taking a blue ball from the bag? 

(Write your answer as a fraction in its lowest terms in the form a/b)

The first three patterns of a sequence made of matchsticks are shown below.

 

 

The patterns continue to grow in this way.

 

n stands for the pattern number.

m stands for the number of matchsticks in that pattern number.

 

Select the rule that connects n and m.

n = 2m

m = 7n + 1

n = 7m + 1

m = 7n + 8

The first three patterns of a sequence made of matchsticks are shown below.

 

 

The patterns continue to grow in this way.

 

How many triangles will there be in pattern number 49?

Work out the size of angle x shown in the diagram below.

Do not use a protractor.

 

 

x = ° 

(Just write the number)

Look at these number bricks.

 

 

In this question, the two lower numbers always multiply together to form the number above.

 

Find the numbers shown by the letters A, B and C in the arrangement of bricks below.

 

Column A

Column B

A
3
B
1.5
C
4.5
  • Question 1

What is 50% of a tenth?

Write your answer as a decimal.

 

CORRECT ANSWER
0.05
EDDIE SAYS
On tenth is 0.1.
50% or half of 0.1 is 0.05
  • Question 2

Choose the fraction which is exactly half-way between:

 

5/13 and 3/7

CORRECT ANSWER
37/91
EDDIE SAYS
5/13 is equivalent to 35/91
3/7 is equivalent to 39/91
37 is half-way between 35 and 39
  • Question 3

Match each expression on the left with its simplified version on the right.

 

CORRECT ANSWER

Column A

Column B

2(w + 3)
2w + 6
2(w - 3)
2w - 6
(w + 3) + (w - 4)
2w - 1
(w + 3) - (w + 4)
-1
(w + 3) - (w - 4)
7
EDDIE SAYS
Remember that when you take away -4, it is the same as adding +4.
  • Question 4

What percentage of 20 is 13?                                                  

 

% 

(Just write the number)

CORRECT ANSWER
65
EDDIE SAYS
13/20 = 65/100
  • Question 5

Jack makes a sequence of numbers.

 

His rule is:

Add the same amount to each number.

 

Select the three missing numbers in his sequence.

 

- 3                        17

CORRECT ANSWER
2
7
12
EDDIE SAYS
The gap between -3 and 17 is 20.
A rise of 20 must happen in 4 stages, so the rule is to add 5.
  • Question 6

The diagram shows a square divided into three unequal parts.

 

(Not drawn to scale)

 

Part P is 1/3 of the area of the whole square.

Part Q is 2/9 of the area of the whole square.

 

What fraction of the area of the whole square is part R?

 

(Write the fraction in its lowest terms in the form a/b)

CORRECT ANSWER
4/9
EDDIE SAYS
1/3 + 2/9 = 3/9 + 2/9 = 5/9
9/9 - 5/9 = 4/9
  • Question 7

Two numbers are in the ratio 2 : 5.

One of the numbers is 0.1.

 

Select all the possible answers for the other number.

CORRECT ANSWER
0.04
0.25
EDDIE SAYS
2:5 = 0.2:0.5 = 0.1:0.25
2:5 = 4:10 = 0.4:1 = 0.04:0.1
  • Question 8

Solve this equation to find the value of m.                               

 

46 - 5m = 2m - 3

m =

(Just write the number)

CORRECT ANSWER
7
EDDIE SAYS
2m - 3 = 46 - 5m
7m - 3 = 46
7m = 49
m = 7
  • Question 9

A bicycle originally costs £150.

 

 

It is reduced to £120 in the sale.

 

By what percentage has the price of the bicycle been reduced in the sale?

 

% 

(Just write the number)

CORRECT ANSWER
20
EDDIE SAYS
The actual reduction is 150 - 120 = £30
30/150 = 1/5 = 20%
  • Question 10

Write down the missing number.

 

= 0.1
120
CORRECT ANSWER
12
EDDIE SAYS
The missing number is 120 × 0.1 = 12
  • Question 11

Work out the mean, mode, median and range of the following set of numbers:

 

4,  4,  6,  7,  4,  -4,  0

CORRECT ANSWER

Column A

Column B

mean
3
mode
4
median
4
range
11
EDDIE SAYS
The total is 21, so the mean is 21 ÷ 7 = 3.
The mode is the most frequently occurring.
The median is the middle one when listed in order.
The range is the biggest - smallest = 7 - -4 = 11.
  • Question 12

Work out:

 

3 - 3
4 9

 

  

(Write your answer as a fraction in its lowest terms in the form a/b)

CORRECT ANSWER
5/12
EDDIE SAYS
Change to 36ths to get:
27/36 - 12/36 = 15/36 = 5/12
Or notice that 3/9 reduces to 1/3 and work out 3/4 - 1/3
  • Question 13

Select the two decimals which are closest in value to each other.

 

0.3      0.03      0.33      0.1      0.01

CORRECT ANSWER
0.03
0.01
EDDIE SAYS
0.3 and 0.33 are 0.03 apart
0.01 and 0.03 are only 0.02 apart
  • Question 14

Look at this equation.

 

a - 3b = 20

 

When b = 15, what is the value of a?               


a =

(Just write the number)

CORRECT ANSWER
65
EDDIE SAYS
When b = 15, a - 3b = a - 45, which gives us:
a - 45 = 20
a = 65
  • Question 15

Look at this equation.

 

a - 3b = 20

 

When a = 14, what is the value of b?               


b =

(Just write the number)

CORRECT ANSWER
-2
EDDIE SAYS
When a = 14, we get:
14 - 3b = 20
14 - 20 = 3b
-6 = 3b
3b = -6
b = -2
  • Question 16

There are 10 balls in a bag.

The probability of picking a blue ball from the bag is 0.4

A blue ball is removed from the bag and not replaced.

 

What is now the probability of taking a blue ball from the bag? 

(Write your answer as a fraction in its lowest terms in the form a/b)

CORRECT ANSWER
1/3
EDDIE SAYS
There must be 0.4 ×10 = 4 blue balls in the bag.
One is removed leaving 3 blue balls out of the 9 remaining balls
3/9 reduces to 1/3
  • Question 17

The first three patterns of a sequence made of matchsticks are shown below.

 

 

The patterns continue to grow in this way.

 

n stands for the pattern number.

m stands for the number of matchsticks in that pattern number.

 

Select the rule that connects n and m.

CORRECT ANSWER
m = 7n + 1
EDDIE SAYS
The sequence goes 8, 15, 22 ...
7 matches are added each time, so 7n must be in the formula.
  • Question 18

The first three patterns of a sequence made of matchsticks are shown below.

 

 

The patterns continue to grow in this way.

 

How many triangles will there be in pattern number 49?

CORRECT ANSWER
98
EDDIE SAYS
In pattern number 1, there are 2 triangles.
In pattern number 2, there are 4 triangles.
In pattern number 3, there are 6 triangles.
  • Question 19

Work out the size of angle x shown in the diagram below.

Do not use a protractor.

 

 

x = ° 

(Just write the number)

CORRECT ANSWER
28
EDDIE SAYS
There are 180° in a triangle and on a straight line.
∠ADB = 180° - 90° - 30° = 60°
∠CDB = 180° - 60° = 120°
x° = 180° - 120° - 32° = 28°
  • Question 20

Look at these number bricks.

 

 

In this question, the two lower numbers always multiply together to form the number above.

 

Find the numbers shown by the letters A, B and C in the arrangement of bricks below.

 

CORRECT ANSWER

Column A

Column B

A
1.5
B
3
C
4.5
EDDIE SAYS
A = 1.5 ÷ 1 = 1.5
B = 1.5 × 2 = 3
C = 1.5 × 3 = 4.5
---- OR ----

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