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

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

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

Key stage:  KS 2

Curriculum topic:  Practice Papers

Curriculum subtopic:  SAT Calculator

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

This worksheet contains 20 questions similar to those found in past 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 and you should use a calculator.

Which square number is closest to 500? 

 

Jack thinks of a positive whole number and calls it n.

Look at the expressions below.

For each expression, click to show if it must be even or odd, or if you cannot be sure.

 

 even odd cannot be sure
n
2n
3n
4n
2n - 1
2n + 1

Here is a parallelogram drawn on a graph.

What is the area of the parallelogram in square units?

 

   units²

(Just write the number)

The factors of 14 are 1, 2, 7 and 14.

These factors add to give a factor sum of 24.

 

The factors of 23 are 1 and 23.

These factors also add to give a factor sum of 24.

 

Find another number which also has a factor sum of 24.

 

Find the value of b in this equation.                     

 

82 - 20b = 13

 

b = 

(Just write the number)

 

 

Anna bakes a small birthday cake.

It is 5 cm tall and has a diameter of 24 cm.

 

 

Calculate the area of the circular base of the cake in cm².

Give your answer to the nearest whole number.                         

 

Area =   cm²

(Just write the number)

The diagram shows two similar rectangles.                   

 

Calculate the height of rectangle B in cm.

 

 cm

(Just write the number)

The mean height of five children is 128 cm.

A child of height 149 cm joins the group.

 

What is now the mean height of all six children in cm?

 

 cm

(Just write the number)

Calculate the area of this trapezium in cm².       

                 

 

Area =   cm²

(Just write the number)

Four different sized bowls are placed next to each other and water is poured into them.

 

Bowl A has a capacity of 1500 ml but is only 62% full.

Bowl B has a capacity of 1 litre but is only 95% full.

Bowl C has a capacity of 250 cl but is only 38% full.

Bowl D has a capacity of 3 litres but is only one third full.

 

Which two bowls contain the same amount of water?

A

B

C

D

Jenny chooses a prime number.

She squares it and then rounds it to the nearest hundred.

Her answer is 1000.

 

What number did Jenny choose?

Look at these equations.

5a = b

2b = 5c

 

If c = 7, calculate the value of a.

a = 

Look at this diagram, which shows a rectangle ABCD, which is to be rotated through 90º anticlockwise about the point D to give the rectangle A'B'C'D'.

Write down the coordinates of B'.

 

 

 

(10, 8)

(8, 10)

(10, 10)

(8, 8)

Find the volume of this shape, which is made of cuboids.

The dimensions are given below.

 

a = 14 cm

b =11 cm

c = 8 cm

d = 10 cm

 

Volume =  cm³

(Just write the number)

Mark has £2000 to buy bricks.

 

Bricks cost £136.05 + 20% VAT for a pack of 400 bricks.

He buys as many whole packs as he can afford.

 

How many bricks can Mark buy?

 

 

Look at this spinner.

 

 

What is the probability that the spinner will land on a multiple of 4?

 

 

(Write the answer as a fraction in its lowest terms using the / sign e.g. 3/4)

Use the graph to change £400.25 into euros (€).

 

 

(Just write the number to 2 decimal places)

p is a whole number and is even.                          

 

Find p when:

         

16 < 4p - 1 < 27

 

p =

Use trial and improvement to find the solution to this equation, which lies between 5 and 6, giving your answer to 1 decimal place.             

         

x² - 2x = 20

 

This is how to start:

 

When x = 5, x² - 2x = 25 - 10 = 15, which is too small.

When x = 6, x² - 2x = 36 - 12 = 24, which is too large.

When x = 5.5, x² - 2x = 30.25 - 11 = 19.25, which is too small.

 

x = 

(Give your answer to one decimal place)

  • Question 1

Which square number is closest to 500? 

 

CORRECT ANSWER
484
EDDIE SAYS
√500 = 22.36...
22² = 484 which is 16 away from 500
23² = 529 which is further away.
  • Question 2

Jack thinks of a positive whole number and calls it n.

Look at the expressions below.

For each expression, click to show if it must be even or odd, or if you cannot be sure.

 

CORRECT ANSWER
 even odd cannot be sure
n
2n
3n
4n
2n - 1
2n + 1
EDDIE SAYS
n can be even or odd.
2n is always a multiple of 2, so must be even.
3n is always a multiple of 3, so can be both.
4n is always a multiple of 4, so must be a multiple of 2 too.
2n - 1 is one less than the even number 2n, so must be odd.
2n + 1 is one more than the even number 2n, so must be odd.
  • Question 3

Here is a parallelogram drawn on a graph.

What is the area of the parallelogram in square units?

 

   units²

(Just write the number)

CORRECT ANSWER
12
EDDIE SAYS
Base is 3 units (i.e. 7 - 4)
Height is 4 units (i.e. 7 - 3)
Area is 3 × 4 = 12 units²
  • Question 4

The factors of 14 are 1, 2, 7 and 14.

These factors add to give a factor sum of 24.

 

The factors of 23 are 1 and 23.

These factors also add to give a factor sum of 24.

 

Find another number which also has a factor sum of 24.

 

CORRECT ANSWER
15
EDDIE SAYS
The number must be less than 23.
15 has factors which add to 1 + 3 + 5 + 15 = 24.
  • Question 5

Find the value of b in this equation.                     

 

82 - 20b = 13

 

b = 

(Just write the number)

CORRECT ANSWER
3.45
EDDIE SAYS
-20b = 13 - 82 = -69
20b = 69
b = 69 ÷ 20 = 3.45
  • Question 6

 

 

CORRECT ANSWER
189
EDDIE SAYS
42% of 950 = 950 ÷ 100 × 42 = 399
5/9 of 378 = 378 ÷ 9 × 5 = 210
399 - 210 = 189
  • Question 7

Anna bakes a small birthday cake.

It is 5 cm tall and has a diameter of 24 cm.

 

 

Calculate the area of the circular base of the cake in cm².

Give your answer to the nearest whole number.                         

 

Area =   cm²

(Just write the number)

CORRECT ANSWER
452
EDDIE SAYS
Area = πr²
diameter, d = 24 cm, so radius, r = 12 cm
Area = π× 12² = 452.389... cm²
  • Question 8

The diagram shows two similar rectangles.                   

 

Calculate the height of rectangle B in cm.

 

 cm

(Just write the number)

CORRECT ANSWER
7.5
EDDIE SAYS
The ratio of lengths is 4:6 = 2:3
Height of B = 5 × 3 ÷ 2 = 7.5 cm
  • Question 9

The mean height of five children is 128 cm.

A child of height 149 cm joins the group.

 

What is now the mean height of all six children in cm?

 

 cm

(Just write the number)

CORRECT ANSWER
131.5
EDDIE SAYS
Total height of five children = 5 × 128 = 640 cm
Total height of six children = 640 cm + 149 cm = 789 cm
Mean height of six children = 789 ÷ 6 = 131.5 cm
  • Question 10

Calculate the area of this trapezium in cm².       

                 

 

Area =   cm²

(Just write the number)

CORRECT ANSWER
92.4
EDDIE SAYS
Area = ½(sum of parallel sides) × height.
Area = ½(15.5 + 6.5) × 8.4 = 11 × 8.4 = 92.4 cm²
  • Question 11

Four different sized bowls are placed next to each other and water is poured into them.

 

Bowl A has a capacity of 1500 ml but is only 62% full.

Bowl B has a capacity of 1 litre but is only 95% full.

Bowl C has a capacity of 250 cl but is only 38% full.

Bowl D has a capacity of 3 litres but is only one third full.

 

Which two bowls contain the same amount of water?

CORRECT ANSWER
B
C
EDDIE SAYS
Bowl A contains 0.62 × 1500 = 930 ml
Bowl B contains 0.95 × 1000 = 950 ml
Bowl C contains 0.38 × 2500 = 950 ml
Bowl D contains 3000 ÷ 3 = 1000 ml
  • Question 12

Jenny chooses a prime number.

She squares it and then rounds it to the nearest hundred.

Her answer is 1000.

 

What number did Jenny choose?

CORRECT ANSWER
31
EDDIE SAYS
√3000 = 31.6.... so we try prime numbers around 31
29² = 841
31² = 961
37² = 1369
  • Question 13

Look at these equations.

5a = b

2b = 5c

 

If c = 7, calculate the value of a.

a = 

CORRECT ANSWER
3.5
EDDIE SAYS
2b = 5 × 7 = 35
b = 35 ÷ 2 = 17.5
5a = 17.5
a = 17.5 ÷ 5 = 3.5
  • Question 14

Look at this diagram, which shows a rectangle ABCD, which is to be rotated through 90º anticlockwise about the point D to give the rectangle A'B'C'D'.

Write down the coordinates of B'.

 

 

 

CORRECT ANSWER
(10, 8)
EDDIE SAYS
A will be at (10, 10) and B will be 2 squares below A.
  • Question 15

Find the volume of this shape, which is made of cuboids.

The dimensions are given below.

 

a = 14 cm

b =11 cm

c = 8 cm

d = 10 cm

 

Volume =  cm³

(Just write the number)

CORRECT ANSWER
644
EDDIE SAYS
Think of it as a large cuboid of cheese of dimensions a × b × d, from which we remove a cuboid of dimensions a × c × c
Volume = a × b × d - a × c × c
Volume = 14 × 11 × 10 - 14 × 8 × 8 = 1540 - 896 = 644 cm³
  • Question 16

Mark has £2000 to buy bricks.

 

Bricks cost £136.05 + 20% VAT for a pack of 400 bricks.

He buys as many whole packs as he can afford.

 

How many bricks can Mark buy?

 

 

CORRECT ANSWER
4800
EDDIE SAYS
Each pack costs 136.05 × 1.2 = £163.26
£2000 ÷ £163.26 = 12.25...
So he can buy 12 whole packs = 12 ×400 = 4800 bricks
  • Question 17

Look at this spinner.

 

 

What is the probability that the spinner will land on a multiple of 4?

 

 

(Write the answer as a fraction in its lowest terms using the / sign e.g. 3/4)

CORRECT ANSWER
1/4
EDDIE SAYS
Out of 8 possible numbers, there are 2 multiples of 4 (i.e. 4 and 8).
Probability is 2/8 which reduces to 1/4.
  • Question 18

Use the graph to change £400.25 into euros (€).

 

 

(Just write the number to 2 decimal places)

CORRECT ANSWER
480.30
EDDIE SAYS
£100 = €120 so £1 = €1.20
£400.25 = €400.25 × 1.2 = €480.30
  • Question 19

p is a whole number and is even.                          

 

Find p when:

         

16 < 4p - 1 < 27

 

p =

CORRECT ANSWER
6
EDDIE SAYS
16 < 4p - 1
4p - 1 > 16
4p > 17
p > 4¼

4p - 1 < 27
4p < 28
p < 7½

So p must be 5 or 6 or 7.
  • Question 20

Use trial and improvement to find the solution to this equation, which lies between 5 and 6, giving your answer to 1 decimal place.             

         

x² - 2x = 20

 

This is how to start:

 

When x = 5, x² - 2x = 25 - 10 = 15, which is too small.

When x = 6, x² - 2x = 36 - 12 = 24, which is too large.

When x = 5.5, x² - 2x = 30.25 - 11 = 19.25, which is too small.

 

x = 

(Give your answer to one decimal place)

CORRECT ANSWER
5.6
EDDIE SAYS
When x = 5.6, x² - 2x = 31.36 - 11.2 = 20.16, which is too large.
When x = 5.55, x² - 2x = 30.8025 - 11.1 = 19.7025, which is too small.
So the answer lies between 5.55 and 5.6, which means that x = 5.6 to 1 decimal place.
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