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GCSE Non-Calculator Questions 2 (2013/Foundation Tier)

This worksheet contains a sample of practice questions based on the 2013 GCSE Foundation Level syllabus. Calculators may not be used.

'GCSE Non-Calculator Questions 2 (2013/Foundation Tier)' worksheet

Key stage:  KS 4

Curriculum topic:  GCSE Practice Papers

Curriculum subtopic:  Selection of Topics for Non-Calculator Practice

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Formula Sheet

Foundation Tier

  

                                      

Area of trapezium = ½ (a + b) h

 

 

Volume of prism = area of cross-section x length

Work out:

 

5 + 7 x 3

 

Write down the value of the 3 in the number

 

70308

Estimate the following to the nearest whole number

 

√65

From this list of numbers, select all the prime numbers:

 

17     19     20     25     27     32     33     37    

17

19

20

25

27

32

33

37

Work out:

 

25% of 76

Work out:

 

¾ of 124

Write the following number to the nearest thousand:

 

7489

Work out:

 

7 x 2
8 3

 

(Give your answer as a fraction in the form a/b)

Here is a cuboid.

Write down the number of edges.

   

             

 

Work out:

 

62 - 23

Select all the factors of

 

18

0

1

2

3

4

5

6

9

18

36

Simplify the following expressions and match the questions to the answers.

Column A

Column B

5x - 3x
15x
3 × 5x
8x
15x ÷ 3
2x
5x + 3x
5x

When a = 3 and b = -1, work out the value of:

 

4a + 7b

Factorise:

 

6a - 12

 

(Do not put any spaces in your answer)

Place these numbers in order of size, starting with the largest:

 

1/2       0.6       0.45       1/3

Column A

Column B

1 (largest)
0.6
2
0.45
3
1/3
4 (smallest)
1/2

O   O         O   O   O   O   O  

 

There are 2 red balls and  5 blue balls in a bag.

What is the probability of choosing a blue ball when you select one at random?

2/5

2/7

5/7

5/2

Identify the type of correlation shown in each scatter graph below.

 

               

           A                               B                                  C

Column A

Column B

A
no correlation
B
positive correlation
C
negative correlation

Solve:

 

4x - 8 = 28

 

(Just write the value of x)

These two triangles are similar.

State the missing length in cm.

(Just write the number)

 

 

Expand and simplify:

 

3(2x + 3) - 6(x - 3)

Triangle ABC is right-angled.

Calculate the size of x°.

(Just write the number)

 

Here is a recipe to make pastry for a pie that serves 6 people:

 

300 g flour

¼ teaspoon salt

150 g butter

4 tablespoons water

 

How much butter will be needed to make pastry for a pie that will serve 9 people?

Here is a diagram of Kate's garden.

 

 

She wants to sow grass seed to make a lawn covering the whole garden shown.

Each bag of grass seed contains enough seed to cover an area of 30 m2.

A bag of grass seed costs £7.50.

How much does Kate spend in pounds to sow her lawn with grass seed?

(Just write the number)

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

ABCD is a square of side 12 cm.

M is the midpoint of BC.

T is a point on AB such that AT = 1/3 AB.

Calculate the area of the coloured region DTMC in cm2.

(Just write the number)

 

  • Question 1

Work out:

 

5 + 7 x 3

 

CORRECT ANSWER
26
EDDIE SAYS
Multiplication takes priority so 7 × 3 = 21
5 + 21 = 26
  • Question 2

Write down the value of the 3 in the number

 

70308

CORRECT ANSWER
300
EDDIE SAYS
3 in the hundreds column
  • Question 3

Estimate the following to the nearest whole number

 

√65

CORRECT ANSWER
8
EDDIE SAYS
8² = 64
  • Question 4

From this list of numbers, select all the prime numbers:

 

17     19     20     25     27     32     33     37    

CORRECT ANSWER
17
19
37
EDDIE SAYS
17, 19 and 37 only have two factors, 1 and the number itself.
  • Question 5

Work out:

 

25% of 76

CORRECT ANSWER
19
EDDIE SAYS
25% is ¼
76 ÷ 4 = 38 ÷ 2 = 19
  • Question 6

Work out:

 

¾ of 124

CORRECT ANSWER
93
EDDIE SAYS
¼ of 124 = 31
¾ of 124 = 3 × 31 = 93
  • Question 7

Write the following number to the nearest thousand:

 

7489

CORRECT ANSWER
7000
EDDIE SAYS
7489 is between 7000 and 8000, but closer to 7000.
  • Question 8

Work out:

 

7 x 2
8 3

 

(Give your answer as a fraction in the form a/b)

CORRECT ANSWER
7/12
EDDIE SAYS
Reduce within the fractions to get:

7 × 1
4 3

Then multiply the top numbers and the bottom numbers in turn.
  • Question 9

Here is a cuboid.

Write down the number of edges.

   

             

 

CORRECT ANSWER
12
EDDIE SAYS
An edge is where two faces meet.
There are 4 at the front, 4 at the back and 4 connecting the front and the back.
  • Question 10

Work out:

 

62 - 23

CORRECT ANSWER
28
EDDIE SAYS
6² = 6 × 6 = 36
2³ = 2 × 2 × 2 = 8
  • Question 11

Select all the factors of

 

18

CORRECT ANSWER
1
2
3
6
9
18
EDDIE SAYS
18 × 1
9 × 2
6 × 3
  • Question 12

Simplify the following expressions and match the questions to the answers.

CORRECT ANSWER

Column A

Column B

5x - 3x
2x
3 × 5x
15x
15x ÷ 3
5x
5x + 3x
8x
EDDIE SAYS
When adding and subtracting, collect like terms.
When multiplying and dividing by numbers, just multiply and divide the numbers.
  • Question 13

When a = 3 and b = -1, work out the value of:

 

4a + 7b

CORRECT ANSWER
5
EDDIE SAYS
4 × 3 + 7 × -1 = 12 + -7 = 12 - 7 = 5
  • Question 14

Factorise:

 

6a - 12

 

(Do not put any spaces in your answer)

CORRECT ANSWER
6(a-2)
EDDIE SAYS
6 is the highest common factor of 6 and 12.
Divide both terms by 6 to find the terms which go inside the brackets.
  • Question 15

Place these numbers in order of size, starting with the largest:

 

1/2       0.6       0.45       1/3

CORRECT ANSWER

Column A

Column B

1 (largest)
0.6
2
1/2
3
0.45
4 (smallest)
1/3
EDDIE SAYS
Change them all to hundredths before comparing.

0.50    0.60    0.45    0.333...
  • Question 16

O   O         O   O   O   O   O  

 

There are 2 red balls and  5 blue balls in a bag.

What is the probability of choosing a blue ball when you select one at random?

CORRECT ANSWER
5/7
EDDIE SAYS
There are 5 blue balls out of 7 balls in total.
  • Question 17

Identify the type of correlation shown in each scatter graph below.

 

               

           A                               B                                  C

CORRECT ANSWER

Column A

Column B

A
positive correlation
B
negative correlation
C
no correlation
EDDIE SAYS
Positive correlation shows the points going from bottom left to top right.
Negative correlation shows the points going from top left to bottom right.
Graph C shows no correlation as the points are scattered all over.
  • Question 18

Solve:

 

4x - 8 = 28

 

(Just write the value of x)

CORRECT ANSWER
9
EDDIE SAYS
Add 8 to both sides to get:
4x = 36
Divide both sides by 4 to get:
x = 9
  • Question 19

These two triangles are similar.

State the missing length in cm.

(Just write the number)

 

 

CORRECT ANSWER
21
EDDIE SAYS
The lengths in the larger triangle are 3 times the matching lengths in the smaller similar triangle.
  • Question 20

Expand and simplify:

 

3(2x + 3) - 6(x - 3)

CORRECT ANSWER
27
EDDIE SAYS
Multiply out the brackets to get:
6x + 9 - 6x + 18

The x terms cancel out to leave:
9 + 18 = 27
  • Question 21

Triangle ABC is right-angled.

Calculate the size of x°.

(Just write the number)

 

CORRECT ANSWER
12
EDDIE SAYS
∠ADB = 180° - 90° - 40° = 50°
∠CDB = 180° - ∠ADB = 180° - 50° = 130°
x° = 180° - 130° - 38° = 50° - 38° = 12°
  • Question 22

Here is a recipe to make pastry for a pie that serves 6 people:

 

300 g flour

¼ teaspoon salt

150 g butter

4 tablespoons water

 

How much butter will be needed to make pastry for a pie that will serve 9 people?

CORRECT ANSWER
225g
225 g
EDDIE SAYS
9 ÷ 6 = 1½
150 × 1½ = 150 + half of 150 = 150 + 75 = 225
  • Question 23

Here is a diagram of Kate's garden.

 

 

She wants to sow grass seed to make a lawn covering the whole garden shown.

Each bag of grass seed contains enough seed to cover an area of 30 m2.

A bag of grass seed costs £7.50.

How much does Kate spend in pounds to sow her lawn with grass seed?

(Just write the number)

CORRECT ANSWER
45
EDDIE SAYS
Area of trapezium = ½(20 + 12) × 10 = 16 × 10 = 160 m²
160 ÷ 30 = 16 ÷ 3 = 5 and a third.
6 bags are needed costing 6 × 7.50 = £45
  • Question 24

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

CORRECT ANSWER
19
EDDIE SAYS
With 20 people, we are looking for the 10th and 11th mark when placed in order. These are 17 and 21, the mean of which is 19.
  • Question 25

ABCD is a square of side 12 cm.

M is the midpoint of BC.

T is a point on AB such that AT = 1/3 AB.

Calculate the area of the coloured region DTMC in cm2.

(Just write the number)

 

CORRECT ANSWER
96
EDDIE SAYS
Area of whole square = 12 × 12 = 144 cm²
AT = 12 ÷ 3 = 4 cm and so BT = 8 cm
Area Δ ATD = ½ × 4 × 12 = 24 cm²
Area Δ TBM = ½ × 8 × 6 = 24 cm²
Blue area = 144 - 24 - 24 = 96 cm²
---- OR ----

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