GCSE November 2022 Edexcel Foundation Paper 1

✏ Working:

\( 0.3 \) means 3 tenths.

As a fraction, this is written as \( \frac{3}{10} \).

✏ Working:

✏ Working:

First, work out the brackets:

Now the calculation is:

✏ Working:

✏ Working:

Let’s check the numbers:

• \( 9 \)? \( 60 \div 9 \) is not a whole number. ❌
• \( 10 \)? \( 60 \div 10 = 6 \). ✅ 10 is a factor.
• \( 11 \)? ❌
• \( 12 \)? \( 60 \div 12 = 5 \). ✅ 12 is a factor.
• \( 13 \)? ❌

✏ Working:

Multiply the numbers: \( 3 \times 5 = 15 \)

Combine with the letters: \( 15 \times w \times t \)

Remove the multiplication signs: \( 15tw \)

✏ Working:

1 Adult Ticket: £33.00

2 Child Tickets: \( 2 \times 24.50 \)

   24.50
×      2
________
   49.00

Total Tickets = \( 33.00 + 49.00 = £82.00 \)

✏ Working:

1 Adult Meal: £15.00

2 Child Meals: \( 2 \times 10 = £20.00 \)

Total Meals = \( 15.00 + 20.00 = £35.00 \)

✏ Working:

   23
   82
+  35
_____
  140
   1

Total Cost = £140

✏ Working:

\( 200 – 140 = 60 \)

✏ Working:

Count the letters:

• A: 5 times
• B: 2 times
• C: 1 time

Answer: A

✏ Working:

Mark a cross halfway between 0 and \( \frac{1}{2} \).

✏ Working:

There is 1 ‘C’ out of 8 letters.

Answer: \( \frac{1}{8} \)

✏ Working:

✏ Working:

So, \( 4n = 24 \)

Divide by 4:

✏ Working:

✏ Working:

He can buy 5 full jars.

✏ Working:

New jars calculation:

He can buy 11 jars.

Twice the original number (5) is 10.

He can actually buy 11, which is more than twice 5.

Answer: No. He can buy 11 jars, but twice the original amount is 10.

Answer (i): 2

Answer (ii): Mark cross at the intersection point.

(i) Drawing: A straight diagonal line passing through \( (0,0), (1,1), (2,2) \), etc.

(ii) Equation: The line where every \( y \) coordinate equals the \( x \) coordinate is:

\( y = x \)

✏ Working:

\( \frac{1}{6} \) of 120 = \( 120 \div 6 = 20 \) minutes.

✏ Working:

10% of 120 = 12

20% of 120 = \( 12 \times 2 = 24 \) minutes.

✏ Working:

Time used so far:

Badminton: 50

Pool: 20

Gym: 24

Total used = \( 50 + 20 + 24 = 94 \) minutes.

Cafe Time = \( 120 – 94 = 26 \) minutes.

✏ Working:

94 minutes = 1 hour 34 minutes.

Start time: 1:30 pm

Add 1 hour: 2:30 pm

Add 34 mins: 3:04 pm

She arrived at the cafe at 3:04 pm.

Answer: No, she was 4 minutes late.

✏ Working:

Look at the year 2000 column.

The “Men” section is the bottom block (Solid Dark).

The height of this block goes from 0 to 60.

Answer: 60

✏ Working:

Look at the year 2010 column.

Children is the top block (Light Grey).

It starts at height 150 and ends at height 200.

Number = \( 200 – 150 = 50 \).

Answer: 50

✏ Working:

Children (Top block 2020): Ends at 280, starts at 200. \( 280 – 200 = 80 \).

Men and Women (Bottom two blocks combined): From 0 to 200.

Ratio Children : (Men + Women) is \( 80 : 200 \).

Simplify (divide by 40): \( 2 : 5 \).

✏ Working:

Time = \( 1.5 \) hours.

Distance = \( 54 \times 1.5 \)

Method: \( 54 \times 1 = 54 \)

\( 54 \times 0.5 = 27 \) (half of 54)

Total = \( 54 + 27 = 81 \) miles.

✏ Working:

Real distance in cm = \( 6 \times 25,000 \)

\( 6 \times 25 = 150 \), so \( 150,000 \) cm.

Convert to meters: \( 150,000 \div 100 = 1,500 \) m.

Convert to km: \( 1,500 \div 1,000 = 1.5 \) km.

✏ Working:

Point P is at \( (-3, -2) \).

Point Q is at \( (2, 4) \).

✏ Working:

x-coordinate: \( \frac{-3 + 2}{2} = \frac{-1}{2} = -0.5 \)

y-coordinate: \( \frac{-2 + 4}{2} = \frac{2}{2} = 1 \)

✏ Working:

✏ Working:

Collect \( x \) terms: \( 2x + x + x + 2x = 6x \)

Collect numbers: \( -5 + 1 – 1 = -5 \)

So: \( 6x – 5 = 52 \)

Add 5 to both sides:

Divide by 6:

✏ Working:

✏ Working:

Total counters = 100

Blue = 30

Not Blue = \( 100 – 30 = 70 \)

Probability = \( \frac{70}{100} \) or 0.7

✏ Working:

Ratio Blue : Green = 2 : 3

Blue counters = 30.

2 parts = 30, so 1 part = 15.

Green = 3 parts = \( 3 \times 15 = 45 \).

✏ Working:

Counters remaining for Red and Yellow:

Total – (Blue + Green) = \( 100 – (30 + 45) = 100 – 75 = 25 \).

If Red and Yellow are equal, we would need to divide 25 by 2.

\( 25 \div 2 = 12.5 \).

You cannot have half a counter.

Answer: No, because 25 is an odd number and cannot be divided equally into two whole numbers.

✏ Working:

Total shares = \( 5 + 3 + 2 = 10 \).

1 share = \( 240 \div 10 = 24 \).

• Cola = \( 5 \times 24 = 120 \)
• Lemonade = \( 3 \times 24 = 72 \)
• Orange = \( 2 \times 24 = 48 \)

✏ Working:

Remove \( \frac{1}{2} \) of lemonade: \( 72 \div 2 = 36 \) removed.

Lemonade left = \( 72 – 36 = 36 \).

Remove \( \frac{1}{12} \) of orange: \( 48 \div 12 = 4 \) removed.

Orange left = \( 48 – 4 = 44 \).

Cola left = 120 (none removed).

✏ Working:

Total remaining = \( 120 + 36 + 44 = 200 \).

Cola = 120.

Percentage = \( \frac{120}{200} \times 100 \)

\( \frac{120}{200} = \frac{60}{100} = 60\% \)

✏ Working:

   500
  /   \
 2    250
     /   \
    2    125
        /   \
       5     25
            /  \
           5    5

Prime factors are: 2, 2, 5, 5, 5

✏ Working:

\( 2 \times 2 = 2^2 \)

\( 5 \times 5 \times 5 = 5^3 \)

✏ Working:

Whole numbers: \( 1 + 2 = 3 \)

Fractions: \( \frac{3}{5} + \frac{1}{4} \)

Common denominator (20):

Total: \( 3\frac{17}{20} \)

✏ Working:

Convert \( 2\frac{2}{3} \) to improper fraction:

Now divide by 6 (which is \( \frac{6}{1} \)):

Keep, Change, Flip:

Simplify by dividing top and bottom by 2:

Shown.

✏ Working:

So the inside becomes \( 2^3 \).

✏ Working:

✏ Working:

   32
×   4
_____
  128

✏ Working:

\( 0.004 \) has 3 decimal places.

\( 0.32 \) has 2 decimal places.

Total = \( 3 + 2 = 5 \) decimal places.

We need to move the decimal point in \( 128 \) back 5 times.

128.0 \(\to\) 12.8 \(\to\) 1.28 \(\to\) 0.128 \(\to\) 0.0128 \(\to\) 0.00128

✏ Working:

✏ Working:

Calculate \( \frac{15}{80} \) of 40,000.

First, simplify the division:

Then multiply by 15:

✏ Working:

Multiply the first ratio by 2 to make \( b = 6 \).

\( a : b = 2 : 6 \)

Now combine with \( b : c = 6 : 5 \).

\( a : b : c = 2 : 6 : 5 \)

✏ Working:

Total parts = \( 2 + 6 + 5 = 13 \).

\( a \) is 2 parts.

Fraction = \( \frac{2}{13} \).

✏ Working:

We know \( p = 5n \).

Substitute \( n = 2m \) into this:

So the ratio \( m : p \) is \( m : 10m \).

Simplify by dividing by \( m \):

\( 1 : 10 \)

✏ Working:

The base is a rectangle.

✏ Working:

Halve it three times:

\( 10000 \div 2 = 5000 \)

\( 5000 \div 2 = 2500 \)

\( 2500 \div 2 = 1250 \)

✏ Working:

Subtract 3 from both sides:

Multiply by 2:

Divide by 5:

✏ Working:

Factors of 9: 1, 9 or 3, 3.

\( 1 + 9 = 10 \). (Correct)

\( 3 + 3 = 6 \). (Incorrect)

So the numbers are 1 and 9.

Answer: \( (x + 1)(x + 9) \)