GCSE November 2022 Edexcel Foundation Paper 3

💡 Strategy: To compare decimals easily, it helps to give them all the same number of decimal places. The longest number here has 3 decimal places (\(0.408\)), so let’s add zeros to the others so they all have 3 decimal places.

💡 Comparison: Now we can just compare them as if they were whole numbers (410, 500, 460, 408).

💡 Understanding Place Value: Let’s look at the columns for the number \(12345\).

• \(1\) is in the Ten Thousands place
• \(2\) is in the Thousands place
• \(3\) is in the Hundreds place
• \(4\) is in the Tens place
• \(5\) is in the Units (Ones) place

💡 Method 1 (Equivalent Fractions): Decimals are based on tenths (\(/10\)), hundredths (\(/100\)), etc. Can we turn \(\frac{4}{5}\) into tenths?

💡 Method 2 (Calculator): Since this is a calculator paper, you can type \(4 \div 5\).

💡 Rule: To round to the nearest whole number, we look at the first digit after the decimal point (the tenths column).

Number: \(19.\textbf{4}949\)

The digit is \(4\).

💡 Rounding Rule: If the digit is 5 or more, round up. If it is 4 or less, round down (stay the same).

Since \(4\) is less than \(5\), we keep the whole number as it is.

💡 Definition: A multiple of 3 is a number found in the 3 times table. We can check by dividing by 3 or adding the digits (if the sum of digits is in the 3 times table, the number is a multiple of 3).

💡 Strategy: Draw a horizontal line across the graph at \(16^\circ\text{C}\) and count how many data points are above this line.

Looking at the graph:

• Jan: 8 (Below)
• Feb: 9 (Below)
• Mar: 11 (Below)
• Apr: 15 (Below)
• May: 20 (Above)
• Jun: 23 (Above)
• Jul: 25 (Above)
• Aug: 24 (Above)
• Sep: 21 (Above)
• Oct: 20 (Above)
• Nov: 14 (Below)
• Dec: 10 (Below)

💡 Strategy: Look for two points that are at the exact same height on the graph.

Checking the values:

May is \(20^\circ\text{C}\)

Oct is \(20^\circ\text{C}\)

💡 Method: Find \(\frac{1}{4}\) of \(208\).

💡 Method: Subtract the large bars from the total.

💡 Method: Multiply the quantities by their prices. Be careful with units (£ vs p).

Large bars: \(£1\) each.

Small bars: \(60\text{p} = £0.60\) each.

💡 Formula: \(\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}\)

💡 Method: Read the x-value (horizontal) first, then the y-value (vertical).

Point A is 1 unit left (-1) and 2 units up (2).

💡 Method: Go to \(x = 1\) (1 right) and \(y = 4\) (4 up).

Draw a cross at this intersection.

💡 Method: The line \(y = -3\) is a horizontal line where the y-coordinate is always -3.

It passes through \((0, -3)\), \((1, -3)\), \((2, -3)\), etc.

💡 Analysis: Look at the differences between the numbers.

\(20 \rightarrow 16\) (Subtract 4)

\(16 \rightarrow 13\) (Subtract 3)

The amount we subtract seems to go down by 1 each time (-4, -3, …).

Why we do this: The volume of a cuboid is calculated by multiplying its length, width, and height.

Formula: \( \text{Volume} = \text{length} \times \text{width} \times \text{height} \)

Why we do this: Since everything relates back to Amol or Gemma (who relates to Amol), let’s represent Amol’s sweets as 1 part.

Let Amol = \( 1 \)

Why we do this: Gemma has 6 times Amol’s amount.

Gemma = \( 6 \times 1 = 6 \)

Why we do this: Harry has half of Gemma’s amount.

Harry = \( \frac{1}{2} \times 6 = 3 \)

Why we do this: The sum of the interior angles in any quadrilateral is always 360°.

Why we do this: Check the sum of angles for a triangle. They must add up to exactly 180°.

Why we do this: Locate 850 on the vertical (grams) axis. Move horizontally to the line, then down to the horizontal (ounces) axis.

850 is halfway between 800 and 900.

Why we do this: The graph only goes up to 35 ounces. We need to find a value on the graph that we can multiply to get 80 ounces.

Strategy: Find the value for 8 ounces (or 20, or 10) and scale it up.

Why we do this: We are told 3 kg costs £1.74. We need the unit cost to find out how much the 2 kg of carrots in the first part cost.

Why we do this: To isolate the cost of the onions in the first statement.

Why we do this: Subtract the cost of the carrots from the total cost.

Why we do this: We know 2.5 kg costs £1.20. We need to find the cost of 4 kg. First, find 1 kg.

Why we do this: To answer the specific question asked.

Why we do this: A pie chart must show what each sector represents.

There are no labels on the sectors (Jersey Royal, Charlotte, Maris Piper) or a key to explain what they are.

Why we do this: The sizes of the sectors should match the data.

Total potatoes = \( 90 + 105 + 105 = 300 \)

Charlotte and Maris Piper have the same number (105), so their angles should be equal (\( \frac{105}{300} \times 360 = 126^\circ \)).

Jersey Royal is smaller (90), so its angle should be smaller (\( 108^\circ \)).

In the diagram, the sectors do not look like 108°, 126°, and 126°. For example, the top right sector looks like a right angle (90°).

Why we do this: Count the first 3 non-zero digits: 8, 7, 5. The next digit is 6.

Since 6 is 5 or greater, round the last digit up (5 becomes 6).

Replace remaining digits with zeros to keep place value.

Why we do this: Follow BIDMAS. Calculate numerator and denominator separately first.

Why we do this: Transforming the key points (vertices) allows us to draw the new shape easily.

The vertices of the original shape are:

• A: (-2, -3)
• B: (-2, -4)
• C: (-4, -4)

Why we do this: A 90° anticlockwise rotation about the origin (0,0) changes coordinates \( (x, y) \) to \( (-y, x) \).

Let’s transform each point:

• A: (-2, -3) \( \rightarrow \) \( (-(-3), -2) = (3, -2) \)
• B: (-2, -4) \( \rightarrow \) \( (-(-4), -2) = (4, -2) \)
• C: (-4, -4) \( \rightarrow \) \( (-(-4), -4) = (4, -4) \)

Why we do this: Join the new points to form the rotated shape.

The new shape is in the 4th quadrant.

Why we do this: Look for the horizontal part of the graph where the distance doesn’t change.

The flat line starts at 08:30 and ends at 08:45.

Why we do this: Find 08:50 on the x-axis and read up to the graph line.

08:50 is 5 minutes after she starts cycling home at 08:45. The journey home takes 15 minutes (08:45 to 09:00).

At 08:50, she is \( \frac{1}{3} \) of the way home in time, so she has covered \( \frac{1}{3} \) of the distance down?

Wait, reading the graph: At 08:50 (466px), the line is at approx 4.6 – 4.7 km.

Why we do this: Speed = Distance ÷ Time.

At 20 minutes (08:20), read the distance from the graph.

The graph passes through (08:20, 4 km).

Why we do this: We need 25 scones, but the recipe is for 10.

\[ 25 \div 10 = 2.5 \]

We need 2.5 times the ingredients.

Why we do this: We want \( a \) on its own. First, move the \(-9\) to the other side by doing the opposite (adding 9).

Why we do this: Currently \( a \) is multiplied by 3. To get \( a \) alone, divide both sides by 3.

Why we do this: To share an amount in a ratio, you must first find the total number of parts.

Rob divided the total amount (120) by each part of the ratio individually. This is incorrect.

Correct Method: Add the parts \( 3 + 5 = 8 \), then divide \( 120 \div 8 \).

Why we do this: A two-way table is the clearest way to find the missing number. We fill in what we know and calculate the gaps.

Why we do this: Now we know the total boys, boys doing French, and boys doing German, we can find the boys doing Spanish.

Why we do this: Formula for cylinder volume is \( V = \pi r^2 h \). We are given diameter = 80 cm, so radius = 40 cm.

Why we do this: She has 4 identical tanks to fill.

Why we do this: The ratio is 1 : 100. This means 1 part fertiliser makes \( 1 + 100 = 101 \) parts of mixture.

Let’s convert the fertiliser she has into total mixture volume to compare with the tank volume.

Why we do this: If the possible mixture volume is greater than the tank capacity, she has enough.

Why we do this: Similar triangles have the same shape but different sizes. We compare corresponding sides to find the multiplier (scale factor).

Side AC corresponds to Side DF.

AC = 5 cm, DF = 20 cm.

Why we do this: EF corresponds to base BC. Multiply BC by the scale factor.

Why we do this: Side AB corresponds to Side DE (22 cm). Since we are going from the large triangle to the small one, we DIVIDE by the scale factor.

Why we do this: The probabilities on any set of branches must add up to 1.

Sports Quiz: \( 1 – 0.3 = 0.7 \)

Music Quiz: \( 1 – 0.35 = 0.65 \)

Why we do this: To find the probability of two independent events both happening, we multiply their probabilities.

Follow the “Win” branch for Sports and the “Win” branch for Music.

Why we do this: To convert cm to m, we divide by 100. To convert cm³ to m³, we divide by \( 100^3 \) (which is 1,000,000).

Why we do this: Convert the distance (km to m) and the time (hours to seconds) separately.

1 km = 1000 m

1 hour = 60 minutes = 3600 seconds

Why we do this: Total = Mean × Count.

Why we do this: Subtract the men’s total from the grand total.

Why we do this: The negative power (-4) means the number is small. Move the decimal point 4 places to the left.

Why we do this: Use a calculator carefully with powers, or handle numbers and powers separately.

Why we do this: Add the top numbers (x-components) and add the bottom numbers (y-components).

Why we do this: Multiply vector \( \mathbf{a} \) by 2, then subtract vector \( \mathbf{c} \).

Why we do this: Vector \( 2\mathbf{d} \) is in the same direction as \( \mathbf{d} \) but twice as long.

If \( \mathbf{d} \) goes “Right 2, Down 1” (based on visual), then \( 2\mathbf{d} \) goes “Right 4, Down 2”.

Start at P and count the squares.