GCSE November 2019 Edexcel Foundation Paper 3

What is a factor?

A factor is a whole number that divides into another number exactly, leaving no remainder.

We need to find numbers that divide into 12.

How do we find a fraction of an amount?

To find \( \frac{1}{3} \) of a number, we divide the number by 3.

Understanding decimals

The first digit after the decimal point is the “tenths” column.

0.7 means “seven tenths”.

What is a multiple of 6?

A multiple of 6 is a number that is in the 6 times table (6, 12, 18, 24…).

How many metres in a kilometre?

“Kilo” means 1000.

So, 1 kilometre = 1000 metres.

What are we counting?

We need to count the shaded (grey) squares separately from the unshaded (white) squares.

Order matters

The question asks for the ratio of shaded to unshaded.

What does substitution mean?

We replace the letter \( u \) with the number 8.

Note: \( 4u \) means \( 4 \times u \).

How is the sequence changing?

Let’s look at the difference between each term.

To find the next term, we add 6. To find the one after that, we add 7.

Strategy:

Go through the list one by one and count them. Crossing them off as you go helps avoid mistakes.

Completed Table:

Rules for Bar Charts:

• Label the axes (Frequency on vertical, Pet on horizontal).
• Choose a suitable scale (e.g., 1 square = 1 pet).
• Bars must be equal width.
• Gaps between bars must be equal.

Look for the highest frequency or the tallest bar.

Dog has the highest frequency (8).

Definition: A diameter is a straight line passing from side to side through the centre of a circle.

Definition: A segment is the area between a chord and an arc.

To draw this, draw any straight line across the circle (not through the center, though that creates a semi-circle which is technically a segment, usually we draw a smaller one) and shade the area enclosed.

Step 1: Calculate the total cost of the lights.

We need to multiply the number of lights by the cost per light.

Step 2: Calculate how much money he hands over.

He uses five £20 notes.

Step 3: Calculate the change.

Change = Money Paid – Total Cost

Step 1: Calculate the discount.

We need to find \( \frac{1}{5} \) of £120.

Step 2: Calculate the sale price.

Subtract the discount from the normal price.

First, find out how much weight comes from the 3 small boxes she definitely bought.

Subtract the weight of the small boxes from the total weight to find out how much weight is made up of large boxes.

Divide the remaining weight by the weight of a single large box.

What is range?

Range = Highest Value – Lowest Value

Using the Stem and Leaf diagram:

• The lowest value is the first number: Stem 3, Leaf 1 -> 31
• The highest value is the last number: Stem 7, Leaf 4 -> 74

What is Perimeter?

Perimeter is the distance around the outside of the shape (Add all sides).

What did Coby do?

He did \( 7 \times 3 \). This is Length multiplied by Width.

Length \( \times \) Width is the formula for Area, not Perimeter.

Analyze the answer \( x = -2 \)

Look at the bottom side of the triangle. Its length is labeled as \( x \text{ cm} \).

If \( x = -2 \), then the length of the bottom side is \(-2 \text{ cm}\).

Can a length be negative?

No, a physical length must be a positive number.

There is a lot of information here. A two-way table or “tree” logic is the best way to organize it.

Goal: Find “Girls with Packed Lunches”.

We know: Total = 800.

31% of all students have packed lunches.

First, find total number of boys (55% of students).

Now, find how many boys have packed lunches.

We know 60% of boys have school dinners.

This means 40% of boys must have packed lunches (100% – 60% = 40%).

Total Packed Lunches = Boys with Packed Lunch + Girls with Packed Lunch

We know Total (248) and Boys (176).

Total Probability Rule: All probabilities must add up to 1.

We know Red (0.4) and Yellow (0.25).

We need to split 0.35 in the ratio 3 : 4.

Total parts = \( 3 + 4 = 7 \).

Substitute the \( x \) values into the equation \( y = 4x – 6 \).

Plot the coordinates from your table: (-1, -10), (0, -6), (1, -2), (2, 2), (3, 6), (4, 10).

Draw a straight line through them.

Draw a horizontal line at \( y = 3 \).

Count how far each corner of the triangle is from the line \( y = 3 \).

• Point (1, 4) is 1 unit above. Reflected point is 1 unit below: (1, 2).
• Point (2, 4) is 1 unit above. Reflected point is 1 unit below: (2, 2).
• Point (1, 7) is 4 units above. Reflected point is 4 units below: (1, -1).

Method 1: Divide first

Since 4 is multiplying the whole bracket, we can divide both sides by 4.

Alternative Method (Expand):

\( 4x – 24 = 44 \)

\( 4x = 68 \)

\( x = 17 \)

First, write down the members of set A and set B from the universal set.

Find numbers that are in BOTH A and B (Multiples of 3 AND Even).

Set A only: Numbers in A but not B.

\( \{3, 9\} \)

Set B only: Numbers in B but not A.

\( \{2, 4, 8, 10\} \)

Outside: Numbers in \( \mathscr{E} \) but not in A or B.

Check off numbers used: 2, 3, 4, 6, 8, 9, 10, 12.

Remaining: \( \{1, 5, 7, 11, 13\} \)

What is profit?

Profit is the difference between the selling price and the cost price.

Formula:

Always divide by the original amount he bought it for.

Method: FOIL (First, Outside, Inside, Last)

Multiply each term in the first bracket by each term in the second bracket.

Look for common factors in numbers and algebra.

Numbers: 9 and 6 both divide by 3.

Algebra: \( x^2 \) and \( x \) both contain x.

Common factor = \( 3x \).

Tip: Calculate the numerator (top) and denominator (bottom) separately if you find entering it all at once difficult, or use the fraction button.

Count from the first non-zero digit.

1 (1st), 5 (2nd), 7 (3rd), 6 (4th).

Look at the next digit (6) to decide whether to round up.

Method: Draw a straight line that goes through the middle of the points.

It should follow the general trend of the data (upwards).

1. Find 34 on the Science (horizontal) axis.

2. Go up to your line of best fit.

3. Go across to the Maths (vertical) axis.

We don’t know the exact times, so we use the midpoint of each group.

Midpoint of \( 5 < t \le 10 \) is \( \frac{5+10}{2} = 7.5 \).

Total Frequency: \( 1 + 2 + 7 + 8 = 18 \)

Total Time (\( \sum fx \)): \( 7.5 + 25.0 + 122.5 + 180.0 = 335 \)

Linear vs Volume:

\( 1 \text{ cm} = 10 \text{ mm} \)

For volume (cubic units), we must cube the conversion factor.

\( 1 \text{ cm}^3 = 10 \times 10 \times 10 \text{ mm}^3 = 1000 \text{ mm}^3 \)

Find the difference between the start time (13:30) and arrival time (14:48).

To use the speed formula, time must be in hours (as a decimal).

Divide the minutes by 60.

Formula: \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)

Place the decimal after the first non-zero digit (3) and count the places moved.

The power is negative (-3), so move the decimal 3 places to the left.

In standard form, the power of 10 is the most important part for size.

Formula: Sum of interior angles = \( (n-2) \times 180 \)

For a pentagon (\( n=5 \)):

Since it is regular, all angles are equal.

So, the total angle at the vertex is \( 108^\circ \).

We are given an angle of \( 117^\circ \) in the parallelogram.

Co-interior angles (angles between parallel lines) add to \( 180^\circ \).

The angle of the parallelogram at the vertex shared with the pentagon is:

Angle \( x \) and the parallelogram angle (\( 63^\circ \)) make up the full interior angle of the pentagon (\( 108^\circ \)).

Shape A is a quarter circle with radius \( r = 15 \).

Area of full circle = \( \pi r^2 \).

Area of quarter circle = \( \frac{\pi r^2}{4} \).

We are told Area A is 9 times Area B.

So, \( \text{Area B} = \text{Area A} \div 9 \).

Let radius of B be \( r \).

\( \pi r^2 = 6.25\pi \)

Divide both sides by \( \pi \).