GCSE Nov 2019 Edexcel Foundation Paper 1 (Non-Calculator)

What are we being asked to do?

We need to identify what the digit 7 represents based on its position in the number 1074.

What this tells us:

The 7 is in the Tens column. This means it represents 7 tens.

Why we do this:

We need to round to 1 decimal place, so we look at the digit in the first decimal place and the digit immediately to its right (the decider).

How to round:

If the decider is 5 or greater, we round up. If it is less than 5, we stay the same.

Why we do this:

Multiplying by 100 moves the decimal point two places to the right (or moves the digits two places to the left).

Why we do this:

To simplify a fraction, we divide both the numerator (top) and denominator (bottom) by their highest common factor.

How we do this:

Divide by 7 to reach the simplest form.

Check: Can we divide 2 and 5 any further? No, they are prime numbers.

Why we do this:

“Percent” means “per 100”. To convert a percentage to a decimal, we divide by 100.

How we do this:

Dividing by 100 moves the decimal point two places to the left.

Understanding the Key:

The key tells us that one full square \( \square \) represents 8 pictures.

Why we do this:

We need to represent 12 pictures using squares where 1 square = 8 pictures.

Strategy:

We need to calculate the value for each month and sum them up.

Why we do this:

We have one time in “hours and minutes” and another as a fraction of hours. It’s easiest to convert everything to minutes to find the difference.

What this tells us:

Now we simply subtract the smaller number of minutes from the larger.

Why we do this:

The total is in kilograms, but the blocks are in grams. We need to work in the same units. The question asks for the answer in grams.

Why we do this:

We know the weight of 4 blocks. Let’s find their total weight first.

What this tells us:

The remainder after subtracting the 4 known blocks from the total will be the weight of the 5th block.

Why we do this:

Angles on a straight line always add up to \( 180^\circ \).

How we do this:

Add the known angles and subtract from 180.

Strategy:

Coordinates are given as \( (x, y) \). We need to find \( x=3 \) on the horizontal axis and \( y=2 \) on the vertical axis.

Method:

We can read it directly from the graph or calculate it using the midpoint formula: \( (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) \).

Strategy:

We need to find all combinations of Heads (H) and Tails (T) for 3 throws. To ensure we don’t miss any, we can list them systematically.

Start with all Heads, then change the last one, then the middle one, etc.

Check: Since there are 2 outcomes per throw and 3 throws, there should be \( 2 \times 2 \times 2 = 8 \) total outcomes.

Step 1: Calculate total spent so far.

Step 2: Calculate remaining money.

Step 3: Compare with cost of jacket.

Why we do this:

We need to check if $60 is less than £40 using approximation. The exact rate is 0.749, which is close to 0.75 or \( \frac{3}{4} \).

Method:

Multiply the numbers first, then combine the letters.

Method:

Group the \( x \) terms together and the \( y \) terms together. Pay attention to the signs.

Method:

We can use column multiplication. Multiply 23 by 5, then 23 by 10, then add.

Step 1: Fill in what we know directly.

Total = 120.

Females = 75.

Male Stand = 29.

Method:

Probability = (Number of desired outcomes) / (Total number of people).

What to look for:

The “stay” is represented by the horizontal section of the graph where the distance doesn’t change.

Formula:

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

Why we do this:

We need to find the value of \( x \) first before we can calculate \( 2x^2 \).

Order of Operations (BIDMAS):

We must do the Index (squared) before the Multiplication (times 2).

Finding the angle:

The sum of angles in a pie chart is \( 360^\circ \).

In School A, we have monkeys (\( 60^\circ \)) and two sectors labelled \( x^\circ \) (lions and tigers).

Finding the number of students:

Finding the angle:

The angle for tigers is marked with a right angle symbol, which means \( 90^\circ \).

Comparison:

School A: 200 students

School B: 190 students

What the symbols mean:

• A filled (solid) circle means “included”. We use \( \le \) or \( \ge \).
• An empty (hollow) circle means “not included”. We use \( < \) or \( > \).

Strategy:

Break both numbers down into their prime factors using a factor tree or division.

Method:

The LCM contains the highest power of each prime factor present in either number.

Alternatively, use a Venn diagram: Multiply the union of all factors.

What we know: Total = 60. Half are women.

What we know: “The number of women… is 3 times the number of men.”

What we know: The rest are children.

Goal: Find ratio Children : Men in the form \( n : 1 \).

Why we do this:

It is much easier to multiply fractions than mixed numbers.

Method:

Multiply numerators together and denominators together.

Why we do this:

The question asks for the answer as a mixed number.

Instructions:

1. Place the compass point on \( P \).
2. Draw an arc that crosses the line \( CD \) at two points (let’s call them A and B).
3. Keep the compass width the same (or change it to be more than half the distance AB).
4. Place the compass point on A and draw an arc below the line.
5. Place the compass point on B and draw an arc to intersect the previous one.
6. Draw a straight line from \( P \) through the intersection of the arcs.

Why we do this:

We know two angles in the large triangle \( ABC \). We can calculate the third angle because angles in a triangle sum to \( 180^\circ \).

What we know:

\( \angle DCB : \angle ACD = 2 : 1 \)

Total parts = \( 2 + 1 = 3 \).

The total angle \( ACB \) is \( 54^\circ \).

Method:

We can focus on triangle \( ACD \). The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Angle \( BDC \) is exterior to triangle \( ACD \).

Alternatively, use the angles in triangle \( BCD \).

Why we do this:

To find the mean of all bricks, we first need the total weight of all bricks.

\( \text{Total Weight} = \text{Count} \times \text{Mean} \)

Method:

Divide the total weight by the total number of bricks (10).

Compare:

Donna thinks it is less than 7kg.

The actual mean is 7.1kg.

Rule:

When raising a power to another power, you multiply the indices: \( (a^m)^n = a^{m \times n} \).

Method:

Divide the numbers, and subtract the powers for the letters.

Remember that \( y \) is the same as \( y^1 \).

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

Scale: 1 cm represents 4 km.

Construction:

1. Place a protractor at P, aligned with the North line.
2. Mark \( 070^\circ \) (clockwise from North).
3. Draw a straight line through this mark.
4. Measure 4.5 cm along this line and mark point Q.

Measurement:

Now measure the distance from the new point Q to the lighthouse L using a ruler.

Then convert back to real kilometers (\( \text{cm} \times 4 \)).

Then measure the bearing from L (North line at L clockwise to line LQ).

What is angle AOB?

It is the sum of the three smaller angles at O.

What does “not obtuse” mean?

An obtuse angle is between \( 90^\circ \) and \( 180^\circ \).

Since this is an angle in a triangle, it must be less than \( 180^\circ \).

If it is not obtuse, it must be \( 90^\circ \) or less (Acute or Right).

Solve the inequality:

Strategy: Find the scale factor between the corresponding sides.

Side \( BC = 15 \) corresponds to side \( RQ = 10 \).

Understanding Congruence:

Triangles \( EGH \) and \( KGF \) are identical in size and shape.

We need to match the corresponding sides:

• \( HG = 4 \) corresponds to \( FG \). So \( FG = 4 \).
• \( EG \) corresponds to \( KG \).