Year 11 Paper 1: Foundation Number and Algebra
Covers number and calculation, fractions, decimals and percentages, ratio and proportion, linear algebra, quadratics and simultaneous equations, and statistics and probability.
Year 11 here means a typical teaching order, not a syllabus rule. No exam board defines what belongs to Year 11, and schools sequence the course differently. Check it against your own scheme of work before using it to decide what a class has covered.
Questions
Question 1 [2 marks]
Number and Calculation
A stationery shop orders 34 boxes of pens. Each box contains 48 pens.
The shop already has 156 pens in stock. Work out the total number of pens now in the shop.
Question 2 [2 marks]
Linear Equations and Inequalities
Solve 6x - 11 = 31.
Question 3 [2 marks]
Statistics and Probability
A fair six-sided dice is rolled once. Find the probability of rolling a number greater than 4.
Question 4 [3 marks]
Ratio and Proportion
A fruit drink is made from mango juice and orange juice in the ratio 3:4.
Freya makes 490 ml of the drink.
How many millilitres of orange juice does she need?
Question 5 [3 marks]
Fractions, Decimals and Percentages
A laptop costs 480 pounds before a 15% discount is applied.
Find the sale price of the laptop in pounds.
Question 6 [4 marks]
Quadratics and Simultaneous Equations
Expand and simplify (x - 6)^2 - (x - 2)(x + 2).
Question 7 [4 marks]
Statistics and Probability
The ages, in years, of 7 people in a choir are 34, 28, 41, 28, 55, 39, 28.
Find the median age, the mode, and state which of these two averages best represents a typical age, giving a reason.
Question 8 [4 marks]
Quadratics and Simultaneous Equations
Factorise completely 2x^3 - 8x.
Question 9 [4 marks]
Statistics and Probability
A spinner has sections labelled A, B, C and D.
P(A) = 0.3, P(B) = 0.25 and P(C) = 0.2.
Find P(D).
Question 10 [4 marks]
Number and Calculation
The HCF of two numbers is 12. The LCM of the same two numbers is 360.
One of the numbers is 72. Find the other number.
Question 11 [4 marks]
Fractions, Decimals and Percentages
Write these in order of size, starting with the smallest: 5/8, 0.62, 59%.
Question 12 [4 marks]
Statistics and Probability
A bag contains 4 red counters and 6 blue counters.
A counter is drawn at random, its colour noted, and then replaced. A second counter is then drawn at random.
Find the probability that both counters are the same colour.
Model solutions
| Question 1[2 marks] | |
|---|---|
| Answer or working | Marks |
| 34 x 48 = 1632 | M1 |
| 1788 pens | A1 |
| Question 2[2 marks] | |
|---|---|
| Answer or working | Marks |
| adding 11 to both sides to get 6x = 42 | M1 |
| x = 7 | A1 |
| Question 3[2 marks] | |
|---|---|
| Answer or working | Marks |
| identifying 2 favourable outcomes (5 and 6) out of 6 | M1 |
| 1/3 | A1 |
| Question 4[3 marks] | |
|---|---|
| Answer or working | Marks |
| one ratio part = 490 / 7 = 70 | M1 |
| multiplying by 4 | M1 |
| 280 ml | A1 |
| Question 5[3 marks] | |
|---|---|
| Answer or working | Marks |
| the multiplier 0.85 | M1 |
| 480 x 0.85 | M1 |
| 408 pounds | A1 |
| Question 6[4 marks] | |
|---|---|
| Answer or working | Marks |
| expanding (x - 6)^2 = x^2 - 12x + 36 | M1 |
| expanding (x - 2)(x + 2) = x^2 - 4 | M1 |
| subtracting to get x^2 - 12x + 36 - x^2 + 4 | M1 |
| -12x + 40 | A1 |
| Question 7[4 marks] | |
|---|---|
| Answer or working | Marks |
| arranging the ages in order: 28, 28, 28, 34, 39, 41, 55 | M1 |
| median = 34 | A1 |
| mode = 28 | A1 |
| stating the median, with a valid reason such as the mode being lower than most of the ages | B1 |
| Final answer: median = 34, mode = 28; the median better represents a typical age | |
| Question 8[4 marks] | |
|---|---|
| Answer or working | Marks |
| taking out the common factor 2x: 2x(x^2 - 4) | M1 |
| recognising x^2 - 4 as a difference of two squares | M1 |
| sqrt(x^2) = x and sqrt(4) = 2 | M1 |
| 2x(x - 2)(x + 2) | A1 |
| Question 9[4 marks] | |
|---|---|
| Answer or working | Marks |
| probabilities summing to 1 | M1 |
| 0.3 + 0.25 + 0.2 = 0.75 | M1 |
| 1 - 0.75 | M1 |
| 0.25 | A1 |
| Question 10[4 marks] | |
|---|---|
| Answer or working | Marks |
| using HCF x LCM = product of the two numbers | M1 |
| 12 x 360 = 4320 | M1 |
| dividing 4320 by 72 | M1 |
| 60 | A1 |
| Question 11[4 marks] | |
|---|---|
| Answer or working | Marks |
| converting 5/8 to a decimal, 0.625 | M1 |
| converting 59% to a decimal, 0.59 | M1 |
| comparing all three as decimals: 0.59, 0.62, 0.625 | M1 |
| 59%, 0.62, 5/8 | A1 |
| Question 12[4 marks] | |
|---|---|
| Answer or working | Marks |
| P(red) = 4/10 and P(blue) = 6/10, unchanged after replacement | M1 |
| P(both red) = 4/10 x 4/10 = 16/100 | M1 |
| P(both blue) = 6/10 x 6/10 = 36/100 | M1 |
| 52/100, or 13/25 | A1 |
| Final answer: 13/25 | |