Simply Maths UK
Your turn
Every video ends with a question for you to try. Have a go on paper first, then open the answer. Newest questions are at the top of each paper.
Question 9
Coming Tue 3 Nov, 08:00 · video and answer
# OCR Foundation · Paper 2 · June 2025 · Q9
(a) Simplify 3a + 5b − a − 2b. (b) Multiply out 4(3 − y). (c) Multiply out 3y(y + 2).
(a) 2a + 3b (b) 12 − 4y (c) 3y² + 6y
Question 8
Coming Mon 2 Nov, 08:00 · video and answer
# OCR Foundation · Paper 2 · June 2025 · Q8
Bottle A has 2 litres of water and bottle B has 400 ml. Water is poured from A into B until both contain the same amount. How many millilitres are poured?
Total 2400 ml, so 1200 ml each. Pour 2000 − 1200 = 800 ml.
Question 7
Coming Sun 1 Nov, 08:00 · video and answer
# OCR Foundation · Paper 2 · June 2025 · Q7
(a) Write 3/5 as a decimal. (b) Write 0.09 as a percentage. (c) Write 17/4 as a mixed number.
(a) 0.6 (b) 9% (c) 4 1/4
Question 6
Coming Sat 31 Oct, 08:00 · video and answer
# OCR Foundation · Paper 2 · June 2025 · Q6
(a) Work out (i) 12 − 3 × 2 (ii) −2 + 4² (b) Insert one pair of brackets: 8 × 6 ÷ 3 − 1 = 8
(a)(i) 6 (ii) 14 (b) 8 × (6 ÷ 3 − 1) = 8
Question 5
Coming Fri 30 Oct, 08:00 · video and answer
# OCR Foundation · Paper 2 · June 2025 · Q5
Sam's swimming bar chart: (a) Hours in February? (b) How many more in March than January? (c) Draw April: 20 hours. (d) "50% less than March": correct?
This one needs a drawing: the answer is worked out in the video.
Question 4
Coming Thu 29 Oct, 08:00 · video and answer
# OCR Foundation · Paper 2 · June 2025 · Q4
(a) Name shapes C and D. (b) Order of rotational symmetry of C. (c) Mark the equal sides of a kite.
This one needs a drawing: the answer is worked out in the video.
Question 3
Coming Wed 28 Oct, 08:00 · video and answer
# OCR Foundation · Paper 2 · June 2025 · Q3
(a) Half of 1/3 (b) 2/7 + 3/7
(a) 1/6 (b) 5/7
# OCR Foundation · Paper 2 · June 2025 · Q2
A right-angled triangle has base 12 cm and height 5 cm. Work out its area.
Area = ½ × 12 × 5 = 30 cm²
# OCR Foundation · Paper 2 · June 2025 · Q1
From 14 19 25 27 33 45: the prime, the square, and two numbers that differ by 18.
Prime: 19 Square: 25 Differ by 18: 27 and 45
Question 29
Coming Sat 7 Nov, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q29
(a) Write 0.0052 in standard form. (b) A town: 8.4 × 10⁵ people, 2.1 × 10⁴ km². Find the population density.
(a) 5.2 × 10⁻³ (b) 8.4 × 10⁵ ÷ 2.1 × 10⁴ = 40 people per km²
Question 28
Coming Fri 6 Nov, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q28
Triangle ABC: AB = 15 cm, BC = 8 cm. Semicircle on diameter BC. Find the whole perimeter.
This one needs a drawing: the answer is worked out in the video.
Question 27
Coming Thu 5 Nov, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q27
6 people dig a trench in 14 hours. How long would 8 people take? Answer in hours and minutes.
6 × 14 = 84 person-hours. 84 ÷ 8 = 10.5 hours = 10 hours 30 minutes.
Question 26
Coming Wed 4 Nov, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q26
460 counters are blue, red or yellow. Blue : red = 1 : 3. Red : yellow = 2 : 5. How many red counters are there?
Make red the same in both: blue : red : yellow = 2 : 6 : 15 (23 parts). One part = 460 ÷ 23 = 20, so red = 120.
Question 25
Coming Tue 3 Nov, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q25
A school asks 10 students in the library how much they read. Give one criticism of this method.
This one needs a drawing: the answer is worked out in the video.
Question 24
Coming Mon 2 Nov, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q24
Opposite = 6 cm, adjacent = 8 cm. Work out the angle x.
tan x = 6 ÷ 8, so x = tan⁻¹(0.75) = 36.9° (1 d.p.)
Question 23
Coming Sun 1 Nov, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q23
A line is parallel to y = 2x and passes through (3, 10). Find its equation in the form y = mx + c.
Same gradient, 2: y = 2x + c, and 10 = 2 × 3 + c, so c = 4. y = 2x + 4
Question 22
Coming Sat 31 Oct, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q22
£5000 at r% per year simple interest. After 6 years it is worth £6500. Find r.
Interest = £1500 over 6 years = £250 a year. r = 250 ÷ 5000 × 100 = 5.
Question 21
Coming Fri 30 Oct, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q21
Crosses on a scatter diagram go up from left to right. What type of correlation is this?
Positive correlation.
Question 20
Coming Thu 29 Oct, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q20
(a) (5²)³ = 5^□ (b) 1/5 = 5^□
(a) 5⁶ (b) 5⁻¹
Question 19
Coming Wed 28 Oct, 07:30 · video and answer
# OCR Foundation · Paper 1 · May 2025 · Q19
The ratio 50 grams to 1 kilogram can be written in the form 1 : n. Find the value of n.
50 g : 1000 g = 1 : 20, so n = 20.
# OCR Foundation · Paper 1 · May 2025 · Q18
Calculate 3.5² ÷ 2.5 + 1.2 ÷ 0.4²
3.5² ÷ 2.5 = 4.9, 1.2 ÷ 0.4² = 7.5 Total = 12.4
# OCR Foundation · Paper 1 · May 2025 · Q17
A vector goes 4 right and 1 down. Write it as a column vector. Then work out 2 times it.
(4, −1) written as a column: 4 on top, −1 below. 2 times it: (8, −2).
# OCR Foundation · Paper 1 · May 2025 · Q16
A number line has an open dot at 5 and an arrow pointing left. Write down the inequality.
x < 5 (open dot: 5 is not included)
# OCR Foundation · Paper 1 · May 2025 · Q15
Which equation fits each graph? (a) Horizontal line: x = 2, y = 2, y = x (b) U-shape: y = x², y = x³, y = 1/x
(a) y = 2 (a horizontal line is y = a number) (b) y = x²
# OCR Foundation · Paper 1 · May 2025 · Q14
2 litre bottle: £1.60. Sam has £12 and buys the maximum number. Drinks 250 ml a day. Days it lasts?
£12 ÷ £1.60 = 7.5, so 7 bottles = 14 litres. 14000 ml ÷ 250 ml = 56 days.
# OCR Foundation · Paper 1 · May 2025 · Q13
240 drinks: 3/8 tea, the rest coffee. 40 teas and 80 coffees have milk. Coffees with no milk? % with milk?
Tea 90, coffee 150. Coffees with no milk: 150 − 80 = 70. With milk: 120 of 240 = 50%.
# OCR Foundation · Paper 1 · May 2025 · Q12
(a) v = u + at, u = 5, a = 3.5, t = 12 (b) p = ½qr, p = 30, r = 5 Find v and q.
v = 5 + 3.5 × 12 = 47 q = 2p ÷ r = 60 ÷ 5 = 12
# OCR Foundation · Paper 1 · May 2025 · Q11
Three numbers: 6 9 12 A fourth number is added. The mean of the four numbers is 10. Work out the fourth number.
Total = 4 × 10 = 40. The fourth number = 40 − 27 = 13.
# OCR Foundation · Paper 1 · May 2025 · Q10
Write in order of size, smallest first: 2/5 0.41 39% 0.405
39%, 2/5, 0.405, 0.41 (as decimals: 0.39, 0.4, 0.405, 0.41)
# OCR Foundation · Paper 1 · May 2025 · Q9
Factors of N: 1, 2, 3, 4, 6, 8, 12, 24 (a) Write down N (b) M = 2 × 3 × 11: HCF of N and M (c) 100 to 150, factors 5 and 12
(a) N = 24 (b) M = 66, HCF = 6 (c) 120 (a multiple of 60).
# OCR Foundation · Paper 1 · May 2025 · Q8
(a) □ + 9 = −20 (b) 3/□ × 2 = 3/5
(a) −29 (b) 10, because 3/10 × 2 = 6/10 = 3/5.
# OCR Foundation · Paper 1 · May 2025 · Q7
Simplify 3c × 4c², then solve 5m − 2 = 78
3c × 4c² = 12c³. 5m = 80, so m = 16.
# OCR Foundation · Paper 1 · May 2025 · Q6
1 cm = 4 km. A and B are 6 cm apart. (a) Find the actual distance. (b) C is 18 km from B: how far on the drawing?
(a) 6 × 4 = 24 km. (b) 18 ÷ 4 = 4.5 cm.
# OCR Foundation · Paper 1 · May 2025 · Q5
Won 5 games = a 60° sector. (a) How many games were played? (b) Drawn : lost = 3 : 2. Find both angles.
(a) Each game is 12°, so 30 games were played. (b) The other 300° split 3 : 2: drawn 180°, lost 120°.
# OCR Foundation · Paper 1 · May 2025 · Q4
Here is a list of numbers: 8, 15, 9, 21, 15, 4, 12. Write down the mode, then find the median.
Mode = 15. In order: 4, 8, 9, 12, 15, 15, 21, so the median = 12.
# OCR Foundation · Paper 1 · May 2025 · Q3
A 2 by 2 square has its right-hand edge 1 square from a mirror line. Reflect it in the mirror line.
This one needs a drawing: the answer is worked out in the video.
# OCR Foundation · Paper 1 · May 2025 · Q2
Point C is three squares left and two squares down from zero. Write down its coordinates. Then plot point D at (-1, 4).
C = (−3, −2). D: 1 square left of zero, then 4 squares up.
# OCR Foundation · Paper 1 · May 2025 · Q1
Write down an odd number between 20 and 30, and two cube numbers less than 30.
Odd number: any of 21, 23, 25, 27, 29. Cube numbers less than 30: 1, 8, 27 (any two).
Maths tip · When graphs hear the beat
Coming Wed 28 Oct, 14:00 · video and answer
# Maths tip · When graphs hear the beat
Name the last graph in the video (it is drawn without its equation).
y = x² − 2 It is the graph of y = x² moved down by 2: it crosses the y-axis at (0, −2).
# Maths tip · Butterfly fractions
In the video: 1/2 + 2/3 = ? In our comment: 3/4 + 1/5 = ?
1/2 + 2/3 = 3/6 + 4/6 = 7/6 (or 1 1/6) 3/4 + 1/5 = 15/20 + 4/20 = 19/20
# Maths mysteries · The Collatz problem
Pick any starting number. How many steps does it take to reach 1?
It depends on your number. For example, 7 takes 16 steps: 7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 Nobody has ever found a number that does not reach 1, and nobody has proved that every number does.
# Lesson
Rational or irrational? √16, √5, 0.25, π
√16 = 4, rational √5 is irrational (5 is not a square number) 0.25 = 1/4, rational π is irrational