Daily Practice · Higher Plus
October 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1965 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1965On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 2nd October 1965A car covers 470 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd October 1965Write 7/(x - 6) + 6/(x - 1) as a single fraction.
- 4th October 1965y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 5th October 1965A cuboid measures 4 cm by 9 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th October 1965A bag holds 3 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th October 1965A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 8th October 1965Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 9th October 1965Solve 20x^2 - 13x - 15 = 0.
- 10th October 1965y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 11th October 1965The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 12th October 1965A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 13th October 1965On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th October 1965Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 15th October 1965f(x) = 2x - 4. Work out the inverse function f^-1(x).
- 16th October 1965A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 17th October 1965In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 18th October 1965The probability of winning a game is 2/5. A player expects 28 wins. How many games did they play?
- 19th October 1965A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 20th October 1965A rectangle is 20 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st October 1965Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 22nd October 1965y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 23rd October 1965In a vector proof you find that vector PQ = a + 4b and vector RS = 2a + 8b. What does this show about PQ and RS?
- 24th October 1965A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 25th October 1965On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 26th October 1965Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).
- 27th October 1965Use the iteration x(n+1) = cube root of (6x(n) + 4) with x(0) = 2. Work out x(1) to 3 decimal places.
- 28th October 1965y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 29th October 1965A cuboid measures 13 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th October 1965A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st October 1965A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?