Daily Practice · Higher Plus
October 1960 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1960 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1960
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1960A cuboid measures 11 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd October 1960A bag holds 5 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd October 1960On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th October 1960Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 5th October 1960f(x) = 3x + 7. Work out the inverse function f^-1(x).
- 6th October 1960y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 7th October 1960The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 8th October 1960A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 9th October 1960A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 10th October 1960A block has mass 640 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th October 1960Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 12th October 1960y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 16.
- 13th October 1960In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 14th October 1960The probability of winning a game is 1/4. A player expects 7 wins. How many games did they play?
- 15th October 1960On 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?
- 16th October 1960x = 119 and y = 97, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th October 1960Use the iteration x(n+1) = cube root of (12x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 18th October 1960A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 19th October 1960In a vector proof you find that vector PQ = a - 4b and vector RS = 5a - 20b. What does this show about PQ and RS?
- 20th October 1960A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
- 21st October 1960A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 22nd October 1960A car covers 770 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd October 1960Work out the nth term of the quadratic sequence -6, -4, 0, 6, ...
- 24th October 1960y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 25th October 1960A cuboid measures 15 cm by 15 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th October 1960A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th October 1960On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th October 1960Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 29th October 1960The point (-1, -5) lies on y = f(x). Write down its image on y = f(x) + 4.
- 30th October 1960y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 31st October 1960A cuboid measures 10 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.