Daily Practice · Higher Plus
October 1985 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1985 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1985y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 36.
- 2nd October 1985In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 3rd October 1985The probability of winning a game is 3/5. A player expects 90 wins. How many games did they play?
- 4th October 1985On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th October 1985A car covers 770 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th October 1985Solve x^2 + 5x - 6 > 0.
- 7th October 1985A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 8th October 1985In a vector proof you find that vector PQ = 2a - 2b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 9th October 1985A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 10th October 1985A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 11th October 1985Rationalise the denominator of 132/sqrt(11), giving your answer in its simplest form.
- 12th October 1985Write x^2 + 14x - 14 in the form (x + a)^2 + b.
- 13th October 1985y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 14th October 1985A cuboid measures 9 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th October 1985A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th October 1985On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th October 1985Simplify sqrt(75) + sqrt(108), giving your answer in the form a sqrt(b).
- 18th October 1985Work out the coordinates of the turning point of y = x^2 - 16x + 11.
- 19th October 1985y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 20th October 1985A cuboid measures 11 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st October 1985A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd October 1985A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 23rd October 1985A rectangle is 18 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th October 1985Simplify (x^2 - 16)/(x + 4).
- 25th October 1985y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 4.
- 26th October 1985The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 27th October 1985A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 28th October 1985On 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?
- 29th October 1985Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 30th October 1985In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 31st October 1985A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.